text:
\section{Introduction}
Edge detection is one of the most fundamental problems in computer vision and has a wide variety of applications, such as image segmentation~\cite{long2015fully,ronneberger2015u,chen2017deeplab,He2017MaskR,pinheiro2016learning,pinheiro2015learning}, object detection~\cite{He2017MaskR}, and video object segmentation~\cite{caelles2017one,voigtlaender2019feelvos,wang2019fast}. Given an input image, edge detection aims to extract accurate object boundaries and visually salient edges. It is challenging due to many factors including complex backgrounds, inconsistent annotations, and so on.

Edge detection is closely related to the context and semantic image cues. It is thus crucial to obtain appropriate representation to capture both high and low level visual cues. Traditional methods~\cite{kittler1983accuracy,canny1986computational,winnemoller2011xdog,martin2004learning,dollar2006supervised,lim2013sketch} mostly obtain edges based on low-level local cues, \emph{e.g.}} \def\Eg{\emph{E.g.}, color and texture. Benefiting from the effectiveness of convolutional neural networks (CNNs) in learning semantic features, significant progress has been made for edge detection~\cite{kokkinos2015pushing,shen2015deepcontour,bertasius2015deepedge,bertasius2015hfl}. The CNN features progressively capture global and semantic-aware visual concepts with the enlargement of the receptive fields, while many essential fine details are inevitably and gradually lost at the mean time. To include more details, methods in~\cite{xie2015hed,liu2016rds,liu2017rcf,xu2017AMHNet,he2019bdcn} aggregate the features of deep and shallow layers. However, such shallow features reflect mainly local intensity variation without considering semantic context, resulting in noisy edges.

\begin{figure}[!t]
\setlength{\abovecaptionskip}{3pt}
\setlength{\belowcaptionskip}{0pt}
\centering
\includegraphics[width=0.95\linewidth]{fig/figure1_examples.pdf}
\caption{\textbf{Examples of edge detection.} Our method, EDTER, extracts clear boundaries and edges by exploiting both global and local cues. (a, e): Input images from BSDS500~\cite{arbelaez2010bsds}. (b,f): Detected edges by EDTER. (c,d,g,h): Zoomed-in patches.}
\label{fig:figure1}
\vspace{-15pt}
\end{figure}

Inspired by the recent success of vision transformers~\cite{dosovitskiy2020image16x16,zheng2021rethinking,wang2021end,chen2021transformertracking}, especially their capability of modeling long-range contextual information, we propose to tailor transformers for edge detection. Two main challenges, however, need to be solved. Firstly, transformers are often applied to patches with a relatively large size due to computation concerns, while coarse-grained patches are unfavorable for learning accurate features for edges. It is crucial to perform self-attention on fine-grained patches without increasing the computational burden. Second, as shown in Fig.~\ref{fig:figure1} (d), extracting precise edges from intersected and thin objects is challenging. So it is necessary to design an effective decoder for generating edge-aware high-resolution features.

To address the above issues, we develop a two-stage framework (Fig.~\ref{fig:framework}),  named Edge Detection TransformER (EDTER), to explore global context information and excavate fine-grained cues in local regions. In stage I, we split the image into coarse-grained patches and run a global transformer encoder on them to capture long-range global context. Then, we develop a novel Bi-directional Multi-Level Aggregation (BiMLA) decoder to generate high-resolution representations for edge detection. In stage II, we first divide the whole image into multiple sequences of fine-grained patches by sampling with a non-overlapping sliding window. Then a local transformer works on each sequence in turn to explore the short-range local cues. Afterward, all local cues are integrated and fed into a local BiMLA decoder to achieve the pixel-level feature maps. Finally, the information from both stages is fused by a Feature Fusion Module (FFM) and then is fed into a decision head to predict the final edge map. With the above efforts, EDTER can generate crisp and less noisy edge maps (Fig.~\ref{fig:figure1}).

Our contributions are summarized as follows: (1) We propose a novel transformer-based edge detector, Edge Detection TransformER (EDTER), to detect object contours and meaningful edges in natural images. To our best knowledge, it is the first transformer-based edge detection model. (2) EDTER is designed to effectively explore long-range global context (Stage I) and capture fine-grained local cues (Stage II). Moreover, we propose a novel Bi-directional Multi-Level Aggregation (BiMLA) decoder to boost the information flow in the transformer. (3) To effectively integrate the global and local information, we use a Feature Fusion Module (FFM) to fuse the cues extracted from Stage I and Stage II. (4) Extensive experiments demonstrate the superiority of EDTER over the state-of-the-art methods on three well-known edge detection benchmarks, including BSDS500, NYUDv2, and Multicue.

\begin{figure*}[!t]
\setlength{\abovecaptionskip}{3pt}
\setlength{\belowcaptionskip}{0pt}
\centering
\includegraphics[width=0.998\linewidth
]{fig/framework.pdf}
\caption{\textbf{Overall framework.} In Stage I, we first feed the image into a global transformer encoder to compute the global attentions. Then, a global BiMLA decoder (see Fig.~\ref{fig:decoder}) generates the high-resolution features that are used to predict the edge maps via a decision head. In Stage II, similar to Stage I, the partitioned patches are inputted into a local transformer encoder to generate the local attentions. The concatenated attentions are utilized to decode the high-resolution features. At last, a decision head predicts the edge maps with the features of Stage I and Stage II fused by FFM.}
\label{fig:framework}
\vspace{-14pt}
\end{figure*}

\section{Related Work}
As a fundamental task in computer vision, edge detection has been extensively studied over years. In the following, we highlight two lines of works most related to ours.

\vspace{0.2em}
\noindent{\bf Edge Detection.} Early edge detectors~\cite{kittler1983accuracy, canny1986computational, winnemoller2011xdog}, such as Sobel~\cite{kittler1983accuracy} and Canny~\cite{canny1986computational}, focus on analysing the image gradients to extract the edges. These methods provide elementary low-level cues and are widely used in computer vision applications. Learning-based methods~\cite{martin2004learning,dollar2006supervised, lim2013sketch} tend to integrate different low-level features and train a classifier to obtain boundaries and edges. Although these approaches achieve impressive performance compared to early works, they are based on hand-crafted features, limiting the ability to detect semantic boundaries and meaningful edges.

Recently, convolutional neural networks (CNNs) have been successfully introduced the edge detection study~\cite{kokkinos2015pushing, deng2020dscd, xu2017AMHNet, shen2015deepcontour, bertasius2015deepedge, bertasius2015hfl, maninis2016cob, deng2018lpcb, kelm2019rcn, poma2020dexined, PuHGL21iccv}. DeepEdge~\cite{bertasius2015deepedge} exploits object-aware cues extracted by multi-level CNN for contour detection. The method in~\cite{shen2015deepcontour} first partitions contour patches into sub-classes and then learns model parameters to fit each subclass. {More recently, some approaches improve edge detection~\cite{xie2015hed,liu2016rds, liu2017rcf, he2019bdcn, xu2017AMHNet}, segmentation~\cite{Tao2020hierarchical,chen2017deeplab,ZhaoPSPN17}, and object detection~\cite{LinFPN17} by using hierarchical multi-scale features.} Inspired by the seminal work of~\cite{xie2015hed}, most edge detectors~\cite{liu2016rds, liu2017rcf, he2019bdcn, xu2017AMHNet} generate object boundaries from hierarchical features by multi-level learning. Specifically, HED~\cite{xie2015hed} learns rich hierarchical features by performing supervisions on side output layers, which boosts the performance of edge detection. RCF~\cite{liu2017rcf} combines hierarchical features from all convolutional layers into a holistic architecture. To achieve effective results, BDCN~\cite{he2019bdcn} uses layer-specific supervision inferred from a bi-directional cascade structure to guide the training of each layer. PiDiNet~\cite{Su2021pidiNet} integrates the traditional edge detection operators into a CNN model for enhanced performance.

\vspace{0.2em}
\noindent{\bf Vision transformer.} First introduced to handle natural language tasks~\cite{devlin2019bert, lan2020albert, vaswani2017attention}, transformer is later extended to vision tasks owing to its capacity in modeling long-range dependencies including image classification~\cite{dosovitskiy2020image16x16}, semantic segmentation~\cite{zheng2021rethinking}, and object detection~\cite{carion2020detr}. Recently, it is applied in conjunction with CNN in DETR~\cite{carion2020detr} and the other variants~\cite{Li_2021_CVPR_Pose,Dai_2021_CVPR_UPDETR,Kim_2021_CVPR_HOTR,Wang_2021_CVPR_Tracker,Zou_2021_CVPR_HOI}. More recently, vision transformer (ViT)~\cite{dosovitskiy2020image16x16} directly uses the transformer to the sequences of image patches and achieves the state-of-the-art. This architecture brings direct inspiration to other computer vision tasks~\cite{zheng2021rethinking,liu2021swin,vaswani2021scaling,zhang2021multi,Li_2021_Diverse}. For example, SETR~\cite{zheng2021rethinking} shows superior accuracy in semantic segmentation using a pure transformer on image patches. These works demonstrate the effectiveness of transformers in capturing long-range dependencies and global context.

Our work is inspired by the above pioneer studies~\cite{dosovitskiy2020image16x16, zheng2021rethinking,liu2021swin}, but is significantly different in two aspects. First, the proposed EDTER, to the best of my knowledge, is the first usage of the transformer for generic edge detection. Second, our key idea is to learn the features that contain the global image context and fine-grained local cues by a two-stage framework with an affordable computational cost. With the integration of the global context and local cues, EDTER is superior in edge detection.

\section{Edge Detection with Transformer}

\subsection{Overview}

The overall framework of the proposed EDTER is illustrated in Fig.~\ref{fig:framework}. EDTER explores the full image context information and fine-grained cues in two stages. In Stage I, we first split the input image into a sequence of coarse-grained patches and use a global transformer encoder to learn the global context information. Then a Bi-directional Multi-Level Aggregation (BiMLA) decoder is used to generate the high-resolution features. In Stage II, the whole image is divided into multiple sequences of fine-grained patches by sampling with a non-overlapping sliding window. Then we execute a local transformer encoder on each sequence in turn to capture short-range local cues. We integrate all local cues and input them into a local BiMLA decoder to achieve the pixel-level feature maps. Finally, the global and local features are integrated by a Feature Fusion Module (FFM) and then are fed into a decision head to predict the final edge maps.

\subsection{Review Vision Transformer}
The transformer encoders in our framework follow the vision transformer (ViT) in~\cite{dosovitskiy2020image16x16}, as briefly described below.

\vspace{0.4em}
\noindent{\bf Image Partition.} The first step in ViT is to transform a 2D image, denoted by $X \in \mathbb{R}^{H \times W \times 3}$, into a 1D sequence of image patches~\cite{dosovitskiy2020image16x16,zheng2021rethinking}. Concretely, we uniformly split $X$ into a sequence of flattened image patches of size $P \times P$, resulting in $\frac{H}{P} \times \frac{W}{P}$ vision tokens. Then, the sequence is mapped into a latent embedding space by a learnable linear projection. The projected features are called patch embeddings. Further, to preserve positional information, the standard learnable 1D position embeddings are added to the patch embeddings. Finally, the combined embeddings (denoted as $z^0$) are fed into the transformer encoder.

\begin{figure*}[!t]
\setlength{\abovecaptionskip}{3pt}
\setlength{\belowcaptionskip}{0pt}
\centering
\includegraphics[width=0.98\linewidth]{fig/bimla_decoder.pdf}
\caption{The detailed architecture of the BiMLA decoder consists of a top-down path and a bottom-up path.}
\label{fig:decoder}
\vspace{-12pt}
\end{figure*}

\vspace{0.4em}
\noindent{\bf Transformer Encoder.} The standard transformer encoder~\cite{vaswani2017attention} consists of $L$ transformer blocks. Each block has a multi-head self-attention operation (MSA), a multi-layer perceptron (MLP), and two Layernorm steps (LN). Moreover, a residual connection layer is applied after each block. Generally, MSA performs $M$ self-attentions in parallel and projects their concatenated outputs. In the $m^{th}$ self-attention, given the output $z^{l-1}\in \mathbb{R}^{N \times C}$ of the $(l-1)^{th}$ transformer block, the queries $Q \in \mathbb{R}^{N \times U}$, keys $K \in \mathbb{R}^{N \times U}$, and values $V \in \mathbb{R}^{N \times U}$ are computed by
\begin{equation}
    Q = \hat{z}^{l-1}W_Q,\quad K = \hat{z}^{l-1}W_K,\quad V = \hat{z}^{l-1}W_V,
\end{equation}
where $\hat{z}^{l-1}={\rm LN}(z^{l-1})$, $W_Q, W_K,W_V \in \mathbb{R}^{C \times U}$ are the parameter matrices, $C$ is the dimension of embeddings, and $U$ is the dimension of $Q$, $K$, and $V$. Then, we compute the output of the $m^{th}$ self-attention based on the pairwise similarity between two elements of the sequence by
\begin{equation}
    y^m_{\rm sa}={\rm softmax} \Big(\frac{Q{K}^\mathsf{T}}{\sqrt{d}}\Big)V.
\end{equation}
where $y^m_{\rm sa}$ is the computed attention weight. Finally, MSA can be formulated as
\begin{equation}
    y_{\rm msa}={\rm MSA}(\hat{z}^{l-1})=\big[y^1_{\rm sa},y^2_{\rm sa},\dots, y^M_{\rm sa}\big] \ W_{\rm O},
\end{equation}
where $y_{\rm msa}$ is the output of MSA, $W_{\rm O}\in \mathbb{R}^{M \cdot U \times C}$ represents the projection parameters, and $[\cdot]$ is the concatenation. In this work, we fix $M = 16$ following the setting in~\cite{dosovitskiy2020image16x16}.

\subsection{Stage I: Global Context Modeling}
Generally, edges and boundaries in images are defined to be semantically meaningful. It is crucial to capture the abstract cues and the global context of the whole image. In the first stage, we explore the global contextual features on coarse-grained patches by a global transformer encoder $\mathcal{G}_{\rm E}$ and a global decoder $\mathcal{G}_{\rm D}$.

Specifically, we first split the input image into a sequence of coarse-grained patches of size 16$\times$16, and then generate the embeddings $z^0_{\rm g}$ that serve as input of the encoder. Next, the global transformer encoder $\mathcal{G}_{\rm E}$ works on the embeddings $z^0_{\rm g}$ to compute the global attentions,
\begin{equation}
    z_{\rm g} =\{z_{\rm g}^{1}, z_{\rm g}^{2}, \dots, z_{\rm g}^{L_{\rm g}}\} = \mathcal{G}_{\rm E}(z^0_{\rm g}),
\end{equation}
where $z_{\rm g}^{1}, z_{\rm g}^{2}, \dots, z_{\rm g}^{L_{\rm g}} \in \mathbb{R}^{\frac{HW}{256} \times C}$ represent the outputs of successive blocks in $\mathcal{G}_{\rm E}$, and $L_{\rm g}$ is the number of transformer blocks in $\mathcal{G}_{\rm E}$. In our experiments, we set $\mathcal{G}_{\rm E}$ to 24 following~\cite{dosovitskiy2020image16x16}. Next, the sequence of global context features $z_{\rm g}$ are upsampled to high-resolution features by the global decoder $\mathcal{G}_{\rm D}$ for incorporation.

\vspace{0.3em}\noindent{\bf BiMLA Decoder.}
It is crucial to generate edge-aware pixel-level representations for detecting precise and thin edges. Thus, we expect to design a practical decoder that can encourage the transformer encoder to compute the edge-aware attentions and upsample the attentions in a learnable manner. Inspired by the multi-level feature aggregation in vision tasks~\cite{LinFPN17,xie2015hed,liu2017rcf,liu2016rds,he2019bdcn,zheng2021rethinking}, we propose a novel Bi-directional Multi-Level Aggregation (\textbf{BiMLA}) decoder, as illustrated in Fig.~\ref{fig:decoder}, to achieve the goal.

In BiMLA, a bi-directional feature aggregation strategy is designed that includes a top-down path and a bottom-up path to boost the information flow in the transformer encoder. More specifically, we first uniformly divide $L_{\rm g}$ transformer blocks into four groups, and take the embedding features $\{z_{\rm g}^{6}, z_{\rm g}^{12}, z_{\rm g}^{18}, z_{\rm g}^{24}\}$ from the last block of each group as inputs. Then we reshape them to 3D features with the size of $\frac{H}{16}\times\frac{W}{16}\times C$. For the top-down path, we attach the same design (one 1$\times$1 convolutional layer and one 3$\times$3 convolutional layer) to each reshaped feature and obtain four output features $t^{6},t^{12},t^{18},t^{24}$, following the way of SETR-MLA~\cite{zheng2021rethinking}. Likewise, the bottom-up path starts from the lowest level (\emph{i.e.}} \def\Ie{\emph{I.e.}, $z_{\rm g}^{6}$) and gradually approaches the top level (\emph{i.e.}} \def\Ie{\emph{I.e.}, $z_{\rm g}^{24}$) by attaching one 3$\times$3 convolutional layer on multi-level features, and finally produce another four output features $b^{6},b^{12},b^{18},b^{24}$. Besides, unlike SETR-MLA~\cite{zheng2021rethinking} that upsamples the features via bilinear operation, our BiMLA passes each aggregated feature through a deconvolutional block, contains two deconvolutional layers with 4$\times$4 kernels and 16$\times$16 kernels, respectively. Each deconvolutional layer is followed by Batch Normalization (BN) and ReLU operations. The eight upsampled features from the bi-directional path are then concatenated into one tensor. Moreover, BiMLA uses an additional stack of convolutional layers to smooth the concatenated features. The stack consists of three 3$\times$3 convolutional layers and one 1$\times$1 convolutional layer with BN and ReLU. The process of BiMLA decoder is formulated as
\begin{equation}
    f_{\rm g} = \mathcal{G}_{\rm D}(z_{\rm g}^{6}, z_{\rm g}^{12}, z_{\rm g}^{18}, z_{\rm g}^{24}),
\end{equation}
where $f_{\rm g}$ is the pixel-level global features, and $\mathcal{G}_{\rm D}$ represents the global BiMLA decoder. After obtaining the coarse-grained global context features, we will capture the fine-grained local context features in the next stage.

\subsection{Stage II: Local Refinement}
It is essential to explore fine-grained context features for pixel-level predictions, especially for edge detection. The ideal edge width is one pixel, while 16$\times$16 patches are not conducive to extracting thin edges. Taking pixels as tokens sounds an intuitive remedy, however, it is practically infeasible due to heavy computational cost. Our solution is to use a non-overlapping sliding window to sample the image and then calculate the attentions within the sampled regions. The number of patches in the window is fixed, so the computational complexity is linearly related to the image size.

Thus motivated, we propose to capture the short-range fine-grained context features in Stage II, as shown at the bottom of Fig.~\ref{fig:framework}. In particular, we perform the non-overlapping sliding window with a size of $\frac{H}{2} \times \frac{W}{2}$ on image $X \in \mathbb{R}^{H \times W \times 3}$, and the input image $X$ is decomposed into a sequence $\{ X^{1}, X^{2}, X^{3}, X^{4} \}$. For each window, we split it into fine-grained patches of size 8$\times$8 and compute the attentions by a shared local transformer encoder $\mathcal{R}_{\rm E}$. Then we concatenate the attentions of all windows to obtain $z_{\rm r}=\{z_{\rm r}^1,\dots,z_{\rm r}^{L_{\rm r}}\} \in \mathbb{R}^{\frac{HW}{64}\times C}$. To further economize the computing resource, we set $L_{\rm r} =12$ that means the local transformer encoder consists of $12$ transformer blocks. Similar to global BiMLA, we evenly select $\{z_{\rm r}^3, z_{\rm r}^6, z_{\rm r}^9, z_{\rm r}^{12}\}$ from $z_{\rm r}$ and input them into the local BiMLA ${\mathcal{R}_D}$ to generate the local features with high-resolution,
\begin{equation}
    f_{\rm r} = \mathcal{R}_{\rm D}(z_{\rm r}^3, z_{\rm r}^6, z_{\rm r}^9, z_{\rm r}^{12}),
\end{equation}
where $f_{\rm r}$ indicates the local features. Different from global BiMLA, we replace the 3$\times$3 convolutional layer with the 1$\times$1 convolutional layer in local BiMLA, so as to avoid artificial edges caused by the padding operation.

\vspace{0.5em}
\noindent{\bf Feature Fusion Module.} Finally, we incorporate the context cues from both levels by a Feature Fusion Module (FFM) and predict the edge maps by a local decision head. FFM takes the global context as the prior knowledge and modulates the local context, which produces the fusion features containing global context and fine-grained local details. As shown in Fig.~\ref{fig:framework}, FFM consists of a spatial feature transform block~\cite{wang2018sft} and two 3$\times$3 convolutional layers followed by BN and ReLU operations. The former is for modulating, and the latter is for smoothing. Then the fusion features are fed into the local decision head $\mathcal{R}_{\rm H}$ to predict the edge maps $E_{\rm r}$,
\begin{equation}
    E_{\rm r}=\mathcal{R}_{\rm H} \big ({\rm FFM}(f_{\rm g}, f_{\rm r}) \big),
\end{equation}
where $\mathcal{R}_{\rm H}$ is the local decision head that consists of a 1$\times$1 convolutional layer and a sigmoid operation.

\subsection{Network Training}
\label{training}
To train the two-stage framework EDTER, we first optimize Stage I to generate global features that represent the whole image context information. Then, we fix the parameters of Stage I and train Stage II to generate edge maps.

\vspace{0.5em}
\noindent{\bf Loss Function.} We employ the loss function proposed in~\cite{xie2015hed} for each edge map. Given an edge map $E$ and the corresponding ground truth $Y$, the loss is calculated as
\begin{equation}
\begin{split}\ell \left (E,Y \right) & = - \sum_{i,j} \big( Y_{i,j}\alpha{\rm log}(E_{i,j}) \\
    &  + (1-Y_{i,j})(1-\alpha){\rm log}(1-E_{i,j}) \big),
\end{split}
\end{equation}
where $E_{i,j}$ and $Y_{i,j}$ are the $(i,j)^{th}$ element of matrix $E$ and $Y$, respectively. Moreover, $\alpha=|Y^-|/(|Y^-|+|Y^+|)$ indicates the percentage of negative pixel samples, where $|\cdot|$ denotes the number of pixels. In practice, the annotations of BSDS500~\cite{arbelaez2010bsds} are labeled by multiple annotators. Inconsistent annotations lead to problematic convergence behavior~\cite{xie2015hed}. Following~\cite{liu2017rcf}, we first normalize multiple labels to an edge probability map with ranges $[0, 1]$, and then use a threshold $\eta$ to select pixels. The pixel is marked as a positive sample if the probability value is higher than $\eta$; otherwise, it is indicated as a negative sample.

\vspace{0.5em}
\noindent{\bf Training Stage I.} For training Stage I, we first incorporate the global decision head on the global feature maps to generate the edge maps $E_{\rm g}$ by
\begin{equation}
    E_{\rm g}=\mathcal{G}_{\rm H}(f_{\rm g}),
\end{equation}
where $\mathcal{G}_{\rm H}$ indicates the global decision head that consists of a 1$\times$1 convolutional layer and a sigmoid layer. Moreover, we obtain multiple side outputs $S^{1}_{\rm g}, S^{2}_{\rm g}, \dots ,S^{8}_{\rm g}$ by performing the same design (a 4$\times$4 deconvolutional layer and a 16$\times$16 deconvolutional layer) to the intermediate features $t^{6},t^{12},t^{18},t^{24}$ and $b^{6},b^{12},b^{18},b^{24}$ extracted by the global BiMLA decoder, which progressively enforce the encoder to emphasize edge-aware attentions.

Stage I is optimized by minimizing the losses between each edge map and the ground truth. The loss function of Stage I is formulated as
\begin{equation}
\mathcal{L}_{\rm g} = \mathcal{L}_{\rm g}^{E} + \lambda\mathcal{L}_{\rm g}^{\rm side}
=\ell \left (E_{\rm g},Y \right)+\lambda\sum_{k=1}^{8} \ell \left(S_{\rm g}^k, Y \right),
\end{equation}
where $\mathcal{L}_{\rm g}^{E}$ is the loss for $E_{\rm g}$, $\mathcal{L}_{\rm g}^{\rm side}$ denotes side loss, and $\lambda$ is the weight for balancing $\mathcal{L}_{\rm g}^{E}$ and $\mathcal{L}_{\rm g}^{\rm side}$. In our experiments, we set $\lambda$ to 0.4.

\vspace{0.5em}
\noindent{\bf Training Stage II.} After training Stage I, we fix the parameters of Stage I and move on to Stage II. Similar to the training of Stage I, we perform the same operation (a 4$\times$4 deconvolutional layer and an 8$\times$8 deconvolutional layer) on the intermediate features extracted from the local BiMLA decoder to generate the side outputs $S^{1}_{\rm r}, S^{2}_{\rm r}, \dots ,S^{8}_{\rm r}$. Finally, the loss function of Stage II is defined as
\begin{equation}
\mathcal{L}_{\rm r} = \mathcal{L}_{\rm r}^{E} + \lambda\mathcal{L}_{\rm r}^{\rm side}
=\ell \left (E_{\rm r},Y \right)+\lambda\sum_{k=1}^{8} \ell \left(S_{\rm r}^k, Y \right),
\end{equation}
where $\mathcal{L}_{\rm r}^{E}$ and $\mathcal{L}_{\rm r}^{\rm side}$ are the losses for $E_{\rm r}$ and side outputs, respectively. We again set $\lambda=0.4$.

\section{Experiments}

\subsection{Datasets}
We conduct the experiments on three popular benchmarks: BSDS500~\cite{arbelaez2010bsds}, NYUDv2~\cite{silberman2012indoor} and Multicue~\cite{mely2016multicue}.

\textbf{BSDS500}~\cite{arbelaez2010bsds} contains 500 RGB natural images, 200 for training, 100 for validation, and 200 for testing. Each image is manually annotated by five different subjects on average. Our model is trained on the training and validation sets and evaluated on the testing set. Similar to~\cite{xie2015hed,liu2017rcf,he2019bdcn}, we augment the dataset by rotating each image at 16 different angles and flipping the image at each angle. Moreover, most previous works~\cite{liu2017rcf,liu2016rds,wang2017ced,he2019bdcn} use PASCAL VOC Context Dataset~\cite{everingham2010pascal} as the additional training data, which provides full-scene segmentation annotations with more than 400 classes, and consists of 10,103 images for training. The outside boundaries extracted from the segmentation annotations are beneficial to infer semantic and context cues in Stage I. Therefore, we first pre-train Stage I on PASCAL VOC Context Dataset~\cite{everingham2010pascal} and then fine-tune it on BSDS500~\cite{arbelaez2010bsds}. The PASCAL VOC Context Dataset~\cite{everingham2010pascal} is only used for training Stage I.

\textbf{NYUDv2}~\cite{silberman2012indoor} contains 1,449 pairs of aligned RGB and depth images, and it is split into 381 training, 414 validation, and 654 testing images. Following~\cite{xie2015hed,liu2017rcf}, we combine the training and validation sets as the training data, and then augment them by rotating the images and annotations to 4 different angles, randomly flipping, and scaling.

\textbf{Multicue}~\cite{mely2016multicue} is composed of 100 challenging natural scenes captured by a binocular stereo camera. Each scene contains a left-view and a right-view short sequences. The last frame of left-view sequences from each scene is labeled with edges and boundaries. Following~\cite{xie2015hed,liu2017rcf,he2019bdcn}, we randomly select 80 images for training and the remaining 20 images for testing. We repeat the process three times and average the scores of three independent trials as the final results. The data augmentation follows~\cite{xie2015hed,liu2017rcf}.

\begin{figure}[t]
\setlength{\abovecaptionskip}{3pt}
\setlength{\belowcaptionskip}{0pt}
\centering
\includegraphics[width=0.95\linewidth,height=.35\linewidth]{fig/ablation_fig.pdf}
\caption{Qualitative comparison of different decoders in EDTER on BSDS500. From left to right are the input images, the results of EDTER using SETR-MLA and BiMLA decoder, respectively.}
\label{fig:ablation_fig}
\vspace{-14pt}
\end{figure}

\subsection{Implementation Details}
We implement our EDTER using PyTorch~\cite{paszke2017automatic}. We initialize the transformer blocks of our model using the pre-trained weights by ViT~\cite{dosovitskiy2020image16x16}. We set the threshold $\eta$ as 0.3 to select positive samples for BSDS500 and Multicue Edge, and 0.4 for Multicue Boundary. Each image has only one annotation in NYUDv2, thus no $\eta$ is needed. We use SGD optimizer with momentum=0.9 and weight decay=2e-4, and adopt a polynomial learning rate decay schedule~\cite{Zhao17PyramidScene} on all datasets. The initial learning rate is set as 1e-6 for BSDS500, NYUDv2 and Multicue Boundary, and 1e-7 for Multicue Edge. During training, we set the same iteration numbers for both stages. Specially, we train 80k iterations for BSDS500 and Multicue boundary, 40k for NYUDv2, and 4k for Multicue Edge. Each image is randomly cropped to 320$\times$320 in training. Compared with BSDS500, the annotations of NYUDv2 are unitary, and the scale of Multicue is small, which quickly overfits of the model trained on them. Therefore, we set the batch size to 8 for BSDS500, and 4 for NYUDv2 and Multicue. All the experiments are conducted on a V100 GPU. The training of EDTER takes about 26.4 hours (15.1 for Stage I and 11.3 for Stage II). The inference runs at 2.2 \textit{fps} on a V100. During Training, the GPU consumption of Stage I and Stage II are about 15GB and 14GB for 320$\times$320 images respectively. Besides, EDTER brings 332.0G FLOPs in Stage I and 470.25G FLOPs in Stage II.

During evaluation, we record three metrics for all datasets: fixed contour threshold (ODS), per-image best threshold (OIS), and average precision (AP). Moreover, a non-maximum suppression~\cite{canny1986computational} is performed on the predicted edge maps before evaluation. Following previous works~\cite{xie2015hed,liu2017rcf}, the localization tolerance controls the maximum allowed distance in matches between edge results and the ground truth, which is set to 0.0075 for BSDS500 and Multicue, and 0.011 for NYUDv2.

\begin{table
\setlength{\abovecaptionskip}{0pt}
\caption{Ablation study of the effectiveness of the proposed two-stage strategy, BiMLA decoder and FFM in EDTER on BSDS500. All results are computed with a single scale input.}
\centering
\footnotesize
\renewcommand\arraystretch{0.9}
\renewcommand\tabcolsep{5.8pt}
\begin{tabular}{c|cc|c|ccc}
    \toprule
    \multirow{2}{*}{Stage}   & \multicolumn{2}{c|}{Decoder}  & \multirow{2}{*}{FFM}   & \multirow{2}{*}{ODS}  & \multirow{2}{*}{OIS}  & \multirow{2}{*}{AP} \\
    \cline{2-3}
    &SETR-MLA        &BiMLA      & & & & \\
    \toprule
    \multirow{2}{*}{I}
    &$\surd$    &$\times$
    &\multirow{2}{*}{\diagbox{\textcolor{white}{.}}{\textcolor{white}{.}}}    & 0.790     & 0.806     & 0.836\\
    &$\times$   &$\surd$    &    & {\bf 0.817}   & {\bf 0.835}   & {\bf 0.867}\\
    \toprule
    \multirow{3}{*}{II}
    &$\surd$    &$\times$   &$\surd$    & 0.799     & 0.816     & 0.848\\
    &$\times$   &$\surd$    &$\surd$    & {\bf 0.824}  & {\bf 0.841}  & {\bf 0.880}\\
    &$\times$   &$\surd$    &$\times$   & 0.820     & 0.835     & 0.867\\
    \bottomrule
\end{tabular}
\vspace{-12pt}
\label{tab:decoder_ffm}
\end{table}

\subsection{Ablation Study}

\noindent{\bf Effectiveness of key components in EDTER.} We first conduct experiments to verify the impact of key EDTER components: BiMLA and FFM. The quantitative results are summarized in Table~\ref{tab:decoder_ffm}. First, the performance of ODS, OIS, AP is largely improved (about 2.5\%, 3\%, 3\%) by BiMLA compared with SETR-MLA~\cite{zheng2021rethinking} in both stages. The performance of Stage II significantly surpasses Stage I under either decoder. It illustrates that the two-stage strategy fuses more critical information for edge detection. Besides, we present the predicted edge maps by the SETR-MLA and BiMLA decoders shown in Fig.~\ref{fig:ablation_fig}. With the BiMLA decoder, EDTER can accurately detect edges in some local areas (red bounding boxes) and produce less noisy edges. To verify the effectiveness of FFM, we remove the FFM and directly concatenate the feature maps from two stages to construct a variant of EDTER. Without using FFM (row 5), the scores drop by 0.4\%, 0.6\%, and 1.3\% in ODS, OIS, and AP, respectively.

\noindent{\bf Effectiveness of stages and patch size.} We run ablation experiments to verify the effectiveness of the two-stage strategy. The comparative results are presented in Table~\ref{tab:stage_size}. Compared with Stage I (row 1), we add the second stage and set the patch size to 8$\times$8 (row 2), which obtains the performance gain by 0.7\%, 0.6\%, 1.3\% in ODS, IS, and AP, respectively. Moreover, as visualized in Fig.~\ref{fig:ablation_2stage}, the predicted edges of Stage II are more clear and crisp in some local details. It shows that the effectiveness of the two-stage strategy for edge detection. Then, to analyze the impact of the patch size, we create a variant that uses the patch size of 4$\times$4 in Stage II (row 3). Concretely, in Stage II, the image is first decomposed into a sequence $\{X^1,X^2,\dots,X^{16}\}$ by the sliding window with a size of $\frac{H}{4}\times\frac{W}{4}$, and then we split each window into a sequence of 4$\times$4 patches and generate local cues. Compared with row 2 using 8$\times$8 patches in Stage II, the performance is slightly improved. Moreover, we report experiments with EDTER model variants that use more stages to capture local context, obtained by adding Stage III and setting the patch size to 4$\times$4. In Table~\ref{tab:stage_size} (row 4), the scores are marginally increased by fusing context cues of three stages. Since the edge extracted from the networks inevitably occupies multiple pixels, 4$\times$4 patches seldom bring significant gains. Considering the trade-off between computational efficiency and performance, we employ the setting of \textit{16$\times$16 in Stage I} and \textit{8$\times$8 in Stage II} to perform all subsequent experiments.

\begin{figure}[t]
\setlength{\abovecaptionskip}{3pt}
\setlength{\belowcaptionskip}{0pt}
\centering
\includegraphics[width=0.95\linewidth,height=.35\linewidth]{fig/ablation_stageI_II.pdf}
\caption{Qualitative comparison of different stages in EDTER on BSDS500. From left to right are the input images, the results of EDTER-Stage I and EDTER-Stage II, respectively.}
\label{fig:ablation_2stage}
\vspace{-7pt}
\end{figure}

\begin{table
\setlength{\abovecaptionskip}{0pt}
\caption{Quantitative results of EDTER with training on different patch sizes and stage numbers on BSDS500. ``-'' means Stage III is not extended. All results are computed with a single scale input.}
\centering
\footnotesize
\renewcommand\arraystretch{0.9}
\renewcommand\tabcolsep{8.2pt}
\begin{tabular}{c|c|c|ccc}
    \toprule
    \multicolumn{3}{c|}{Patch Size}  & \multirow{2}{*}{ODS}  & \multirow{2}{*}{OIS}  & \multirow{2}{*}{AP} \\
    \cline{1-3}
    Stage I         &Stage II   &Stage III  &       &       & \\
    \toprule
    16$\times$16    &-          &-          &0.817  &0.835  &0.867\\
    16$\times$16    &8$\times$8 &-          &0.824  &0.841  &0.880\\
    16$\times$16    &4$\times$4 &-          &0.825  &0.843  &0.882\\
    16$\times$16    &8$\times$8 &4$\times$4 &0.826  &0.843  &0.883\\
    \bottomrule
\end{tabular}
\label{tab:stage_size}
\vspace{-14pt}
\end{table}

\subsection{Comparison with State-of-the-arts}

\begin{table}[tbp]
\setlength{\abovecaptionskip}{0pt}
\caption{Results on BSDS500~\cite{arbelaez2010bsds} testing set. The best two results are highlighted in \BEST{red} and \SBEST{blue}, respectively, and same for other tables. MS is the multi-scale testing, and VOC means training with extra PASCAL VOC data.}
\centering
\footnotesize
\renewcommand\arraystretch{0.9}
\renewcommand\tabcolsep{5.0pt}
\begin{tabular}{c|l|c|ccc}
    \toprule
    \multicolumn{2}{c|}{Method}          &\makecell[c]{Pub.'Year}     & ODS       & OIS       & AP    \\
    \toprule
    \multirow{9}{*}{\rotatebox{90}{Traditional Method}}
    & Canny~\cite{canny1986computational}     & PAMI'86     & 0.600     & 0.640     & 0.580 \\
    & Felz-Hutt~\cite{felzenszwalb2004felz}   & IJCV'04      & 0.610     & 0.640     & 0.560 \\
    & gPb-owt-ucm~\cite{arbelaez2010contour}  & PAMI'10     & 0.726     & 0.757     & 0.696 \\
    & SCG~\cite{xiaofeng2012scg}              & NeurIPS'12   & 0.739     & 0.758     & 0.773 \\
    & Sketch Tokens~\cite{lim2013sketch}      & CVPR'13      & 0.727     & 0.746     & 0.780 \\
    & PMI~\cite{isola2014pmi}                 & ECCV'14      & 0.741     & 0.769     & 0.799 \\
    & SE~\cite{dollar2014fast}                & PAMI'14     & 0.746     & 0.767     & 0.803 \\
    & OEF~\cite{hallman2015oef}               & CVPR'15      & 0.746     & 0.770     & 0.820 \\
    & MES~\cite{sironi2015mes}                & ICCV'15      & 0.756     & 0.776     & 0.756 \\
    \toprule
    \multirow{19}{*}{\rotatebox{90}{CNN-based Method}}
    & DeepEdge~\cite{bertasius2015deepedge}   & CVPR'15      & 0.753     & 0.772     & 0.807 \\
    & CSCNN~\cite{hwang2015cscnn}             & ArXiv'15       & 0.756     & 0.775     & 0.798 \\
    & MSC~\cite{sironi2015msc}                & PAMI'15     & 0.756     & 0.776     & 0.787 \\
    & DeepContour~\cite{shen2015deepcontour}  & CVPR'15      & 0.757     & 0.776     & 0.800 \\
    & HFL~\cite{bertasius2015hfl}             & ICCV'15      & 0.767     & 0.788     & 0.795 \\
    & HED~\cite{xie2015hed}                   & ICCV'15      & 0.788     & 0.808     & 0.840 \\
    & Deep Boundary~\cite{kokkinos2015pushing}& ICLR'15      & 0.813     & 0.831     & 0.866 \\
    & CEDN~\cite{yang2016cedn}                & CVPR'16      & 0.788     & 0.804     & - \\
    & RDS~\cite{liu2016rds}                   & CVPR'16      & 0.792     & 0.810     & 0.818 \\
    & COB~\cite{maninis2016cob}               & ECCV'16      & 0.793     & 0.820     & 0.859 \\
    & DCD~\cite{liao2017dcd}                  & ICME'17      & 0.799     & 0.817     & 0.849 \\
    & AMH-Net~\cite{xu2017AMHNet}             & NeurIPS'17   & 0.798     & 0.829     & 0.869 \\
    & RCF~\cite{liu2017rcf}                   & CVPR'17      & 0.811     & 0.830     & - \\
    & CED~\cite{wang2017ced}                  & CVPR'17      & 0.815     & 0.833     & 0.889 \\
    & LPCB~\cite{deng2018lpcb}                & ECCV'18      & 0.815     & 0.834     & - \\
    & BDCN~\cite{he2019bdcn}                  & CVPR'19      & 0.828     & 0.844     & 0.890 \\
    & DexiNed~\cite{poma2020dexined}          & WACV'20      & 0.729     & 0.745     & 0.583 \\
    & DSCD~\cite{deng2020dscd}                & ACMMM'20     & 0.822     &\SBEST{0.859}     & - \\
    & PiDiNet~\cite{Su2021pidiNet}            & ICCV'21      & 0.807     & 0.823     & - \\
    \toprule
    \multirow{4}{*}{\rotatebox{90}{Ours}}
    & EDTER                  & -      & 0.824           & 0.841         & 0.880 \\
    & EDTER-VOC              & -      & 0.832           & 0.847         & 0.886 \\
    & EDTER-MS               & -      & \SBEST{0.840}   & 0.858 & \SBEST{0.896} \\
    & EDTER-MS-VOC           & -      & \BEST{0.848}    & \BEST{0.865}  & \BEST{0.903} \\
    \bottomrule
\end{tabular}
\label{tab:bsds}
\vspace{-9pt}
\end{table}

\vspace{0.5em}
\noindent{\bf On BSDS500.} We compare our model with \textit{traditional detectors} including Canny~\cite{canny1986computational}, Felz-Hutt~\cite{felzenszwalb2004felz}, gPb-owt-ucm~\cite{arbelaez2010contour}, SCG~\cite{xiaofeng2012scg}, Sketch Tokens~\cite{lim2013sketch}, PMI~\cite{isola2014pmi}, SE~\cite{dollar2014fast}, OEF~\cite{hallman2015oef} and MES~\cite{sironi2015mes}, and \textit{deep-learning-based detectors} including DeepEdge~\cite{bertasius2015deepedge}, CSCNN~\cite{hwang2015cscnn}, DeepContour~\cite{shen2015deepcontour}, HFL~\cite{bertasius2015hfl}, HED~\cite{xie2015hed}, Deep Boundary~\cite{kokkinos2015pushing}, CEDN~\cite{yang2016cedn}, RDS~\cite{liu2016rds}, COB~\cite{maninis2016cob}, DCD~\cite{liao2017dcd}, AMH-Net~\cite{xu2017AMHNet}, RCF~\cite{liu2017rcf}, CED~\cite{wang2017ced}, LPCB~\cite{deng2018lpcb}, BDCN~\cite{he2019bdcn}, DexiNed~\cite{poma2020dexined}, DSCD~\cite{deng2020dscd} and PiDiNet~\cite{Su2021pidiNet}. The best results of all the methods are taken from their publications.

\begin{figure}[tbp]
\setlength{\abovecaptionskip}{0pt}
\setlength{\belowcaptionskip}{0pt}
\centering
\includegraphics[width=0.85\linewidth,height=.71\linewidth]
{fig/pr_bsds.pdf}
\caption{The precision-recall curves on BSDS500.}
\label{fig:pr_bsds}
\vspace{-15pt}
\end{figure}

\begin{figure*}[!t]
\small
\setlength{\abovecaptionskip}{3pt}
\setlength{\belowcaptionskip}{0pt}
    \centering
	\begin{tabular}{cccccc}
		\hspace{-.2cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/input/226033.jpg} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/gt/226033.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/rcf/226033_rcf.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/ced/226033.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/bdcn/226033.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/ours/226033.png}\vspace{-.06cm} \\
		\hspace{-.2cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/input/206062.jpg} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/gt/206062.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/rcf/206062_rcf.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/ced/206062.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/bdcn/206062.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/ours/206062.png}\vspace{-.06cm} \\
		\hspace{-.2cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/input/376086.jpg} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/gt/376086.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/rcf/376086_rcf.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/ced/376086.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/bdcn/376086.png} & \hspace{-.45cm}
		\includegraphics[width=.155\textwidth]{fig/fig2/ours/376086.png}\vspace{-.06cm} \\
		\hspace{-.2cm} (a) Input
		& \hspace{-.45cm} (b) Ground truth
		&\hspace{-.45cm} (c) RCF~\cite{liu2017rcf}
		&\hspace{-.45cm} (d) CED~\cite{wang2017ced}
		&\hspace{-.5cm} (e) BDCN~\cite{he2019bdcn} &\hspace{-.45cm} (f) EDTER (Ours) \\
	\end{tabular}
    \caption{Qualitative comparisons on three challenging samples in the testing set of BSDS500.}
    \label{fig:fig_sota}
    \vspace{-12pt}
\end{figure*}

Quantitative results are shown in Table~\ref{tab:bsds}, and Fig.~\ref{fig:pr_bsds} shows Precision-Recall curves of all methods. By training on the trainval set of BSDS500, our method achieves the F-measure ODS of 0.824 with single-scale testing and obtains 0.840 with multi-scale inputs, which already outperforms most edge detectors. With the extra training data and multi-scale testing (following the settings of RCF, CED, BDCN, \emph{etc.}} \def\vs{\emph{vs.}), our method achieves 84.8\% (ODS), 86.5\% (OIS) 90.3\% (AP), which is superior to all the state-of-the-art edge detectors. Some qualitative results are shown in Fig.~\ref{fig:fig_sota}. We observe that the proposed EDTER shows a clear advantage in prediction quality, both crisp and accurate.

\vspace{0.2em}
\noindent{\bf On NYUDv2.} In NYUDv2, we conduct experiments on RGB images and compare against the state-of-the-art methods including gPb-ucm~\cite{arbelaez2010bsds}, Silberman~\emph{et al. }\cite{silberman2012indoor}, gPb+NG~\cite{gupta2013perceptual}, SE~\cite{dollar2014fast}, SE+NG+~\cite{gupta2014seng}, OEF~\cite{hallman2015oef}, SemiContour~\cite{zhang2016semicontour}, HED~\cite{xie2015hed}, RCF~\cite{liu2017rcf}, AMH-Net~\cite{xu2017AMHNet}, LPCB~\cite{deng2018lpcb}, BDCN~\cite{he2019bdcn}, and PiDiNet~\cite{Su2021pidiNet}. All results are based on single-scale input. Table~\ref{tab:nyud} shows the quantitative results of our method and other competitors. Our method achieves the best scores of 77.4\%, 78.9\%, and 79.7\% of ODS, OIS, and AP, respectively. Compared to the second best, we increase the scores by 2.6\%, 2.6\%, 2.7\% in three metrics, respectively. More results including HHA, RGB-HHA inputs, and visualizations are reported in the \href{https://github.com/MengyangPu/EDTER}{supplementary material}.

\begin{table
\setlength{\abovecaptionskip}{0pt}
\caption{Quantitative comparisons on NYUDv2~\cite{silberman2012indoor}. All results are computed with a single scale input.}
\centering
\footnotesize
\renewcommand\arraystretch{0.9}
\renewcommand\tabcolsep{5.0pt}
\begin{tabular}{c|l|c|ccc}
    \toprule
    \multicolumn{2}{c|}{Method} &\makecell[c]{Pub.'Year}    & ODS   & OIS   & AP        \\
    \toprule
    \multirow{7}{*}{\rotatebox{90}{Traditional}}
    & gPb-ucm~\cite{arbelaez2010bsds}     & PAMI'11     & 0.632 & 0.661 & 0.562     \\
    & Silberman \emph{et al. }~\cite{silberman2012indoor}  & ECCV'12     & 0.658 & 0.661 & -  \\
    & gPb+NG~\cite{gupta2013perceptual}   & CVPR'13     & 0.687 & 0.716 & 0.629     \\
    & SE~\cite{dollar2014fast}            & PAMI'14     & 0.695 & 0.708 & 0.679     \\
    & SE+NG+~\cite{gupta2014seng}         & ECCV'14     & 0.706 & 0.734 & 0.738     \\
    & OEF~\cite{hallman2015oef}           & CVPR'15     & 0.651 & 0.667 & -         \\
    & SemiContour~\cite{zhang2016semicontour}       & CVPR'16   & 0.680 & 0.700 & 0.690   \\
    \toprule
    \multirow{6}{*}{\rotatebox{90}{CNN-based}}
    & HED~\cite{xie2015hed}       & ICCV'15     & 0.720 & 0.734 & 0.734     \\
    & RCF~\cite{liu2017rcf}       & CVPR'17     & 0.729 & 0.742 & -         \\
    & AMH-Net~\cite{xu2017AMHNet} & NeurIPS'17  & 0.744 & 0.758 & 0.765     \\
    & LPCB~\cite{deng2018lpcb}    & ECCV'18     & 0.739 & 0.754 & -         \\
    & BDCN~\cite{he2019bdcn}      & CVPR'19     & \SBEST{0.748} & \SBEST{0.763} & \SBEST{0.770}     \\
    & PiDiNet~\cite{Su2021pidiNet}& ICCV'21     & 0.733 & 0.747 & -         \\
    \toprule
    & EDTER (Ours)                & -           & \BEST{0.774}  & \BEST{0.789}  & \BEST{0.797}\\
    \bottomrule
  \end{tabular}
\label{tab:nyud}
\vspace{-14pt}
\end{table}

\begin{table}[t]
\setlength{\abovecaptionskip}{0pt}
\caption{Comparisons on Multicue~\cite{mely2016multicue}. All results are computed with a single scale input.}
\centering
\footnotesize
\renewcommand\arraystretch{0.9}
\renewcommand\tabcolsep{1.5pt}
\begin{tabular}{c|l|c|ccc}
    \toprule
    & Method                          & Pub.'Year & ODS           & OIS           & AP            \\
    \toprule
    \multirow{8}{*}{\rotatebox{90}{Edge}}
    & Human~\cite{mely2016multicue}   & VR'16     & .750 (0.024) & -             & -             \\
    & Multicue~\cite{mely2016multicue}& VR'16     & .830 (0.002) & -             & -             \\
    & HED~\cite{xie2015hed}           & ICCV'15   & .851 (0.014) & .864 (0.011) & -             \\
    & RCF~\cite{liu2017rcf}           & CVPR'17   & .857 (0.004) & .862 (0.004) & -             \\
    & BDCN~\cite{he2019bdcn}          & CVPR'19   & \SBEST{.891 (0.001)} & \SBEST{.898 (0.002)} & \SBEST{.935(0.002)}  \\
    & DSCD~\cite{deng2020dscd}        & ACMMM'20  & .871 (0.007) & .876 (0.002) & -             \\
    & PiDiNet~\cite{Su2021pidiNet}    & ICCV'21   & .855 (0.007) & .860 (0.005) & -              \\
    & EDTER (Ours)                    & -         & \BEST{.894 (0.005)} & \BEST{.900 (0.003)} & \BEST{.944 (0.002)}     \\
    \toprule
    \multirow{8}{*}{\rotatebox{90}{Boundary}}
    & Human~\cite{mely2016multicue}   & VR'16     & .760 (0.017) & -             & -             \\
    & Multicue~\cite{mely2016multicue}& VR'16     & .720 (0.014) & -             & -             \\
    & HED~\cite{xie2015hed}           & ICCV'15   & .814 (0.011) & .822 (0.008) & .869 (0.015) \\
    & RCF~\cite{liu2017rcf}           & CVPR'17   & .817 (0.004) & .825 (0.005) & -             \\
    & BDCN~\cite{he2019bdcn}          & CVPR'19   & \SBEST{.836 (0.001)} & \SBEST{.846 (0.003)} & \SBEST{.893 (0.001)} \\
    & DSCD~\cite{deng2020dscd}        & ACMMM'20  & .828 (0.003) & .835 (0.004) & -             \\
    & PiDiNet~\cite{Su2021pidiNet}    & ICCV'21   & .818 (0.003) & .830 (0.005) & -             \\
    & EDTER (Ours)                    & -         & \BEST{.861 (0.003)} & \BEST{.870 (0.004)} & \BEST{.919 (0.003)}\\
    \bottomrule
  \end{tabular}
\label{tab:multicue}
\vspace{-12pt}
\end{table}

\vspace{0.1em}
\noindent{\bf On Multicue.} Multicue consists of two kinds of annotations, \emph{i.e.}} \def\Ie{\emph{I.e.}, Multicue Edge and Multicue Boundary. For each type of annotations, we compare against the state-of-the-art methods including HED~\cite{xie2015hed}, RCF~\cite{liu2017rcf}, BDCN~\cite{he2019bdcn}, DSCD~\cite{deng2020dscd}, and PiDiNet~\cite{Su2021pidiNet}. We report the comparisons in Table~\ref{tab:multicue}, and the results show consistent performance. Our method produces competitive results on Multicue Edge. For Multicue Boundary, EDTER achieves the F-measure ODS of 86.1\%, higher than all other competitors. The visualization results are provided in the \href{https://github.com/MengyangPu/EDTER}{supplementary material}.

\section{Conclusion and Limitation}
In this paper, we propose a novel two-stage edge detection framework, namely EDTER. By introducing the vision transformer, EDTER captures both coarse-grained global context and fine-grained local context in two stages. Moreover, it employs a novel Bi-directional Multi-Level Aggregation (BiMLA) decoder to explore high-resolution representations. Besides, a Feature Fusion Module (FFM) incorporates global and local contexts to predict the edge results. Experimental results illustrate that EDTER yields competitive results in comparison with state-of-the-arts.

\vspace{0.5em}
\noindent\textbf{Limitation.} The width of the edges extracted by EDTER occupies multiple pixels, which still has a gap with the ideal edge width. Without any post-processing, generating clear and thin edges is still a future direction to explore.

\vspace{0.6em}
\noindent\textbf{Acknowledgements.}
This work is supported by Beijing Natural Science Foundation (M22022, L211015), Fundamental Research Funds for the Central Universities (2019JBZ104), and National Natural Science Foundation of China (61906013, 62106017).

{\small
\bibliographystyle{ieee_fullname}

redpajama_set_name: RedPajamaArXiv


Phytopathogenic fungi affecting crop and post-harvested vegetables are a major threat to food production and food storage. To face these drawbacks, producers have become increasingly dependent on agrochemicals. However, intensive use of these compounds has led to the emergence of pathogen resistance and severe negative environmental impacts. There are also a number of plant diseases for which chemical solutions are ineffective or non-existent as well as an increasing demand by consumers for pesticide-free food. Thus, biological control through the use of natural antagonistic microorganisms has emerged as a promising alternative to chemical pesticides for more rational and safe crop management.
The genome of the plant-associated B. amyloliquefaciens GA1 was sample sequenced. Several gene clusters involved in the synthesis of biocontrol agents were detected. Four gene clusters were shown to direct the synthesis of the cyclic lipopeptides surfactin, iturin A and fengycin as well as the iron-siderophore bacillibactin. Beside these non-ribosomaly synthetised peptides, three additional gene clusters directing the synthesis of the antibacterial polyketides macrolactin, bacillaene and difficidin were identified. Mass spectrometry analysis of culture supernatants led to the identification of these secondary metabolites, hence demonstrating that the corresponding biosynthetic gene clusters are functional in strain GA1. In addition, genes encoding enzymes involved in synthesis and export of the dipeptide antibiotic bacilysin were highlighted. However, only its chlorinated derivative, chlorotetaine, could be detected in culture supernatants. On the contrary, genes involved in ribosome-dependent synthesis of bacteriocin and other antibiotic peptides were not detected as compared to the reference strain B. amyloliquefaciens FZB42.
The production of all of these antibiotic compounds highlights B. amyloliquefaciens GA1 as a good candidate for the development of biocontrol agents.
Phytopathogenic fungi affecting crop and post-harvested vegetables are a major threat to food production and food storage. Worldwide, this has led to important economic losses, particularly over the past few decades as agricultural production has intensified. Post-harvest food spoilage also represents a potential health hazard for humans due to the production by phytopathogens of toxic metabolites in the affected sites . To face these drawbacks, producers have become increasingly dependent on agrochemicals. However, intensive use of these compounds has led to the emergence of pathogen resistance and severe negative environmental impacts. There are also a number of plant diseases for which chemical solutions are ineffective or non-existent as well as an increasing demand by consumers for pesticide-free food. Thus, biological control through the use of natural antagonistic microorganisms has emerged as a promising alternative to chemical pesticides for more rational and safe crop management. There is a large body of literature reporting the potential use of rhizosphere-associated bacteria in stimulating plant growth and biocontrol agents [2–4]. Among them, several strains belonging to the genus Bacillus and particularly to the B. subtilis and B. amyloliquefaciens species were reported effective for the biocontrol of multiple plant diseases caused by soilborne [5, 6] or post-harvest pathogens [7–9]. Members of the Bacillus genus are thus among the beneficial bacteria mostly exploited as microbial biopesticides. Bacillus-based products represent about half of the commercially available bacterial biocontrol agents .
From a global viewpoint, the beneficial protective effect of these agents may rely on different mechanisms. By taking benefit from the nutrients secreted by the plant root, these bacteria efficiently colonise root systems and the surrounding soil layer (rhizosphere). In turn, they beneficially influence the plant through direct growth stimulation and/or by protecting it from infection by phytopathogens. Antibiosis through the production of antifungal metabolites and antibiotics is probably the best known and most important mechanism used by biocontrol bacteria to limit pathogen invasion in host plant tissues. Competition for iron traces in soils through siderophore production has also been postulated to be an important mechanism for the biocontrol activity of some rhizobacteria . Another important mechanism relies on the ability of some strains to activate defence systems in the host plant. In other words, the beneficial bacterium can trigger a systemic resistance reaction that renders the host less susceptible to subsequent infection in distal tissues. This long-lasting phenomenon has been termed rhizobacteria-induced systemic resistance (ISR).
It is well known that some Bacillus species may synthesise numerous antimicrobial or, more generally, bioactive compounds with well-established activity in vitro . However, except for a very limited number of strains [13, 14], few studies that relate the global potential for antibiotic production with the biocontrol activity of a particular Bacillus strain have been reported. In this context, the B. amyloliquefaciens strain GA1 (formerly B. subtilis GA1, see below) displays high in vitro inhibitory activity toward growth of multiple fungal and oomycete plant pathogens . When used as seed treatment, strain GA1 was shown to alleviate seedling diseases through direct antibiosis against soilborne pathogens (unpublished data). The strain was also shown to reduce post-harvest infection of apples caused by B. cinerea, the causative agent of grey mold disease . These data suggest the secretion of multiple antibiotics and demonstrate the potential application of B. amyloliquefaciens GA1 as a biocontrol agent. In the present work, the genome of strain GA1 was sample sequenced to better characterise the genetic determinants directing the synthesis of antimicrobial metabolites that could be used in the field.
The recN and recA sequences from strain GA1 had 83% and 98% identity, respectively, with the sequence of B. amyloliquefaciens FZB42, while scores of 68% and 84% were obtained for B. subtilis. The phylogenetic tree (figure 1) constructed using cancatenated recA and recN sequences of related members of the Bacillus genus revealed that strain GA1 grouped with B. amyloliquefaciens FZB42 and is phylogenetically separated from B. subtilis. However, the phylogenetic tree suggests that the two strains are somewhat distant genetically.
Likelihood phylogenetic tree depicting the phylogenetic relationship between strain GA1 and other representatives of the Bacillus genera: B. amyloliquefaciens FZB42 (NC_009725), B. anthracis str. Ames (NC_003997), B. cereus ATCC 10987 (NC_003909) B. cereus ATCC 14579 (NC_004722), B. halodurans C-125 (BA_000004), B. licheniformis ATCC 14580 (NC_006270), B. pumilus SAFR-032 (NC_009848), B. subtilis subsp. subtilis str. 168 (NC_000964), B. thuringiensis str. Al Hakam (NC_008600), B. weihenstephanensis KBAB4 (NC_010184). All sequences were aligned on Clostridium botulinum Ba4 str. 657 (NC_012658). Values for frequencies less than 50% are not given. The scale bars represent the number of substitutions per base position.
Sequencing 500 clones from a shotgun library led to the determination of 461.5 kb of the B. amyloliquefaciens GAI chromosome and the identification of 358 protein-coding sequences. These presented, on average, 89% identity on amino acid level with that of B. amyloliquefaciens FZB42 and 76% with that of B. subtilis. Among these sequences, the partial ORFs of eight giant gene clusters directing the synthesis of bioactive peptides and polyketides by modularly organised mega-enzymes, the so-called non-ribosomal peptide synthetase (NRPS) and polyketide synthetase (PKS), were identified (figure 2). In addition, the sfp gene coding for a 4'-phosphopantetheinyl transferase responsible for the conversion of the apo-ACP domains of PKS and NRPS to their active holo-forms, was also detected in strain GA1 together with the regulatory gene yczE (data not shown).
Overview of the different gene fragments identified in strain GA1. The grey arrows represent the different genes involved in the metabolite synthesis in B. amyloliquefaciens FZB42 while the black arrows represent the flanking genes. Black lines correspond to the gene fragments obtained during the sequencing of strain GA1, while grey lines indicate flanking regions amplified by PCR on strain GA1 genomic DNA with primer pairs described in Table 1. The values in parentheses give the percentage of the gene cluster determined in strain GA1.
Fourteen gene fragments with homology toward gene clusters directing the synthesis of cyclic lipopeptide were obtained (figure 2). Of these, eleven had a high amino acid identity with srf (80-96%) or fen (41-92%) operon directing the synthesis of surfactin and fengycin in B. amyloliquefaciens FZB42. In strain GA1, the two gene clusters were found located in the same genetic environment as in strain FZB42 ; i.e. at the hxlR-CDS22 and yngL-dacC loci for srf and fen operon, respectively (figure 2). Similarly to B. amyloliquefaciens FZB42 and B. subtilis 168, the comS gene, encoding a competence signal molecule, was found embedded within srfAB (figure 2). Three gene fragments directing the synthesis of an iturin lipopeptide were also detected. These fragments presented 48-82% amino acid identity with the ituDABC operon encoding the iturin A synthetase in B. subtilis RB14 . In strain GA1, this operon was found located between the ORFs xynD and yxjF (figure 2). In addition, five gene fragments presented a high amino acid identity (87-93%) with the dhb gene directing the synthesis of the siderophore bacillibactin in B. amyloliquefaciens FZB42. They were found at an exactly conserved locus, i.e. between CDS304 and yuilV ORFs (figure 2). By contrast, the nrs operon directing the synthesis of a not yet identified NRPS peptide in B. amyloliquefaciens FZB42  could not be detected by PCR techniques in strain GA1 (figure 3).
Detection of the nrs operon in B. amyloliquefaciens strains FZB42 and GA1. The grey arrows indicate the gene organisation in strain FZB42. The black lines represent the different gene fragments amplified by PCR using primer pairs as described in Table 1.
Several gene fragments involved in polyketide synthesis were also identified. Of these, thirteen presented a high amino acid identity with PKS genes directing the synthesis of the antibacterial compounds macrolactin (86-98%), difficidin (77-96%) and bacillaene (84-96%). In strain GA1, all these gene clusters were found to be collinear to that of B. amyloliquefaciens FZB42 ; i.e. between CDS175 and pdhA for macrolactin, proI and CDS254 for difficidin and mutl and yoak for bacillaene (figure 2).
In addition to these NRPS and PKS metabolites, genes involved in the synthesis of ribosomaly synthetised antibacterial compounds were detected in strain GA1. Indeed, their deduced amino acid sequence presented high identity (76-100%) with bacB, bacC, bacD and bacE genes encoding enzymes responsible for the synthesis and export of the di-peptide bacilysin, and were found located between ORFs ywfH and ywfA as in FZB42 strain. By contrast, none of the genes involved in B. amyloliquefaciens FZB42 in the resistance toward the bacteriocin mersacidin, nor those directing the biosynthesis of the cyclic bacteriocin subtilosin found in some strains of B. amyloliquefaciens could be detected by PCR techniques in strain GA1 (figure 4) [13, 17].
Culture supernatants of B. amyloliquefaciens GA1 collected after 12 and 72 h of growth in Landy medium were concentrated by solid phase extraction and analysed by HPLC-ESI-MS. For samples collected after 72 h, three groups of mass peaks were detected (Table 1). Signals at m/z from 1030.8 to 1074.8 and from 1471.9 to 1543.8 were identified as surfactins and fengycins on the basis of data obtained both from the literature and from the analysis of pure compounds. For fengycins, signals at m/z of 1485.9 and 1513.9 and at 1499.9 and 1527.8 highlight an Ala/Val dimorphy at position 6 of the peptide ring for the C16 and C17 homologues, which is the characteristic trait of fengycin A and B. Mass peaks at m/z 1066.1 and 1079.7 were found in accordance with the calculated mass values of sodium adducts of the C14 and C15 homologues of iturin A. By contrast, no peaks corresponding to the calculated mass of the various bacillomycin D homologues or to those of mycosubtilin could be detected under these conditions. This suggests that the iturins produced by strain GA1 correspond to the iturin A group. MALDI-TOF-MS analyses of crude supernatant were consistent with the mass patterns obtained by HPLC-ESI-MS (data not shown). From samples collected after 12 h of growth, signals at m/z 425.4, 511.4, 525.4 and 629.3 were assigned to the molecular ions of the antimicrobial polyketide macrolactin A, 7-o-malonyl macrolactin A, 7-o-succinyl macrolactin A and macrolactin D respectively, whereas signals at m/z 559.2, 583.5 and 605.5 were assigned to oxydifficidin, bacillaene A and bacillaene B (Table 1) based on data from the literature [18, 19].
The production of siderophores by B. amyloliquefaciens GA1 was investigated by plating cells on CAS solid medium. After 72 h of incubation, the disappearance of the blue colour due to the ternary complex chrome azurol-S/iron (III)/hexadecyltrimethylammonium bromide in favour of a bright orange halo traduces the uptake of the ferric ions by the cells and thus the production of siderophore (i.e. bacillibactin) (data not shown).
HPLC-ESI-MS analysis of freeze-dried samples of culture in Basic 77 medium gave peaks at m/z 289.2 and 291.1, which represents the typical mass spectrometric signature of the dipeptide antibiotic chloroteatine, a chlorinated derivative of bacilysin (Table 1) . Surprisingly, no mass peak corresponding to this latter compound could be detected under our conditions. When samples were analysed by MALDI-TOF mass spectrometry, none of the bacteriocin subtilosin, mercacidin or subtilin mass signals could be detected (data not shown).
Recent taxonomic studies have revealed that B. subtilis is heterogeneous and should be considered as a group of closely related species . In addition, B. subtilis and B. amyloliquefaciens are phenotypically similar and can be easily confused. Based on phenotypic and biochemical characterisations, strain GA1, initially isolated from strawberry cultures, was first assigned to B. subtilis (unpublished data, ). However, substantial molecular evidence suggested that the strain was more related to B. amyloliquefaciens than to B. subtilis. Thus, to accurately characterise the strain taxonomically, recA and recN genes, encoding DNA repair and recombination proteins, were sequenced and used to construct a phylogenetic tree. These two genes were selected because they had previously been shown to be effective in resolving closely related taxa . The obtained phylogenetic tree clearly demonstrates that strain GA1 should be assigned to B. amyloliquefaciens rather than B. subtilis. The higher level of identity obtained for the 358 protein-coding sequence detected in strain GA1 to that of B. amyloliquefaciens FZB42 is in accordance with this result.
Plant-associated bacteria are known to play a key role in plant health by stimulating their growth and protecting them from phytopathogens, with this related to the production of a vast array of biologically active NRPS and PKS secondary metabolites. These metabolites have the same mode of synthesis, the so-called multicarrier thiotemplate mechanism, in which small monomer units, aminoacids and aryl acid in NRPS and acyl-CoAs in PKS are loaded, activated and condensed by mega-enzymes organised in iterative functional units . The aim of this work was to better genetically characterise B. amyloliquefaciens GA1, with particular emphasis on gene clusters encoding these mega-enzymes. As they are encoded by large operons of 55 to 80 kb for PKS and 18 to 42 kb for NRPS, randomly sequencing 10% of the genome yielded enough data to point out the presence of these gene clusters in strain GA1.
Among NRPS antibiotics, Bacillus amyloliquefaciens GA1 was found to produce surfactin, iturin A, fengycin A and fengycin B. These are cyclic lipopeptides (CLP) composed of seven (surfactin and iturin A) or 10 α-amino acids (fengycins) linked to a β-amino (iturins) or β-hydroxy (surfactins and fengycins) fatty acid which may vary from C-13 to C-16 for surfactins, from C-14 to C-17 for iturins and from C-14 to C-18 for fengycins. CLPs have well-recognized potential biotechnology and biopharmaceutical applications due notably to their surface-active properties [24, 25]. These surfactants may also play different roles in the development and survival of Bacillus strains in their natural habitat: increasing bioavailability of hydrophobic water-insoluble substrates, heavy metal binding, bacterial pathogenesis, quorum sensing, motility, biofilm formation etc. [26, 27]. Other works have highlighted additional traits that are also very important for the fitness of Bacillus in the rhizosphere and for its efficacy as biocontrol agent .
The ability of B. subtilis to efficiently colonise surfaces of plant roots is a prerequisite for phytoprotection. This process relies on surface motility and efficient biofilm formation of the Bacillus cell populations that evolve and behave as structured and coordinated microcolonies adhering to root and on soil particle surfaces . By modifying cell surface properties, surfactin and iturin were reported to positively influence cell spreading, swarming and biofilm formation [30–33] and thus may globally favour plant root colonisation. Furthermore, iturins and fengycins display strong antifugal activity and are inhibitory for the growth of a wide range of plant pathogens. Surfactins are not fungitoxic in themselves but retain some synergistic effect on the antifungal activity of iturin A . In the context of biocontrol, the involvement of CLPs in direct antagonism of phytopathogens is thus obvious and was demonstrated by testing the pure compounds in planta or by correlating the biocontrol activity and use of non-producing or overproducing derivatives [5, 35, 36].
The role of fengycins produced by strain GA1 was demonstrated by the very effective disease control provided by treatment of fruits with CLP-enriched extracts and by in situ detection of fengycins in inhibitory amounts . Another recently established role for lipopeptides from beneficial Bacillus isolates is the stimulation of the plant immune system . Surfactins and, to a lesser extent, fengycins can induce a priming state in host plant which allows an accelerated activation of defense responses upon pathogen or insect attack, leading to an enhanced resistance to the attacker encountered . Surfactins can be considered as a novel class of microbial-associated molecular patterns that can be specifically perceived by plant cells as signals to activate defense mechanisms . The use of single strains evolving diverse mechanisms to reduce disease incidence is thus of prime interest. Bacillus isolates such as strain GA1 that co-produce the three CLP families should display such a multi-faceted biocontrol activity. That said, in strain GA1 the itu operon directing the synthesis of iturin A in B. subtilis RB14  was surprisingly found inserted at exactly the same position as the expected bacylomycin D gene cluster from B. amyloliquefaciens FZB42 . This suggests that an inter-species horizontal transfer of genes could have occurred between B. subtilis and B. amyloliquefaciens.
Besides lipopepides, a functional dhb gene cluster was shown in strain GA1 to direct the synthesis of the catecholic siderophore bacillibactin, a cyclic trimeric lactone of the 2,3-dihydroxybenzoyl-Gly-Thr monomer unit. Siderophores are high affinity ferric iron chelators that enhance the microbial acquisition of this element in environments where its bioavailability is extremely low, e.g. in soils. Thus, the presence of siderophore-producing microorganisms in the rhizosphere contributes to plant health by complexing iron and making it less available to phytophathogens that are generally not able to produce comparable Fe-transport systems .
In addition to peptides, polyketides are the other dominant family of secondary metabolites having revelant bioactivities. Similarly to B. amyloliquefaciens FZB42, three functional gene clusters directing the synthesis of difficidin, macrolactin and bacillaene were identified in strain GA1. Difficidin is an unsaturated 22-membered macrocylic polyene lactone phosphate ester  with broad spectrum antibacterial activity . It inhibits protein biosynthesis  and was recently shown promising in its suppressive action against Erwinia amylovara, a devasting plant pathogen causing necrotrophic fire blight disease of apple, pear and other rosaceous plants . By contrast, macrolactin and bacillaene have not yet been demonstrated to be directly related to biocontrol, although they are both antimicrobial agents that could be potentially useful in human medicine. Macrolactin, which consists of a 24-membered ring lactone, had the ability to inhibit murine melanoma cancer cells as well as mammalian herpes simplex viruses. It was also shown effective in protecting lymphoblast cells from HIV . Similarly to difficidin, bacillaene is an inhibitor of prokaryotic protein synthesis constituted by an open-chain enamine acid with an extended polyene system. This compound displays antimicrobial activity toward human pathogens such as Serratia marcescens, Klebsiella pneumoniae and Staphylococcus aureus .
Bacilysin is a dipeptide composed of an L-alanine and the unusual amino acid L-anticapsin and represents one of the simplest peptide antibiotics known with antifungal and antibacterial activities . L-anticapsin, released after uptake in susceptible cells, is an inhibitor of the glucose amine-6-phosphate synthetase, an enzyme essential in cell wall biosynthesis . Due to its antibacterial activity, bacilysin is effective as a biocontrol agent, notably by inhibiting the growth of E. amylovora, the causative agent of fire blight disease . It is also effective on the Absidia ssp., which is responsible for cutaneous and invasive zygomycosis in immunocompromised patients . Besides bacilysin, some strains of B. subtilis also co-produced chlorotetaine, a chlorinated derivative of bacilysin with similar antibacterial activity [20, 49]. Although no direct evidences are available, some experimental data suggest that the two compounds could share the same biosynthetic pathway . Here, mass spectrometry analysis demonstrated that B. amyloliquefaciens GA1 synthetises only chlorotetaine as dipeptide antibiotic. While this behaviour is not clearly understood, this is to our knowledge the first B. amyloliquefaciens strain reported to produce chlorotetaine and the first strain to produce chlorotetaine and not bacilysin.
In conclusion, the genetic and biochemical characterisation of the plant-associated B. amyloliquefaciens GAI demonstrated that the strain possesses a huge potential for biocontrol and plant growth promotion. Its natural competence and its possible genetic manipulation render strain GA1 attractive for further investigations for the development of green pesticides.
Strain GA1 was identified by recA and recN sequence analysis . Extraction and amplification of genomic DNA were performed as described elsewhere . Fragments of recA and recN were amplified using primer pairs recAf/recAr and recNf/recNr, respectively (Table 2) and sequenced at the GIGA Genomics Facility (University of Liege, Liege, Belgium). Based on the 372 bp and 849 bp partial sequences of recN and recA, phylogenetically related bacteria were aligned using BLAST search against the GenBank data base. Multiple alignments with the recN-recA concatenated sequences of related species of the genus Bacillus were implemented using MUSCLE software . A maximum likelihood phylogenetic tree was constructed by the parsinomy method using PAUP* software (version 4.0b8, ) and the sequence from Clostridium botulinum KBAB4 as outgroup. The parameters used for tree construction were as follows: (i) model of nucleotide substitution: GTR plus gamma distribution; (ii) number of substitution rate categories: 6; (iii) rate matrix parameter: estimated by program; (iv) number of bloodstrap replicates: 100.
For partial genome sequencing, a random shotgun approach was used. Total genomic DNA from strain GA1 was shared by nebulisation according to Surzycki . DNA fragments of 2-3 kb in size were cloned into pMOSblue (GE Healthcare, Uppsala, Sweden) to establish a shotgun library. The inserts of 500 recombinant plasmids were sequenced from both ends. Sequences were processed with Vector NTI software (Invitrogen) and similarity search was performed using BLAST algorithm against the GenBank database. The chromosomic location of the different gene clusters identified in strain GAI was performed by sequencing their flanking regions using the FZB42 genomic sequence  as a template for PCR primer design (Table 2). The nrsF, nrsE, nrsD, nrsC, nrsAB, mrsK2, mrsR2, mrsG, mrsE, fbaB, sboA and albA gene fragments were amplified by PCR using the primer pairs listed in Table 1 and genomic DNA from B. amyloliquefaciens strains FZB42 and GA1 or from B. subtilis 168 as a template.
For polyketide and lipopeptide production, B. amyloliquefaciens GAI was grown in Landy medium  at 37°C for 12 h and 72 h, respectively. Samples were extracted from the culture supernatant by solid phase extraction using Chromafix C18ec cartridge (Machery-Nagel, Duren, Germany). After binding and subsequent washing steps with MilliQ water (5 bed volume), metabolites were eluted with methanol (2 bed volume), dried under vacuum and resuspended in 100 μl of methanol. The resulting samples were analysed by reverse-phase high pressure liquid chromatography (Waters Alliance 2695/diode array detector) coupled with single quad mass spectrometer (Waters SQD mass analyser) on an X-Terra MS 150*2.1 mm, 3.5 μm column (Waters). Lipopeptides were eluted as described elsewhere  whereas polyketides were eluted in a binary solvent system (solvent A: water-0.1% formic acid, solvent B: acetonitrile-0.1% formic acid) as follows: 30% B for 5 min followed by a 5 min gradient from 30% B to 45% B and a subsequent 25 min gradient from 45% B to 100% B at a flow rate of 0.5 ml/min at 40°C. The identity of each metabolite was obtained on the basis of the mass of molecular ions detected in the SQD by setting electrospray ionisation (both positive and negative mode) conditions in the MS as source temperature, 150°C; desolvatation temperature, 325°C; nitrogen flow, 550 l/min; cone voltage 80 V. Matrix-assisted laser desorption ionisation time of flight (MALDI-TOF) mass spectrometry was performed on the crude culture supernatant on a Bruker Ultraflex TOF spectrometer (Bruker Daltonics) as described elsewhere . Siderophore production was evaluated using the chrome-azurol-sulphonate (CAS) agar plate assay  using the growth medium described previously .
The ribosomaly synthetised peptide antibiotics were obtained by growing strain GA1 in Basic 77 medium  for 22 h. Peptides were extracted from freeze-dried culture filtrate with 30% acetonitrile-0.1% formic acid before being analysed by HPLC-ESI mass spectrometry. Molecule were eluted at a flow rate of 0,2 ml/min of a water/acetonitrile/formic acid mixture (87/12,9/0,1 v/v/v) and their identity was obtained on the basis of the mass of the molecular ions detected in the SQD by setting electrospray ionization (positive mode) condition in the MS as source temperature, 150°C; desolvatation temperature, 300°C; nitrogen flow, 550 l/min; cone voltage, 80 V. MALDI-TOF mass spectrometry was used in the reflectron mode of detection and with α-cyano-4-hydroxy-cinnamic acid as matrix.
A. Arguelles-Arias and Y. Lara are recipients of a FRIA grant (Fonds pour la Formation dans la Recherche et l'Agriculture, Belgium). P. Fickers and M. Ongena are post-doctoral researcher and research associate, respectively at the FRS-FNRS (Fonds National de la Recherche Scientifique, Belgium). This work received financial support from the program Crédits aux Chercheurs N°1.5.192.08F (FRS-FNRS, Belgium).
AA performed part of the genome characterisation and cultures for LC-MS analysis. MO performed the LC-MS analysis. BH constructed the shotgun library and annotated the sequence. AB and BJ planed and supervised part of the experiments. YL performed the phylogenetic analysis. PF wrote the final version of the manuscript and supervised the work. All authors approved the final version of the manuscript.


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Tenkara on the Fly: Tenkara Iwana 12ft with Fuji Hook Keeper System and level line (fc).
Tenkara Iwana 12ft with Fuji Hook Keeper System and level line (fc).
My current setup, an Iwana 12ft from Tenkara USA with a level line (fluor carbon) of Chris Stewart of Tenkarabum and Fuji hook keepers.
I am currently on the fence whether to keep the hook keepers or to change to a foam spool cut from a pool noodle (yes!).
The hook keepers are great if you want to wind line quickly but they will kink up fluor carbon lines a bit (nothing that you can't stretch in less than 20 seconds though). Also, keeping the fly on can pose some issues if you'd put it in a backpack (get stuck, crush the fly). The foam spool is very light and can be pushed down the collapsed rod onto the grip.
Foam Line Holder - left one is a Level no. 3 Fluor Carbon line, 12ft. and right is a TenakaraUSA furled line, 10.5ft.
Like yourself, I am a new Tenkara fisher. I also own a TenkaraUSA 12' Iwana and I also use the Fuji hook keepers. I find that the hook keepers are very easy to use for transport between fish spots/pools and for brush bashing. I use it whether I have a level or furled line on the rod. I wind the line on kinda loosely, not too tight, and I find it uncurls very easily, definitely requiring a gentle stretch before resuming fishing at the new location. The level lines also require a gentle stretch thruout the day anyway to keep them nice and straight. I do that as I'm changing/redressing flies, which I have to do anyway. The furled line comes right off the keepers and ready to fish immediately. I made one slight addition to the keeper setup, though. I use the extra o-rings from the package and install them on the rod between the hook keepers. Then when I wind the line on the keepers, I hook the fly on one of the middle o-rings. The middle o-rings slide anywhere on the rod and stay where you leave them, providing perfect tension to maintain fly position/tension to hold everything in place for trips between fish spots. An easy roll of the o-ring with you fingers removes its grip on the fly hook and the fly drops off and ready to unwind line off hook keepers. Daniel @ Tenkara USA likes to use the spools because of the possible kinks to the lines like you mentioned, and I may start to use the spools like he recommends. I am a newbie to Tenkara, not to flyfishing. I especially love mountain streams like you and have many new(to me) techniques and equipment to experiment with. Email me if you want to. I would look forward to sharing my thoughts on this exciting new way to fish for trout. I am also seriously considering an Amago puchase and are very interested in your feelings about that rod. I simply love the Iwana rod. It boggles my mind how effective Tenkara fishing for trout has become. No more fly rod for me on a trout stream if it is anywhere near wadeable and suitable current flows, cover.
Some dry's creates twist on the level line/tippet when back-casting or on windy days. I use a small (smallest available) bb-swivel at about 8" below the rod tip for a 15' level-line…seems to work without any impact to the presentation. Is it my casting or do others have the same experience?
When that happens, you are likely fishing with a dry fly that is too big for the size tippet you are using. Another reason might be that the fly is not tied "symmetrically". Do you notice the swivel when casting? Does it change how the line casts?


text:
Erosion threatens Jonathan's village, others, N7.5bn project abandoned
The Akipelai, Ayakoro and Otuoke communities in Bayelsa State are at the risk of being washed away by coastal erosion as the contract awarded to save the areas has been allegedly abandoned by the contractors.
The Shore Erosion Control Works project, with a 14-month completion period, was awarded in March 2012 during former President Goodluck Jonathan's administration.
Jonathan hails from Otuoke, a coastal community some kilometres from Yenagoa, the state capital.
The contract was awarded for N7.5bn by the Nigerian Ports Authority as part of its corporate social responsibility following agitations by the residents.
According to the 2017 Audit Report of the Federation, N4.2bn was made available to the contractors in 2015, representing 56.61 per cent of the contract sum.
During the physical inspection of the project, the audit report noted that it was discovered that the contractors had abandoned the project site and the duration of the project had since lapsed without approval for its extension.
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The report stated that the NPA had shown no concern or taken any significant measure to recover the money from the contractor, "which implies expenditure inefficiency on the part of the and loss of benefits to the communities where the project was meant to be implemented."
A civil society group, Paradigm Leadership Support Initiative, said it embarked on a fact-finding mission to the project sites through its Value for Money advocacy project after analysing and simplifying the 2017 audit report.
The group, which visited the communities in March 2020, said it discovered that the Shore Erosion Control Works project would have positively impacted Ayakoro, Akipelai and Otuoke as most houses were built close to the riverbank.
The PLSI stated in its report, "Young people in these communities complained about the abandoned project and the effects of flooding on their communities.
"One of the youth representatives, who identified himself as Mr LoveGod Daniel, told our reporters that the contractors installed signage of the project only to come back months later to remove it. Mr LoveGod further said that nothing happened since the project signage was installed and removed."
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The group added that the residents confirmed that the contractors are Bayelsa indigenes, noting that project abandonment was an act of corruption and contravened Financial Regulations 224 and 230 (2009).
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text:
Q: Behaviour of Solutions to $x^2y'' + \alpha xy'+ \beta y = 0$ as $x \to 0$ and $x \to \infty$
Consider the Euler equation $x^2y'' + \alpha xy' + \beta y = 0$.
  Find conditions on $\alpha$ and $\beta$ so that:

*

*All solutions approach zero as $x \rightarrow 0$

*All solutions are bounded as $x \rightarrow 0$

*All solutions approach zero as $x \rightarrow \infty$

*All solutions are bounded as $x \rightarrow \infty$

*All solutions are bounded both as $x \rightarrow 0$ and $x \rightarrow \infty$

I am having trouble solving the problem. It must obviously have to do with the solutions to the indicial equation $ r^2 + (\alpha - 1)r + \beta= 0 \implies r = \dfrac{1 - \alpha
\pm \sqrt {(\alpha - 1)^2 - 4\beta^2}}{2} $. When these roots are identical or complex the solutions involve an $\ln x$ term the limit of which when $x \to 0$ is undefined I think? So my feeble argument is that the solutions for $r$ should be distinct to begin with? Please help.

A: A logarithmic term, if present, only changes the behaviour as $x \to 0$ or $x \to \infty$ when $\text{Re}(r) = 0$.  That is, if $\text{Re}(r) \ne 0$ then both
$x^r$ and $x^r \log(x)$ have the same limit or lack of limit as $x \to \infty$ and as $x \to 0$.  I don't know what that "or complex" is doing there: in the Euler equation a logarithmic term only appears when the roots are equal.

A: It's literally worked out here:
http://banach.millersville.edu/~bob/math365/homework/boycediprima/sec05.05.pdf

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Kyle Abraham at Danspace Project
Mar 02, 2010 by Maura Donohue	in Dance
Kyle Abraham is working a successful mix of dazzle and poignancy to great effect. Last weekend, he premiered "The Radio Show" to packed houses at Danspace Project. He's been on my watch list since seeing his solo and group works, "Brick" and "The Dripping Kind" at Dance Theater Workshop two years ago. Last summer, I joined his little group during an audience break-out session in the midst of David Dorfman's "Disavowal," also presented by Danspace Project. Audience members were supposed to sit with the cast member/character we most identified with. He had served as a powerful antagonist, challenging white guilt and entitlement. I don't see myself as "Angry Black Man," but those of us who are at the margins of the Marked half of the spectrum end up there some of the time. Up close and personal, he was immediately warm and receiving. A ferocious out package wrapped around a sweet center. I was already a fan, I became an admirer.
A solo he showed during Camille A. Brown's season at Joyce Soho revealed his continued explorations in smashing formal and popular dance forms together. As then, he continues to use music and sound in "The Radio Show" as obvious sign posts for the converging and sometimes oppositional aesthetic forces at work, setting Beyonce next to pulsing static in the same way he throws a pirouette next to a hair toss or shoulder roll. His own ability to rapidly shift between vernacular and classical dance forms is impressive and part of the great allure of his work, but he's showing more skill at highlighting the outstanding abilities of his virtuosic dancers and letting them rip across some cultural borders.
"The Radio Show" is a memorial of sorts, as well, both to a former hometown radio station, AM860/FM 106.7 in Pittsburgh and and to the father he is losing to Alzheimer's. There is potent grief in the shaking crumple that follows an explosive series of bound and electric chest pops and arm swings. But, there is also the excitement at watching an artist pull both the kinesthetic and emotional meanings out of popularized movement and back into the highly personal realm it came from. Like Bruno Beltrao, Abraham captures the spirit inside of various hip hop movement practices and culture. Unlike Beltrao, however, Abraham is sometimes too enamored with the classical dance technique that is also an ingrained part of his heritage. There are moments where I feel as though the physical, sonic, visual juxtapositions of high/low are a battle, rather than a Both. For me, the excitement (and my grand expectation about where I'll see both of these artists showing there work a few years down the line) is in watching how artists today can tear down the bias against hip hop that seethes through certain populations and ignores it's prevalence and impact on dance globally. Abraham has it in him to be everything, all at once, soon enough his will too.
Tagged with: danspace project, inmixedcompany, Kyle Abraham, mdonohue
About the author Maura Donohue
Maura Nguyen Donohue has been making and performing experimental performance works in NYC since 1995. She has been a member of La MaMa's Great Jones Rep since 1997. From '99-04, as artistic advisor for DTW's Mekong Project, she facilitated residencies in the US and SE Asia. She's currently serves on the board of Movement Research and on the Bessies Committee. Her essay "Ambivalent Selves: The Asian Female Body in American Concert Dance" was published in Contemporary Directions in Asian American Dance. She is Associate Professor at Hunter College, faculty fellow for the Roosevelt House Public Policy Institute, and is the mother of 2.


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