text:
\section{Introduction}
\label{sec:intro}

In the context of computer vision, nowadays almost all mainstream depth estimation methods are deep learning based and can be roughly categorized into two prevalent methodologies, namely, stereo matching and monocular depth estimation. Stereo matching has traditionally been the most investigated area due to its strong connection to the human visual system. The task is to find or estimate the correspondences of all the pixels in two rectified images ~\cite{barnard1982computational,scharstein2002taxonomy,andrew2001multiple}. Virtually, all the current works resort to convolutional neural network (CNN) based methods to calculate the matching cost since it was first introduced to the task by ~\cite{dosovitskiy2015flownet,zbontar2016stereo} in 2015. Following the seminal work of FlowNet~\cite{dosovitskiy2015flownet}, more than 150 papers have been published using CNN-related methods ~\cite{laga2020survey}, pushing the performance forward by more than 50\%. Some deep-seated issues such as thin structures, large texture-less areas, and occlusions have been mitigated or addressed over time~\cite{zhang2019ga, ilg2018occlusions}. So far, stereo matching is the most adopted technique in majority of passive stereo applications.

However, the applications that entail depth estimation grow increasingly demanding as visual systems are greatly downsized and installed on platforms with higher mobility (e.g., UAV, commercial robots). This indicates a more congested, cluttered and dynamic operating environment where the once side issues become major ones, i.e., large disparity, severe occlusion and non-rectilinear images that might be involved. Therefore, most existing stereo matching methods are not set up for this new trend and fail to address these issues properly.

On the other hand, monocular depth estimation (MDE) is spared from these challenges as depth is estimated from a single view. Following~\cite{eigen2014depth}, current works leverage deep models to derive more descriptive cues to achieve superior predictions. More recent works focus on fusing multi-scale information to further improve the pixel level depth estimation~\cite{liang2018learning,lee2019big}. Lately, vision transformer is exploited in the task and yields globally organized and coherent predictions with finer granularity~\cite{ranftl2021vision,bhat2021adabins}. State-of-the-art MDE methods can achieve impressive results with relative accuracy $\delta^3 > 0.99$ with supervised training~\cite{kittiMono1, kittiMono2, kittiMono3, kittimono4}. However, the reliability of MDE estimation is essentially based on the assumption that scenes in the real world are mostly regular. Therefore, due to the lack of stereo relation, the MDE is more delimited to its training dataset and susceptible to ``unfamiliar" scenes. This renders the MDE alone not reliable in safety-critical applications, such as autonomous driving and visual-aided UAV.

From the discussion above, we can see the limitations and advantages of stereo matching and MDE are complementary. Therefore, in this paper we propose a novel method that jointly addresses their limitations by crossing over the stereo and MDE approaches such that stereo information can be injected into the MDE process to rectify and improve the estimation made from depth cues.

We therefore introduce ChiTransformer, an optic-chiasm-inspired self-supervised binocular depth estimation network. ChiTransformer adopts the recent vision transformer (ViT)~\cite{vit} as backbone and extends the encoder-only transformer to an encoder-decoder structure similar to the ones for natural language processing~\cite{devlin2018bert, vaswani2017attention}. Rather than end-to-all connections, interleaved connections are employed for cross-attention to enable progressive instillation of the encoded depth cues from a nearby view to the master view in a self-regressive process. Our main contribution is the design of a retrieval cross-attention layer. Instead of attending over multi-level contextual relation of the encodings in the regular multi-head attention (MHA), the cross-attention mechanism of ChiTransformer aims to retrieve depth cues with strong contextual and feature coincidence from the other view. To achieve this, we condition the initial state (query) with a self-adjoint operator without breaking the convergence rule of modern Hopfield network~\cite{ramsauer2020hopfield}. The positive-definite operator is spectrally decomposed to enable polarized attention within the encoded feature space to emphasize on certain cues while preserving as much of the original information as possible. We show that this design facilitates reliable retrieval and leads to finer feature-consistent details on top of the globally coherent estimation. Moreover, the model can be further extended to non-rectilinear images such as fisheye by using a gated positional embedding~\cite{d2021convit}. We model the epipolar geometry with learnable quadratic polynomials of relative positions. Considering the per-pixel labeled data is challenging to acquire at scale and let alone for the non-rectilinear images, we choose to train the model with self-supervised learning strategy tailored from the work~\cite{godard2019digging}.

In contrast to traditional stereo methods, our approach foregoes pixel-level matching optimization but leverages the context-infused depth cues of both views to improve the overall depth prediction. With a global receptive field, ChiTransformer is not only not restricted to certain epipolar geometry, e.g., the horizontal collinear epipolar lines of rectified regular stereo pairs, but also able to treat large disparity. Furthermore, with the inherent capability of depth estimation within a single image, estimation at large occluded area can be properly handled rather than being masked out, interpolated, or left untreated. Enhanced from current MDE methods, our approach provides reliable prediction with guided cues in stereo pair which makes ChiTransformer more suitable for complex and dynamic environments.

Experiments are conducted on depth estimation tasks that provide stereo pairs. Our result shows that ChiTransformer delivers an improvement of more than 11\% compared to the top-performing self-supervised stereo methods. The architecture is also tested on stereo tasks to evaluate the gain brought by stereo cues and the underlying reliability yielded by the instilled stereo information. To show the potential of ChiTransformer in non-rectilinear images, we train our model to predict the distances on the translated synthetic fisheye sequences from~\cite{eichenseer2016data} and achieve visually satisfactory results.

\begin{figure*}[t]
    \vspace{-5mm}
    \centering
    \includegraphics[width=1.0\textwidth]{figures/Architecture.pdf}
    \vspace{-30px}
    \caption{\footnotesize Architecture of ChiTransformer. A stereo pair (left: master, right: reference) is initially embedded into tokens through a Siamese ResNet-50 tower. The 2D-organized tokens from the two images are flattened and then augmented with learnable positional embeddings and an extra class token, respectively. Then tokens are fed into two self-attention (SA) stacks of size $l_{\text{SA}}$ in parallel. After that, tokens are fed into a series ($\times l_{DCR}$) of depth rectification blocks (DCR) in each of which tokens of reference image go through an SA layer while tokens of master go through a polarized cross-attention (CA) layer, followed by an SA layer. In the polarized CA layer, relevant tokens from the output of reference SA are fetched to rectify the master's depth cues. Tokens from different stages are afterwards reassembled into an image-like arrangement at multiple resolution (blue) and progressively fused and up-sampled through fusion block to generate a fine-grained depth estimation.}
    \label{figure:arch}
    \vspace{-10px}
\end{figure*}

\section{Related Work}\label{sec: Rel.W}\vspace{-7pt}
Since the publications of~\cite{eigen2014depth,fischer2015flownet}, the end-to-end trainable CNN-based models have been the prototype architecture for dense depth~\cite{godard2017unsupervised,ranftl2019towards, godard2019digging} or disparity estimation~\cite{survey18, survey93, survey27, survey115}. The principal idea is to leverage learned representation to improve matching cost ~\cite{khan2018guide, scharstein2002taxonomy} or depth cues ~\cite{bhoi2019monocular} with contextual information of appropriately large local area. The prevalent encoder-decoder structure enables progressive down- and up-sampling of representation at different scales~\cite{diffscales1, chang2018pyramid,liang2018learning,yang2018segstereo,duggal2019deeppruner}, and the intermediate results from previous layers are often reused to recover fine-grained estimation while ensuring sufficiently large context.

After showing exemplary performance on a broad range of NLP tasks, attention or in particular transformer has demonstrated competitive or superior capability in vision tasks such as image recognition~\cite{vit, touvron2021training}, object detection~\cite{carion2020end, zhu2020deformable}, semantic segmentation~\cite{ye2019cross}, super-resolution~\cite{yang2020learning}, image impainting~\cite{zeng2020learning}, image generation~\cite{razavi2019generating}, text-image synthesis~\cite{DaLLe}, etc. The successes also sparked interest in the community of stereo and depth estimation. ~\cite{wang2020parallax} leveraged cascaded attentions to calculate the matching cost along the epipolar lines and achieved competitive results among self-supervised stereo matching methods~\cite{zhou2017unsupervised,li2018occlusion, ahmadi2016unsupervised, jason2016back}. More recently, vision transformer was leveraged in place of convolution network as backbone for dense depth prediction in~\cite{ranftl2021vision} and achieved a significant improvement by 28\% compared to the state-of-the-art convolutional counterparts. A mini-ViT block~\cite{bhat2021adabins} is employed in the refinement stage to facilitate the adaptive depth bin calculation, and the work tops KITTI~\cite{kitti} and NYUv2~\cite{nyu} leaderboards. Inspired by~\cite{ranftl2021vision}, our method leverages the capability of ViT in learning long range complex context information to rectify depth cues instead of performing stereo matching.

Most works discussed above are fully supervised, which necessitate pixel-wise labeled ground truth for training. However, it is challenging to acquire dense annotations at scale in many real-world settings. One of the workarounds is to adopt self-supervised learning. For stereo self-supervised training, usually pixel disparities of synchronized stereo pairs are predicted~\cite{yang2018segstereo,zhou2017unsupervised,li2018occlusion, ahmadi2016unsupervised, jason2016back}, while for monocular self-supervised training, not only depth but also camera pose has to be estimated to help reconstruct the image and constrain the estimation network~\cite{byravan2017se3,zhou2017unsupervised,yin2018geonet,vijayanarasimhan2017sfm,godard2017unsupervised}. Considering the versatility and the potential application environment of our method, we choose self-supervised training for ChiTransformer.

\section{Method}
\label{sec:method}
This section introduces the overall architecture of the ChiTransformer with elaboration on the key building blocks. We follow the configuration of the vision transformer~\cite{vit} as the backbone and maintain the prevalent overall encoder-decoder structure because of their repeatedly verified success in various dense prediction tasks. We show the interplay of the encoded representations or cues between a stereo pair in ChiTransformer and how they can be effectively converted into dense depth prediction. The intuition for the elicitation and success of this method is discussed.

\subsection{Architecture}
\noindent\textit{\textbf{Overview:}} The complete architecture of ChiTransformer is shown in Figure~\ref{figure:arch}. ChiTransformer employs a pair of hybrid vision transformers as backbone with ResNet-50 ~\cite{he2016deep} for patch embedding. The parameters of two ResNet-50 are shared to ensure consistency in representations. The image patch embeddings are first projected to 768 dimensions, then flattened and summed with positional embeddings before fed into attention blocks. For an image of size $H\!\times\!W$, with the patch size of $P\!\times\!P$, the result is a set $T = \{t_0, t_1, \dots, t_{N_p}\}$, where $N_p = \frac{H\cdot W}{P^2}$ and $t_0$ is the class token. Here, patches are in the role of ``words" for transformer, but we will refer to patches as ``words" or ``tokens" interchangeably hereafter. The attention block for the reference view closely follows the design in~\cite{vit} with class token included, whereas master tokens are self-attended in the first multiple SA layers, followed by cross-attention (CA) and self-attention (SA) layers in an interleaved fashion. The output tokens of the master ViT (and reference ViT in training) are then reassembled into an image-like arrangement. Feature representations $I^s$ at different scales $s \in S$ are progressively aggregated and fused into the final depth estimation in the fusion block, which is modified from RefineNet~\cite{lin2017refinenet}. Fusion block is shared for both views in training phase but dedicated to the master view in inference. \\

\noindent\textit{\textbf{Attention layers:}} Self-attention layer is the crucial part for transformers and other attention-based methods to achieve superior performance over their non-attention competitors. The key advantage is that complex context information can be gathered in a global scope. With multiple layers of SA, encodings get progressively tempered with the context information as it goes deeper into the attention layers. This mechanism begets the globally coherent predictions. Therefore, instead of putting immediate connection to the CA layer, we place multiple ($l_{SA} =  4$) SA layers at the output of the ResNet-50. Cues with appropriate amount of context information result in more reliable pattern retrieval in the subsequent CA layers. This design improves both training convergence and prediction performance.

The \textit{cross-attention} layer is our key contribution in ChiTransformer. It is the enabler of the stereopsis through the fusion of high-level depth cue expressions from two views. We argue that the effectiveness of the traditional 4-step strategy would be largely weakened as the sources of ill-posedness, such as occlusion, wider and closer range of depth, depth discontinuity and nonlinearity, become increasingly frequent or prominent. Current deep learning-based methods rely on the learned rich representations to construct cost volume which is then regularized to make estimation. The output quality, in this case, largely depends on both the quality of the representations and the conformity of the scene to the matching regularizing assumptions~\cite{scharstein2002taxonomy}. While good representations can be learned with many approaches, there are few ways to fix up an impaired cost volume when scenes are far away from being appropriate for stereo matching. Therefore, instead of clinging to the matching strategy, we propose a novel pattern retrieval mechanism inspired by associative memory to retrieve the correspondent pattern from the other view. We assume that a set of patterns can be learned to separate well such that each pattern can be retrieved at least in meta-stable state, i.e., fixed average of similar patterns~\cite{ramsauer2020hopfield}. Modeled by modern Hopfield network~\cite{demircigil2017model,krotov2016dense}, the retrieval rule of the associative memory elegantly coincides with the attention mechanism of the transformer. Naturally, we leverage cross-attention layer to retrieve patterns (tokens) from the reference to the master view. To facilitate reliable effective retrieval, we devise a new attention mechanism -- polarized attention, which enables feature-sensitive retrieval while preserving the context information contained in the pattern without breaching the convergence rule. From~\cite{wang2020parallax}, we observe that direct attention over representations at the output of CNN reduces to cosine similarity-based matching. Without position-dependent context information over extensive scope, patterns are liable to ill-posedness and low separability.

Given a token pair $(^mt_i,\ ^mt^{\prime}_i)$, $\forall i$ $\in$ $\{1,$ $\cdots,$ $ N_p\}$, from the preceding CA layer and the class token pair $(^mt_0,\ ^rt_0)$, where $m$ indicates the master view, $r$ the reference view, and $t'$ denotes the retrieved tokens, depth cues are then rectified through the following blending process:
\begin{align}
    &\mathit{f}_{proj}(^mt_i,\ ^mt^{\prime}_i) = \text{MLP}(\left[^mt^{\top}_i,
    ^mt^{\prime\top}_i\right]),
\end{align}
\begin{align}
    &^mt_i =\ ^mt_i + \texttt{Heat}(p_{a_i})\cdot \mathit{f}_{proj}(^mt_i,\ ^mt^{\prime}_i).
\end{align}
We set $^mt^{\prime}_0 = {^r}t_0$ to unify the expression. GELU~\cite{hendrycks2016gaussian} is used for MLP nonlinearity, $p_{a_i}$, the vector of attention scores of $^mt_i$, and $\texttt{Heat}$, the confidence score calculated with stabilized attention entropy as
\begin{equation}
   \texttt{Heat}(p_{a_i}) = 1 - g\left(\text{H}(p_{a_i}), \tau, c\right),
\end{equation}
where $\text{H}(p_{a_i}) = -\sum^{N_p}_{k=1}{p_{a_{i, k}}\log{(p_{a_{i, k}} + \epsilon)}}$, and $g(\cdot)$ is a clamping function (e.g., sigmoid or smoothstep) with temperature $\tau$ and offset $c$. \texttt{Heat} is set to 1 for class token. By doing so, tokens retrieved back in fixed state, i.e., with a very low entropy, would be securely rectified whereas those with high entropy are inhibited from being updated as they are very likely to reside in occluded areas. Thus, the depth in occluded or ``uncertain" areas are left to the power of SA layers to speculate its value with context information and rectified cues from neighboring non-occluded areas.

\vspace{3mm}
\noindent \textit{\textbf{Fusion block:}}
Our convolutional decoder follows the refinement block in~\cite{lin2017refinenet,ranftl2021vision}. The output of attention layers $\boldsymbol{t} \in {\rm I\!R}^{(N_p + 1)\times D}$ is reassembled into an image-like arrangement ${\rm I\!R}^{H^\prime \times W^\prime \times D'}$ through a four-step operation:
\begin{equation}
    \text{RSB} = \left(\text{rescale}\circ\text{reshape}\circ\text{MLP} \circ \text{cat} \right).
\end{equation}
The class token is concatenated with all other tokens (by broadcasting) before being projected to dimension $D^\prime$ to get $\bm{t}_{\setminus 0}$. Then it is reshaped into a 2D shape per the original arrangement of the image embedding. Finally, $\boldsymbol{t}_{\setminus 0}$ is re-sampled to size $\frac{H}{P}s_l \times \frac{W}{P}s_l \times D_l $ for different scales at level $l$. Re-sampling method is 2D transposed convolution for $s_l>1$ (up-sampling), and strided 2D convolution for $s_l<1$ (down-sampling). For our model, features from level $l_{attn} = \{11, 7, 3\}$ in attention blocks (12 in total for ChiTransformer-8) and level $l_{res} = \{1, 0\}$ (first 2 blocks) in ResNet-50 are reassembled. The reassembled feature maps from those levels are consecutively fused through customized feature fusion block from RefineNet~\cite{lin2017refinenet}. At each level, feature map is up-sampled by a factor of 2 and finally the depth estimation map reaches the original resolution of the input images.

The architecture of ChiTransformer is structurally similar and biologically analogous to the \textit{optic-chiasma} structure in our visual system, where visual field covered by both eyes is fused to enable the processing of binocular depth perception by stereopsis~\cite{scharstein2002taxonomy}, hence the name of our model.

\subsection{Polarized Attention}
We propose a new attention mechanism to highlight or suppress features, which is much like signal polarization but in feature domain. Ideally, for a set of tokens represented in tensor  $\bm{t}=(t_1, \cdots, t_N)$ that is well separated, highlighting or suppressing can be potentially achieved in token-wise granularity. However, ideal separability is hard to achieve in practice because the attention tensor $\bm{A}$ for regular attention mechanism is calculated as
\vspace{-1mm}
\begin{equation}
	\boldsymbol{A} = \text{softmax}\left(\beta\boldsymbol{t}^\top   \mathbf{W_t}^\top \mathbf{W}_{\xi}\boldsymbol{\xi}\right),
\vspace{-1mm}
\end{equation}
which is prone to be noisy with joint activation over all channels and hard to learn directly for $\mathbf{W}$'s. While the prevalent MHA seeks for multi-level context instead of retrieval since tokens are mapped to different (sub-)spaces for each head that generates its own attention weights and output with the projected tokens. To achieve retrieval behavior, without loss of generality, we stick to the Hopfield network update rule to ensure retrieval behavior and condition the query pattern with a self-adjoint operator $\mathbf{G} \in \rm{I\!R}^{\mathit{d\times d}}$,
\vspace{-2mm}
\begin{equation}
\boldsymbol{\xi}^\prime = \boldsymbol{t}\text{softmax}\left(\beta\boldsymbol{t}^\top   \mathbf{G} \boldsymbol{\xi} \right),
\vspace{-2mm}
\end{equation}
where $\beta$ is the scale factor set to be $1/\sqrt{d}$. We assume the constraint that the query and memory should stay in the same sub-space which is satisfied by a positive-definite $\mathbf{G}$ decomposed as $\mathbf{G} = \mathbf{M}^\top \mathbf{M}$. It can further be spectrally decomposed to get:
\begin{equation}
\boldsymbol{\xi}^\prime = \boldsymbol{t}\text{softmax}\left(\beta\boldsymbol{t}^\top   \mathbf{U}^\top\mathbf{\Lambda} \mathbf{U}\boldsymbol{\xi} \right),
\vspace{-2mm}
\end{equation}
where $\mathbf{U}$ is an orthogonal matrix and $\mathbf{\Lambda}$ is a positive diagonal matrix.

To achieve feature-sensitive retrieval while factoring in all the information in the embeddings, we desire $\text{diag}(\mathbf{\Lambda})$ not to be zero abounded, i.e., feature selection. To achieve that and also enable multi-modal retrieval, multiple $\mathbf{\Lambda}$s are learned and we desire $\prod^{s}_{i=1}{\mathbf{\Lambda}_i}$ to be close to $\mathbf{I}$ such that if one feature is highlighted in one mode it should be suppressed in other modes. As such, the new attention mechanism becomes
\begin{equation}
    \boldsymbol{\xi}^\prime = \mathbf{W}\overset{s}{\underset{i=1}{\texttt{cat}}}\left[\boldsymbol{t}\cdot\text{softmax}\left(\beta\boldsymbol{t}^\top   \mathbf{U}^\top\mathbf{\Lambda}_i\mathbf{U}\boldsymbol{\xi} \right)\right].
\end{equation}

For our model, $\bm{\xi}$ is the tokens from the master view, $\bm{t}$ is the tokens from reference view, $\mathbf{W}$ projects the concatenated tokens back to its original dimension, and $\bm{\xi}^\prime$ is the retrieved tokens from the reference view. The lowest entropy of the $s$ heads is used in \texttt{Heat} calculation for rectification. The effectiveness of the retrieval mechanism is reflected in Figure~\ref{figure:attn_compare}, where up-scaled attention map of different tokens are overlapped with the reference view.

\begin{figure}[h]
\begin{minipage}{\columnwidth}
    \setlength{\tabcolsep}{0pt}
    \renewcommand{\arraystretch}{0.1}
\begin{center}
\scriptsize
\begin{tabular}{c@{}c@{}}

\includegraphics[width = 0.5\columnwidth]{figures/attnmap/000R.png}
& \includegraphics[width = 0.5\columnwidth]{figures/attnmap/pix_0_over.png}\\[-3mm]

\makebox[1in]{\textcolor{yellow}{\tiny{Reference (right image)}}}
& \makebox[1in]{(12,45)}\\[2mm]

\includegraphics[width = 0.5\columnwidth]{figures/attnmap/pix_49_over.png}
&\includegraphics[width = 0.5\columnwidth]{figures/attnmap/pix_310_over.png} \\[-3mm]

\makebox[1in]{(13,11)}
& \makebox[1in]{(5,22)}\\[2mm]

\includegraphics[width = 0.5\columnwidth]{figures/attnmap/pix_400_over.png}
&\includegraphics[width = 0.5\columnwidth]{figures/attnmap/pix_1582_over.png} \\[-3mm]

\makebox[1in]{(10,39)}
& \makebox[1in]{(7,66)}\\[2mm]

\end{tabular}
\end{center}
\end{minipage}
\vspace{-2mm}
\caption{Attention map of $\boldsymbol{A}^{s=1}_{ij}$ of tokens retrieved in meta-stable state in the CA layer of the $2^{nd}$ DCR. Darker green corresponds to higher attention score. As expected, tokens of distinctive features have more centralized attention, while tokens in texture-less area result in more dispersed attention.}
\vspace{-3mm}
\label{figure:attn_compare}
\end{figure}

\subsection{Learnable Epipolar Geometry}
Token separability may be limited by the memory size and image content (e.g., existence of repetitive or uniform texture in the image). To further ensure secure retrieval without corrupting the encoded information, we constrain the attention mechanism with epipolar geometry through a \textit{gated positional cross attention} (GPCA) following~\cite{d2021convit}. In GPCA, positional embedding is modeled as trainable quadratic polynomial of relative positional encoding $\bm{v}_{pos}^{\top}\bm{r}_{ij}$~\cite{cordonnier2019relationship}. For regular rectified stereo, candidate retrievals reside within collinear horizontcal lines. Therefore, we set $\bm{v}_{pos}  = -\alpha\left(0, 0, 0, 0, 0, 1, \cdots, 0\right)$, $
\bm{r} = \left(1, \delta_1, \delta_2, \delta_1\delta_2, \delta_1^2, \delta_2^2, 0, \cdots, 0\right)$. For non-rectilinear images, e.g., fisheye, $\bm{v}_{pos}$ is a vector of trainable curve coefficients, which will be discussed when we present results on fisheye images.

In the equations above, $\boldsymbol{r}$ is the position vector of $(\delta_1, \delta_2)$ which are the relative coordinates with respect to the query. The locality strength $\alpha > 0$ determines how focused attention is along the horizontal line (i.e., when $\delta_2 = 0$).
The positional attention scores are calculated as softmax normalized $L_2$ distance between the attended tokens and the query:
\begin{equation}
    \bm{A}_{pos,ij} = \text{softmax}\left(\bm{v}_{pos}^{\top}\bm{r}_{ij}\right).
\end{equation}
With the learnable gating parameter $\lambda$, the GPCA attention scores are calculated as:
\begin{equation}
    \boldsymbol{A}^s_{ij} = \texttt{norm}\left[(1-\sigma (\lambda))\boldsymbol{A}^s_{cnt,ij} + \sigma(\lambda)\boldsymbol{A}_{pos,ij}\right],
\end{equation}
where $\texttt{norm}[\mathbf{x}] = \frac{x_{ij}}{\sum_{k}{x_{ik}}}$,  $\sigma$ is the sigmoid function, and $\bm{A}^s_{cnt,ij}$ is the content attention score calculated by polarized attention of head $s$.
To avoid GPCA from being stuck at $\lambda >> 1$, we initialize $\lambda=1$ for all layers.

\subsection{Regularization}
Matrix $\mathbf{U}$ has to be orthogonal to guarantee that query and memory are attended in the same space. However, $\mathbf{U}$ in each layer is trainable parameter; even though it can be initialized with orthogonal matrices, during training process the orthogonality may not hold. Therefore, we introduce an orthogonality regularization loss to $\mathbf{U}$ as:
\vspace{-2mm}
\begin{equation}
    L_o(\mathbf{U}) = \frac{1}{d^2}\left\|\mathbf{U}^{\top}\mathbf{U} -  \mathbf{I}\right\|_{\mathcal{F}},
\vspace{-2mm}
\end{equation}
where $d$ is the size of $\mathbf{U}$ and $\left\|\cdot\right\|_{\mathcal{F}}$ is the Frobenius norm of matrix. Although $\mathbf{U}$ can be orthogonalized through Cayley's parameterization, it is computational expensive for large matrix as inversion is involved and we found it is more difficult to converge and unstable in our case.

To induce the diagonal matrix $\mathbf{\Lambda}$ to be trained into the desired form, we modified Hoyer regularizer~\cite{hoyer2004non} to mitigate the proportional scaling issue and at the same time to pull $\mathbf{\Lambda}$ away from being identity matrix. We introduce the following regularization:
\vspace{-1mm}
\begin{equation}
    L_\Lambda(\mathbf{\Lambda}) = \frac{\left|\prod^{s}_{i=1}{\left|\mathbf{\Lambda}_i\right|_e} - \mathbf{I}\right|_1}{\prod_{i=1}^{s}{\left\|\mathbf{\Lambda}_i\right\|_{\mathcal{F}}}},
\vspace{-1mm}
\end{equation}
where $|\cdot|_e$ is the element-wise absolute function. Identity matrix is only one of the possible but unpreferred solution for $\prod^{s}_{i=1}{|\mathbf{\Lambda_i}|_e} - \textbf{I} = 0$. Take 2D matrix for example, diagonal matrices $\Lambda_1 = (5, \frac{1}{5})$, $\Lambda_2=(\frac{1}{5},5)$ is also a solution. However, when $\Lambda_i$s are approaching to this optimal, the denominator of Eq.~12 is much larger ($\sim\!\!25$) than that of $\Lambda_i$s close to the identity matrix (2.0). In addition, the final loss is a combination of reconstruction loss and regularization loss; with a proper hyperparameter $\mu_\lambda$, the learned $\mathbf{\Lambda}$s will be pulled away from \textbf{I}.

\subsection{Training}
In this section, we provide details of the training method we used. We closely followed the self-supervised stereo training method provided in~\cite{godard2019digging}. The model is trained to predict the target image from the other viewpoint in a stereo pair. Unlike classical binocular and multi-view stereo methods, the image synthesis process in our case is constrained by predicted depth instead of disparity as an intermediary variable. Specifically, given a target image $I_t$, a source image $I_t'$, and the predicted depths $D_t$, through the relative pose between two views $T_{t\rightarrow t^\prime}$ calculated with the provided stereo base width ($0.54m$ for KITTI) and calibration information, the correspondent coordinates between two images can be calculated. Following~\cite{jaderberg2015spatial}, the target image can be reconstructed from source image using bilinear sampling, which is sub-differentiable.

The depth prediction should minimize the photometric reprojection error constructed for both master and reference view as follows:
\begin{align}
    \vspace{-1mm}
    L_p = \omega\cdot\texttt{pe}\left(I_t, I_{t'\rightarrow t}\right) + (1-\omega)\cdot\texttt{pe}\left(I_{t'}, I_{t\rightarrow t'}\right),
    \vspace{-1mm}
\end{align}
where $\omega$ is the weight for master view, and $\texttt{pe}(\cdot)$ is the photometric reconstruction error~\cite{wang2004image}:
\begin{align}
    \texttt{pe}(X, Y) = &\frac{\kappa}{2}\left(1-\text{SSIM}\left(X, Y\right)\right) \nonumber\\ &+ (1 - \kappa)\left\|X - Y\right\|_1
\end{align}
$\kappa$ = 0.85 and $I_{t^\prime\rightarrow t}$ is the reprojected image:
\begin{align}
    I_{t^\prime\rightarrow t} = \texttt{bi-sample}\left<\texttt{proj}\left(D_t, T_{t\rightarrow t^\prime}, K\right)\right>,
\end{align}
where $K$ is the pre-computed intrinsic matrix, \texttt{proj} is the resulting image coordinates projected from source view through \vspace{-10pt}
\begin{align}
    p_t^\prime := KT_{t\rightarrow t^\prime}D_t[p_t]K^{-1}p_t
\end{align}
and $\texttt{bi-sample}\left<\cdot\right>$ is the bilinear sampler.

We also enforce edge-aware smoothness in the depths to improve depth-feature consistency defined as
\begin{align}
    L_s = |\partial_xd_t^\ast|e^{-|\partial_xI_t|} + |\partial_yd_t^\ast|e^{-|\partial_yI_t|},
\end{align}
where $d_t^\ast\!\! =\!\! d/\Bar{d}_t$ is the mean-normalized inverse depth in~\cite{wang2018learning}.

Unlike existing self-supervised stereo-matching methods that rely on predicted values to generate confidence map to detect occlusions, e.g. left-right consistency check, ChiTransformer detects occluded area on the fly in the form of heat map in the rectification stage. During training, heat map from the last GPCA layer is up-sampled to the output resolution and used as a mask $m_h$ in loss computation. For stereo training, static camera and synchronous movement between objects and camera are not issues, hence we do not apply the binary auto-masking to block out the static area in the image.

During inference, only the master ViT output is up-scaled and refined to make the prediction. While in the training stage, both ViT towers in ChiTransformer are trained in tandem to predict depth and calculate losses $L_p$ and $L_s$.

\paragraph{Final Training Loss}

By combining the reconstruction loss, per-pixel smoothness from two views and the regularizations for the matrices $\mathbf{U}$ and $\mathbf{\Lambda}$, the final training loss is:\vspace{-5pt}
\begin{equation}
    \mathcal{L} = \texttt{mean}(m_h\odot L_p) + \mu_s L_s + \mu_o L_o + \mu_\lambda L_\lambda,
\end{equation}
where $\mu_*$ are the hyperparameters that balance the contributions from different loss terms.

Our models are implemented in PyTorch. With pretrained ResNet-50 patch feature extractor and partial refinement layers from~\cite{ranftl2021vision}, the model is trained for 30 epochs using using Adam~\cite{kingma2014adam} with a batch size of 12 and input resolution of $1216 \times 352$. We use learning rate $1e\!-\!5$ for the ResNet-50 and $1e\!-\!4$ for the rest part of the network in the first 20 epoch, and then is decayed to $1e\!-\!5$ for the remaining epochs. We set $\omega\!=\!0.6$, $\mu_s=1e\!-\!4$, $\mu_o=1e\!-\!7$ and $\mu_{\lambda}=1e\!-\!3$ in our experiments.

\vspace{-10pt}
\begin{table}[b]
\footnotesize
\caption{\vspace{-3mm}\textsc{Quantitative Results}}
\label{table:stereo}
\begin{tabularx}{\columnwidth}{p{1mm}|l p{5mm}p{5mm}p{5mm} p{5mm}p{5mm}p{5mm}}
\thickhline
 & \multicolumn{1}{c}{Method}&\multicolumn{3}{c}{NOC}&\multicolumn{3}{c}{ALL}\\
 &            & D1 (bg)    &D1 (fg)    &D1 (all)   & D1 (bg)    &D1 (fg)    &D1 (all)\\
\hline
\parbox[t]{1pt}{\multirow{4}{*}{\rotatebox[origin=c]{90}{Supervised}}}
 & DispNet~\cite{mayer2016large}  & 4.11     & 3.72    & 4.05    & 4.32   & 4.41    & 4.43\\
 & GC-Net~\cite{kendall2017end}   & 2.02     & 5.58    &2.61     &2.21    & 6.16    & 2.87\\
 & iResNet~\cite{liang2018learning}  & 2.07     & 2.76    &  2.19   &  2.25  & 3.40    & 2.44\\
 & PSMNet~\cite{chang2018pyramid}   & 1.71     & 4.31    & 2.14    & 1.86   & 4.62    & 2.32\\
\hline
\parbox[t]{3mm}{\multirow{10}{*}{\rotatebox[origin=c]{90}{Self-supervised}}}
 &Yu et al.~\cite{jason2016back}   & -     & -      & 8.35   & -     & -     & 19.14\\
 &Zhou et al.~\cite{zhou2017unsupervised} & -     & -      & 8.61   & -     & -     & 9.91\\
 &SegStereo~\cite{yang2018segstereo}   & -     & -      & 7.70   & -     & -     & 8.79\\
 &OASM~\cite{li2018occlusion}        & 5.44  & 17.30  & 7.39   & 6.89  & 19.42 & 8.98\\
 &PASMnet_192~\cite{wang2020parallax} & 5.02  & 15.16  & 6.69   & 5.41  & 16.36 & 7.23\\
 &Flow2Stere~\cite{liu2020flow2stereo} & 4.77  & 14.03  & 6.29   & 5.01   & 14.62 & 6.61\\
 &pSGM~\cite{lee2017memory}        & 4.20  & 10.08  & 5.17   & 4.84   & 11.64  & 5.97\\
 &MC-CNN-WS~\cite{tulyakov2017weakly}   & 3.06  & 9.42   & 4.11   & 3.78   & 10.93  & 4.97\\
 &SsSMnet~\cite{diffscales1}     & 2.46  & 6.13   & 3.06   & 2.70   & 6.92   & 3.40\\
 &PVSstereo~\cite{wang2021pvstereo}   & \textbf{2.09}  & 5.73   & 2.69   & \textbf{2.29}  & 6.50  & 2.99\\

 &\textbf{ChiT-8} (ours)       & 2.24  & 4.33   & 2.56   & 2.50    & 5.49   & 3.03\\
 &\textbf{ChiT-12} (ours)   & 2.11  & \textbf{3.79}   & \textbf{2.38}  &2.34    & \textbf{4.05}    & \textbf{2.60}\\
\thickhline
\end{tabularx}
\begin{minipage}{\linewidth}\footnotesize
    \vspace{1mm}
     Comparison of our model to the state-of-the-art self-supervised binocular stereo methods. The lower the better for all metrics.
\end{minipage}
\vspace{-5mm}
\end{table}

\renewcommand{\arraystretch}{1}

\begin{figure*}[t]
\hspace{2mm}
\begin{minipage}{0.9\textwidth}
    \renewcommand{\arraystretch}{0.1}
    \begin{center}
    \scriptsize
    \begin{tabular}{@{}c@{}c@{}c@{}c@{}}
    \rotatebox[origin=l]{90}{\scalebox{0.7}[0.7]{\hspace{5mm}Left Image}} \hspace{1pt}
    & \includegraphics[width = 0.35\textwidth]{figures/mono/MovsChi_1L.jpg}
    & \includegraphics[width = 0.35\textwidth]{figures/mono/MovsChi_2L.jpg}
    & \includegraphics[width = 0.35\textwidth]{figures/mono/MovsChi_3L.jpg}\\

    \rotatebox[origin=l]{90}{\centering\scalebox{0.7}[0.7]{\hspace{5mm}Monodepth2}} \hspace{1pt}
    & \includegraphics[width = 0.35\textwidth]{figures/mono/Monodepth1.jpg} &
    \includegraphics[width = 0.35\textwidth]{figures/mono/Monodepth2.jpg} & \includegraphics[width = 0.35\textwidth]{figures/mono/Monodepth3.jpg} \\
    \rotatebox[origin=l]{90}{\scalebox{0.6}[0.7]{\hspace{4mm}ChiTransformer}} \hspace{1pt}
    & \includegraphics[width = 0.35\textwidth]{figures/mono/chi1.jpg} &
    \includegraphics[width = 0.35\textwidth]{figures/mono/chi2.jpg} & \includegraphics[width = 0.35\textwidth]{figures/mono/chi3.jpg} \\
    \end{tabular}
    \end{center}
\end{minipage}
\vspace{-2mm}\caption{Sample results compared with self-stereo-supervised fully-convolutional network Monodepth2. ChiTransformer shows better global coherence (e.g., sky region, sides of image) and provides feature consistent details.}
\label{figure:monovschi}
\end{figure*}

\vspace{3mm}
\section{Experiments}
\label{exprmt.}
The model is trained on KITTI 2015~\cite{kitti}. We show that our model significantly improves accuracy compared to its top CNN-based counterparts. Side-by-side comparisons are given in this section with the state-of-the-art self-supervised stereo methods~\cite{wang2020parallax,li2018occlusion,wang2021pvstereo}. Ablation study is conducted to validate that several features in ChiTransformer contribute to the improved prediction. Finally, we extend our model to fisheye images and yield visually satisfactory result.

\subsection{KITTI 2015 Eigen Split}

We divide the KITTI dataset following the method of Eigen et al.~\cite{eigen2014depth}. Same intrinsic parameters are applied to all images by setting the camera principal point at the image center and the focal length as the average focal length of KITTI. For stereo training, the relative pose of a stereo pair is set to be pure horizontal translation of a fixed length (0.54m) according to the KITTI sensor setup. For a fair comparison, depth is truncated to 80m according to standard practice~\cite{godard2017unsupervised}.

\begin{figure}
\begin{minipage}{\columnwidth}
    \setlength{\tabcolsep}{0pt}
    \renewcommand{\arraystretch}{0.1}
\begin{center}
\scriptsize
\begin{tabularx}{\columnwidth}{@{}YYYYY@{}}

\multicolumn{5}{c}{ ~~~ \boldmagenta{---}focus region ~~~ \boldyellow{---}occluded area}\\
\multicolumn{5}{c}{\includegraphics[width=\linewidth]{figures/occlusion/occlusion_est.png}}\\
ChiTransformer & F2S\cite{liu2020flow2stereo} & OASM\cite{li2018occlusion} & PASM\cite{wang2020parallax} & PVS\cite{wang2021pvstereo}
\end{tabularx}
\end{center}
\end{minipage}
\vspace{-2mm}
\caption{Comparison of predictions in left side occluded area. }
\vspace{-5mm}
\label{figure:occlude_pred}
\end{figure}

\subsection{Quantitative Results}
We compare the results of the two different configurations of our model with state-of-the-art self-supervised stereo approaches. ChiT-8 has 4 SA layers followed by 4 rectification blocks, while ChiT-12 has 6 SA layers and 6 rectification blocks. The results in Table~\ref{table:stereo} show that ChiTransformer outperforms most of the existing methods, particularly in the prediction of the foreground regions. This trait is as expected that foreground regions are more likely to be abounded by distinctive features that benefit depth cue rectification. Qualitative results in occluded region comparing with existing self-supervised stereo methods are shown in Figure~\ref{figure:occlude_pred}. Their complete predictions are given in supplementary material. With depth cues from both views, ChiTransformer provides more details consistent to the image features compared to existing self-supervised methods.

We also compare our method with top self-stereo-supervised MDE methods to show the reliability gain in terms of accuracy improvement. For a fair comparison, we choose the models that are trained on KITTI with stereo supervision. Methods trained over multiple datasets are not considered. Quantitative results are shown in Table~\ref{table:mono}. Side-by-side prediction comparison is shown in Figure~\ref{figure:monovschi}.
\vspace{2mm}

\begin{table*}
\centering
\begin{threeparttable}
\footnotesize
\caption{\vspace{-3mm}\textsc{Comparison with Self-stereo-supervised Monocular Methods}}
\label{table:mono}
\vspace{-3mm}
\begin{tabular}{m{7cm}cccccccl}
\thickhline
      Method      &AbsRel  &SqRel  &RMSE   &RMSE log   &$\delta<1.25$   &$\delta<1.25^2$     &$\delta<1.25^3$ \\
\hline
Garg et al.~\cite{garg2016unsupervised}   & 0.152   & 1.226   & 5.849   & 0.246   & 0.784  & 0.921  &0.967\\
3Net(R50)~\cite{poggi2018learning}     & 0.129   & 0.996   & 5.281   & 0.223   & 0.831  & 0.939  &0.974 \\
3Net(VGG)~\cite{poggi2018learning}     & 0.119   & 1.201   & 5.888   &0.208    & 0.844  & 0.941  &0.978 \\
SuperDepth+pp (1024$\times$382)~\cite{pillai2019superdepth}   & 0.112   & 0.875   & 4.968  & 0.207  & 0.852   &0.947  &0.977 \\
Monodepth2~\cite{godard2019digging}      & 0.109   &0.873   & 4.960   & 0.209   &0.864   &0.948   & 0.975 \\
\hline
\textbf{ChiT-12} (ours)   & \textbf{0.073}   & \textbf{0.634}   & \textbf{3.105}   & \textbf{0.118}   & \textbf{0.924}  & \textbf{0.989}  &\textbf{0.997} \\
\thickhline
\end{tabular}
\end{threeparttable}
\begin{minipage}{\linewidth}\footnotesize
    \vspace{1mm}
     All models listed in the table above are trained with self-supervised methods using stereo pair. Same as the monocular methods, ChiTransformer relies on depth cues to estimate depth, only with extra information from a second image.
\end{minipage}
\vspace{-15pt}
\end{table*}

\begin{table}
\begin{threeparttable}
\scriptsize
\caption{\textsc{Ablation Study}}
\label{table:ablation}
\begin{tabularx}{\columnwidth}{l p{6mm}p{6mm}p{6mm}p{7mm}p{7mm}p{7mm}}

\thickhline
                            &\scalebox{.9}[1.0]{AbsRel}
                            &\scalebox{.9}[1.0]{RMSE}
                            &\scalebox{.9}[1.0]{RMSElog}
                            &\scalebox{.9}[1.0]{$\delta\!<\!1.25$} &\scalebox{.9}[1.0]{$\delta\!<\!1.25^2$} &\scalebox{.9}[1.0]{$\delta\!<\!1.25^3$}\\

\hspace{-1mm}ChiT+P         &0.106 & 4.845 & 0.204& 0.878 & 0.960 & 0.981\\
\hspace{-1mm}ChiT+G+LEG     &0.101 &4.783  &0.203  &0.895  &0.966 &0.983\\
\hspace{-1mm}ChiT+P+Linear  &0.092 & 4.535 & 0.201 &0.889  &0.964 &0.987\\
\hspace{-1mm}ChiT+P+LEG     &0.085 & 3.924 & 0.181 & 0.906 &0.979 &0.991\\

\thickhline
\end{tabularx}
\begin{tablenotes}
    \footnotesize
      \item \hspace{-.8mm}Evaluations for different settings of ChiTransformer (ChiT) trained on KITTI 2015 with Eigen split. "P" denotes the polarized attention. "G" stands for the direct learning of matrix $G$. "LEG" represents the feature of learnable epipolar geometry. "Linear" is the single line attention zone. ChiT with only P enabled has the lowest score due to inferior token separability. With the addition of LEG, the model: ChiT+P+LEG, becomes the top performer and show the advantage of P over G compared with ChiT+G+LEG. ChiT+P+Linear has the 2nd best performance. The serration effect due to "Linear" is largely mitigated by the long range context information and SA layers.
    \end{tablenotes}
    \vspace{-3mm}
\end{threeparttable}
\end{table}

\renewcommand{\arraystretch}{1}

\vspace{-10pt}
\subsection{Ablation Study}\vspace{-5pt}
To understand how each major feature contributes to the overall performance of ChiTransformer, ablation study is conducted by suppressing or activating specific components of the model. We observe that each component in our model is designed to push the performance a bit forward which aggregates into a sizable improvement. Here we provide some insights on the major features based on observation.
\newline\textbf{Self-attention layer} largely improves the separability of each token with long range complex contextual information. Without SA layer, the retrieval process would take up a hopping behavior and result in erroneous predictions.
\newline\textbf{Polarized attention} We learn the matrix $G$ through its spectral decomposition to gain more control over its behavior. Direct learning of $G$ tends to result in feature negligence as the major features contained within a token dominate or take all the reward. With the complementary feature highlighting-suppressing strategy as we desire $\prod{\Lambda}$ to be close to $\mathbf{I}$, the features from both parties can be attended. Meanwhile, since $\Lambda$ is not porous with zeros, i.e., no Lasso regularization involved, all information contained in the token is more or less attended.
\newline\textbf{Learnable Epipolar Geometry}
Intuitively, for rectified stereo a pixel pair is guaranteed to reside in the same horizontal line and hence the attending space should be that line. However, the slotted attention region hurts the inter-line connection and cause serrated effects on vertical features even that feature is distinctive, e.g., an edge. Whilst the learnable epipolar geometry in GPCA solves the problem by allowing global but focused view over the lines and at the same time further improves the cross-line separability. Quantitative results are given in Table~\ref{table:ablation}. Qualitative results are given in supplementary material.

\begin{figure}
\begin{minipage}{\columnwidth}
    \renewcommand{\arraystretch}{0.1}
    \begin{center}
    \scriptsize
    \begin{tabular}{@{}c@{}c}
     \hspace{1pt}
    \includegraphics[width = 0.48\columnwidth]{figures/fisheye/PoolB_0002_small.png}
    &\includegraphics[width = 0.48\columnwidth]{figures/fisheye/poolB.png}\vspace{2mm}\\
    Synthetic fisheye image & Planar depth estimation
    \end{tabular}
    \end{center}
\end{minipage}
\vspace{-3mm}\caption{Example result of ChiTransformer for fisheye depth estimation. With learnable epipolar curve $\bm{v}_{pos, ij} = (1,a,b,c,d,e)_{ij}$ (constant term is set to 1 to avoid proportional scaling) and circular masks, ChiTransformer can directly work on circular image without warping.}
\vspace{-3mm}
\label{figure:fisheye}
\end{figure}

\vspace{-5pt}
\subsection{Example Results on Fisheye Images}\vspace{-5pt}
Finally, due to its versatility, ChiTransformer can be applied to non-rectilinear (e.g., fisheye) images without warping. An example result is provided in Figure~\ref{figure:fisheye}.

\vspace{-5pt}
\section{Conclusion}\label{conc}\vspace{-5pt}

By investigating the limitations of the two prevalent methodologies of depth estimation, we present ChiTransformer, a novel and versatile stereo model that generates reliable depth estimation with rectified depth cues instead of stereo matching. With the three major contributions: (1) polarized attention mechanism, (2) learnable epipolar geometry, and (3) the depth cue rectification method, our model outperforms the existing self-supervised stereo methods and achieves state-of-the-art accuracy. In addition, due to its versatility, ChiTransformer can be applied to fisheye images without warping, yielding visually satisfactory results.

\vspace{-5pt}
\section{Acknowledgment}\vspace{-5pt}
This research was sponsored in part by VMware Inc. for its university research fund and the Army Research Laboratory under Cooperative Agreement \#W911NF-22-2-0025. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

\newpage
{\small
\bibliographystyle{ieee_fullname}

redpajama_set_name: RedPajamaArXiv


text:
Optical Design for Automatic Identification and Portable Systems
De Marco, Luisa (2012) Optical Design for Automatic Identification and Portable Systems, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Ingegneria elettronica, informatica e delle telecomunicazioni, 24 Ciclo. DOI 10.6092/unibo/amsdottorato/4600.
Download (12MB) | Anteprima
This thesis proposes design methods and test tools, for optical systems, which may be used in an industrial environment, where not only precision and reliability but also ease of use is important. The approach to the problem has been conceived to be as general as possible, although in the present work, the design of a portable device for automatic identification applications has been studied, because this doctorate has been funded by Datalogic Scanning Group s.r.l., a world-class producer of barcode readers. The main functional components of the complete device are: electro-optical imaging, illumination and pattern generator systems. For what concerns the electro-optical imaging system, a characterization tool and an analysis one has been developed to check if the desired performance of the system has been achieved. Moreover, two design tools for optimizing the imaging system have been implemented. The first optimizes just the core of the system, the optical part, improving its performance ignoring all other contributions and generating a good starting point for the optimization of the whole complex system. The second tool optimizes the system taking into account its behavior with a model as near as possible to reality including optics, electronics and detection. For what concerns the illumination and the pattern generator systems, two tools have been implemented. The first allows the design of free-form lenses described by an arbitrary analytical function exited by an incoherent source and is able to provide custom illumination conditions for all kind of applications. The second tool consists of a new method to design Diffractive Optical Elements excited by a coherent source for large pattern angles using the Iterative Fourier Transform Algorithm. Validation of the design tools has been obtained, whenever possible, comparing the performance of the designed systems with those of fabricated prototypes. In other cases simulations have been used.
De Marco, Luisa
Bassi, Paolo ; Canini, Federico
Gnan, Marco
Ingegneria elettronica, informatica e delle telecomunicazioni
Scienze e ingegneria dell'informazione
Benini, Luca
Area 09 - Ingegneria industriale e dell'informazione > ING-INF/02 Campi elettromagnetici
Area 09 - Ingegneria industriale e dell'informazione > 09/F - Ingegneria delle telecomunicazioni e campi elettromagnetici

redpajama_set_name: RedPajamaCommonCrawl


A fluorescent or LED light kept 4 inches (10 cm) away provides the right amount of light. Protect from direct sun.
They should start germinating in 3 to 5 weeks, but may take up to 8 weeks to start sprouting. Increase air ventilation slightly after sprouting to prevent rot, but continue keeping the soil surface moist for 2-3 weeks after sprouting.
Fertilizing -- The first 2 months, feed weekly with a small amount of dilute (1/8 strength) liquid fertilizer. Hydroponic fertilizer is ideal for young seedlings, since it is easily absorbed and contains all essential nutrients. After 2 months, you may switch to a granular fertilizer that contains micronutrients, following the dosage on the package. Or continue feeding weekly with dilute liquid fertilizer.


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text:
The Free Library > Communications > News, opinion and commentary > The Register-Guard (Eugene, OR) > April 15, 2005
The Free Library > General Interest/Informational > General interest > The Register-Guard (Eugene, OR) > April 15, 2005
The Free Library > Date > 2005 > April > 15 > The Register-Guard (Eugene, OR)
BRIEFLY.
<a href="https://www.thefreelibrary.com/BRIEFLY.-a0131710689
MLA style: "BRIEFLY.." The Free Library. 2005 The Register Guard 17 Jan. 2022 https://www.thefreelibrary.com/BRIEFLY.-a0131710689
Chicago style: The Free Library. S.v. BRIEFLY.." Retrieved Jan 17 2022 from https://www.thefreelibrary.com/BRIEFLY.-a0131710689
APA style: BRIEFLY.. (n.d.) >The Free Library. (2014). Retrieved Jan 17 2022 from https://www.thefreelibrary.com/BRIEFLY.-a0131710689
Byline: The Register-Guard
Deaf, mute woman found safe after going missing
A woman who is both deaf and mute was rescued nearly five hours after she went missing near Crale Creek Road during a mushroom-picking expedition with friends.
Allyson Mogstad, 41, of Springfield, was supposed to meet her friends at their car about 6:30 p.m. Wednesday, but she didn't show up, the Lane County Sheriff's Office reported. A friend called for help at 9:10 p.m., concerned about the cold, wet and windy weather. Mogstad had only a raincoat, a knife and a lighter with her.
A search team was quickly dispatched to the area off Highway 58. Searchers heard a faint yell about 11 p.m. that led them to Mogstad, who was in midstage hypothermia, the sheriff's office said. Searchers and deputies helped carry her down the steep forested hill to the road, where an ambulance took her to McKenzie-Willamette Medical Center in Springfield for treatment.
Through an interpreter, she told rescuers that she had climbed a tree and tried to light some of her clothes on fire to attract attention, but was thwarted when she fell to the ground.
COPYRIGHT 2005 The Register Guard
Copyright 2005, Gale Group. All rights reserved. Gale Group is a Thomson Corporation Company.
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OBITUARIES.


text:
Home F1 Alonso wants everything at once: Piquet
Alonso wants everything at once: Piquet
Rahul Venkat
Former Brazilian world champion, Nelson Piquet Sr., has claimed that Fernando Alonso missed out on more F1 titles purely he because he creates 'chaos' wherever he goes.
"Fernando could have won five championships but the reality was that wherever he went, there was chaos," said Piquet. "He is a fantastic driver but he always makes trouble."
"When you go to a team, you must have patience and cooperation, but Alonso wants everything at once."
Piquet had earlier blamed Alonso for his son's failure. Source: AutoEvolution
Piquet's son, Nelson Piquet Jr., who currently drives for Jaguar in Formula-E, partnered Alonso at Renault way back in 2008 and so the senior Piquet knows a fair bit about the Spaniard.
The decision was not entirely surprising, given that Alonso had made his frustration pretty well-known over the past three years. However, his former teammate, Giancarlo Fisichella, still hoped that we would see him back in F1.
"I think now he will go to Indycar. I hope he will win the title and the Indy 500, and then return to F1 – even if it is hard to come back," said Fisichella. Another former teammate who backed Alonso to return is Jenson Button.
"If McLaren is fast and wins races again, he'll be back. He was definitely my toughest teammate but it was also fun," said the Brit.
Alonso raced for Minardi when he burst onto the F1 scene in 2001. His teammate back then, Tarso Marques, defended the Spaniard's attitude and felt that it was quite necessary.
"When I see people saying he creates problems in his teams, I don't agree," said Marques. "I actually think it's a quality rather than a problem."
"Manipulating a team is something every champion does. Motor racing is a sport where to be successful, you have to be selfish. You have to think about yourself first, second and third."
Nelson Piquet
tarso marques
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text:
Marketing Minds
Objectivity, Insight, Expertise
Apple's Branding Strategy
Apple Inc. uses the Apple brand to compete across several highly competitive markets, including the personal computer industry with its Macintosh line of computers and related software, the consumer electronics industry with products such as the iPod, digital music distribution through its iTunes Music Store, the smart phone market with the Apple iPhone, magazine, book, games and applications publishing via the AppsStore for iPhone and the iPad tablet computing device, and movie and TV content distribution with Apple TV. For marketers, the company is also establishing a very strong presence to rival Google in the advertising market, via its Apps business and iAd network.
Steve Jobs, Apple's co-Founder, described Apple as a "mobile devices company" - the largest one in the world (Apple's revenues are bigger than Nokia, Samsung, or Sony's mobility business).
For several years Apple's product strategy involved creating innovative products and services aligned with a "digital hub" strategy, whereby Apple Macintosh computer products function as the digital hub for digital devices, including the Apple iPod, personal digital assistants, cellular phones, digital video and still cameras, and other electronic devices. More recently, the full impact of a very well throught out brand strategy has come into focus - and one in which customer experience is central: the Mac is no longer the hub of all things Apple. Now, Apple offers a harmonised, synchronised, and integrated user experience across all of its main devices (iPad, iPhone, and Mac), using iCloud as the hub. It is in the process of extending this experience outside Apple-controled environments by introducing deep integration with Facebook and Twitter on iPad, iPhone and Mac.
Apple's core competence is delivering exceptional experience through superb user interfaces. The company's product strategy is based around this, with iTunes, the iPhone (with it's touch screen "gestures" that are re-used on the iPad), and the Apple Apps store all playing key roles.
The Apple Brand Personality
Apple has a branding strategy that focuses on the emotions. The Apple brand personality is about lifestyle; imagination; liberty regained; innovation; passion; hopes, dreams and aspirations; and power-to-the-people through technology. The Apple brand personality is also about simplicity and the removal of complexity from people's lives; people-driven product design; and about being a really humanistic company with a heartfelt connection with its customers.
Apple Brand Equity and Apple's Customer Franchise
The Apple brand is not just intimate with its customers, it's loved, and there is a real sense of community among users of its main product lines.
The brand equity and customer franchise which Apple embodies is extremely strong. The preference for Apple products amongst the "Mac community", for instance, not only kept the company alive for much of the 90's (when from a rational economic perspective it looked like a dead duck) but it even enables the company to sustain pricing that is at a premium to its competitors.
It is arguable that without the price-premium which the Apple brand sustains in many product areas, the company would have exited the personal computer business several years ago. Small market share PC vendors with weaker brand equity have struggled to compete with the supply chain and manufacturing economics of Dell. However, Apple has made big advances in becoming more efficient with its manufacturing supply chain,logistics and operations, and it can be assumed that as far as like-for-like hardware manufacturing comparisons are concerned, Apple's product costs are very similar to those of Dell. In terms of price to the consumer, Apple's computer products have an additional cost advantage: the company does not have to pay another company for operating system licences.
The Apple Customer Experience
The huge promise of the Apple brand, of course presents Apple with an enormous challenge to live up to. The innovative, beautifully-designed, highly ergonomic, and technology-leading products which Apple delivers are not only designed to match the brand promise, but are fundamental to keeping it. The recent emphasis on the iPhone 5's manufacturing build quality and design standards reflect this importance.
Apple fully understands that all aspects of the customer experience are important and that all brand touch-points must reinforce the Apple brand.
Apple has expanded and improved its distribution capabilities by opening its own retail stores in key cities around the world in up-market, quality shopping venues. Apple provides Apple Mac-expert retail floor staff staff to selected resellers' stores, and in the past it entered into strategic alliances with other companies to co-brand or distribute Apple's products and services (for example, HP who was selling a co-branded form of iPod and pre-loading iTunes onto consumer PCs and laptops in the mid-2000s - though in retrospect this may now just have been a stepping-stone).
As it has developed the iPhone business, Apple has hugely increased its retail reach through the retail outlets of the telco companies. Apple has also increased the accessibility of iPads and iPods through various resellers that do not currently carry Apple Macintosh systems, and has increased the reach of its online stores.
The very successful Apple retail stores give prospective customers direct experience of Apple's brand values. Apple Retail visitors experience a stimulating, no-pressure environment where they can discover more about the Apple family, try out the company's products, and get practical help on Apple products at the shops' Guru Bars. Apple retail staff are helpful, informative, and let their enthusiasm show without being brash or pushy.
The overall feeling is one of inclusiveness by a community that really understands what good technology should look and feel like - and how it should fit into people's lives.
Apple Brand Architecture
From a brand architecture viewpoint, the company maintains a "monolithic" brand identity - everything being associated with the Apple name, even when investing strongly in the Apple iPhone, iPad, iPod and Apple iTunes products.
Apple's current line-up of product families includes not just these devices and and iTunes, but also iMac, iBook, iLife, iWork, iPhone, iPad, and now iCloud. However, even though marketing investments around iPod are substantial, Apple has not established an "i" brand. While the "i" prefix is used only for consumer products, it is not used for a large number of Apple's consumer products (eg Mac mini, MacBook, Apple TV, HomePod, AirPort Extreme and Time Capsule, Safari, QuickTime, and Magic Mouse).
The list of Apple's Trademarks reflects something of a jumbled past. The predominant sub-brand since the introduction of the Apple Macintosh in January 1984 has always been the Apple Mac. Products whose market includes Microsoft computer users (for example QuickTime, Bonjour, and Safari) have been named so they are somewhat neutral, and therefore more acceptable to Windows users. Yet other product have been developed more for a professional market (eg Aperture, the Final Cut family, and Xserve).
The iPod Halo Effect
Though Apple's iPhone and iTunes music business is profitable in its own right, Apple's venture into these product areas was based on a strategy of using the music business to help boost the appeal of Apple's computing business.
Apple is using iPad, iTunes, iPhone, and (very important at the time) iPod to reinforce and re-invigorate the Apple brand personality. At the same time, these product initiatives are growing a highly relevant, appealing brand image in the minds of consumer segments that Apple has not previously reached.
In a so-called iPod halo effect, Apple hoped that the popularity of iPod and iTunes among these new groups of customers would cause these segments to be interested in Apple's computer products. This does seem to have happened. Since the take-off of the iPod there has been a dramatic rise in Apple's computer sales and market share.
A couple of years ago, Apple's aspirations for the iPod halo effect was was highlighted most strongly when it used the slogan "from the creators of iPod" in its promotion of iMac G5 computers. In this instance, the Apple brand came full-circle - having been built into a branding system that originates in the personal computer market, then leveraged into the consumer electronics market, and then back into the consumer personal computer market.
This halo effect is extended with the hugely successful Apple iPad tablet computer. Great customer experience with iPhone (and familiarity with Apple's touch screen gesture controls), combined with a great product in its own right, has made iPod a huge success that in turn is drawing even more people to Apple's Mac computer products. In a move which brought matters full circle, the 2011 Lion version of Mac OSX gave the Mac the same touch screen gesture controls which iPad and iPod users have learned. In 2014 at the company's World Wide Developer Conference, it further strengthened the link between the Mac and other product lines by making it easy to provide continuity of user experience for a customer using a mix of Apple devices during her daily life.
Apple is employing the halo effect in its Apple Mac product strategy.
The mid-2012 Mountain Lion version of OS X incorporated many small changes to the Mac user interface that make the Mac's style of use much more like the iPad and iOS. By introducing such changes (which have frustrated some long-term Mac users), Apple has clearly decided that greater volumes of Apple Mac can be sold through selling to iPad (or iPhone) users than can be generated by upgrade sales to long-term Mac users.
This extension of a common user experience across Apple products was further strengthened by the introduction of the Apps Store to Mac OS X in mid-2011. Mac users can now buy their OS X applications with the same convenience as iPad or iPhone users can buy iOS Apps.
In mid 2012 Apple further harmonised the user experience of Mac and iPad users by introducing even more features from iPad into the new Mountain Lion version of the Mac operating system. With the introduction of Mountain Lion, Apple dropped the Mac part of the name from the operating system, so that it is now called just "OS X", rather than "Mac OS X". This small but important branding change opens the way for Apple to consolidate, perhaps into a single Operating System, the software used across its multiple devices.
Expect the Halo to Speak - Siri and beyond
Speech will be the next dimension in which Apple will gaining synery across its product lines. The natural language speech processing and interactivity capabilities introduced in October 2011 on the iPhone 4S are being introduced on the iPad (which uses the same operating system and A7 processor as the iPhones).
Apple is giving substance to speech interactivity by giving it a character - a personal assistant called "Siri". Siri can be somewhat customised by using different languages and idioms (for example, there are three versions of English speech available with country-specific accents and pronunciation - US, UK and Australian). Presumably other customisation or personalization features will also be introduced (perhaps user choice of name and other "identity" characteristics).
Siri highlights the marketing genius of Apple: speech control and interactivity are not new features on computers or phones. For example, smartphones running Microsoft's Windows Mobile operating system have had very similar functionality to Siri for some time. When Apple created the Siri "personal assistant" which gives these otherwise rather hard to describe features a character, consumers were given a hook around which they could finally understand what voice interactivity was all about.
Having taught customers to use touch gestures, Apple is now going to teach us how to speak to computers (almost unavoidably, in a specific Apple dialect of speech interaction).
Apple Brand Strength Now Creating Financial Success
So far, Apples' branding strategy is bearing fruit. For example, Apple reports that half of all computer sales through its retail channel are to people new to Macintosh, the company's sales and margins have been growing strongly since 2006, and Apple has achieved several "best ever" quarterly financial results in recent years, and in early 2012 when Apple's share price passed $500 per share for the first time, the company was the most valuable business in the world with a market capitalization which exceeded oil company Exxon, the previous top business.
Leveraging the success of the iPod, Apple launched the iPhone (released in July 07) to extend the brand even further. Apple's buzz marketing efforts in the first half of 2007 were truly superb, culminating in the release of one of the most highly anticipated products for many years - and launching apple into a completely new market: mobile handsets. By July 2008 the buzz about the 3G iPhone resulted in over 1 million units being sold in the first 3 days of its release in over 20 countries around the world. This success was repeated in 2010 with the introduction of the iPad tablet computer, and in March 2011 with the launch of the iPad 2 which sold 1 million units within 24 hours.
Apple Re-entering the Corporate Market via the iPhone and iPad Halo Effect
Though no-one at Apple would say so today, the next phase of Apple's strategy seems focused on the Corporate marketplace.
A long time ago, Apple had a fairly strong market share in large companies.
A long, long time ago (at the end of the 1970's) the first spreadsheet program (VisiCalc) was launched on the Apple II. The first PC (the IBM PC) to run a Microsoft operating system (PC DOS) did not appear until 1981. When Microsoft launched its Excel spreadsheet in 1984 it appeared first on the just-released Apple Mac, such was Apple's presence among accounting and finance departments.
Even though Apple effectively stopped competing for corporate business during the 1990s, the Apple Mac is still used in corporate environments. Microsoft still has a vigorous applications development team totally dedicated to writing business software for the Apple Mac. New versions of Microsoft Office for Apple Mac still come out approximately 2 years before similar functionality is placed in the next version of Microsoft Office for the Windows operating system.
Over the next few years it seems likely that Apple will re-focus on the Corporate marketplace: The company provides regular updates on the proportion of Fortune 500 companies which are either trialing or deploying iPhone (currently over 90%), and the iPad. In 2009, when Apple announced "Snow Leopard" (the then-latest version of the Apple Mac operating system) it included features allowing Mac computers to fully support Microsoft Exchange. This enables corporate IT departments to support business users who wish to use Apple Macs for their main email clients. Apple's Mac OSX Lion release (in Summer 2011) includes all the functionality needed to use a Mac as a business server.
Also, Microsoft continues to bring out advanced versions of Microsoft Office for Apple Mac, and - very significantly - in mid-2008 Apple announced a software upgrade for the iPhone which allows iPhones to be fully supported by Microsoft Exchange email servers. Corporate IT departments can now include iPhones as email clients.
One aspect of Apple's strategy seems clear: to use the popularity of the iPhone and iPad to break back into large corporations, sell lots of those devices, and have Apple Mac back on the desks of large businesses (or more probably - in the laptop bags of middle and senior managers in most large businesses).
The Macbook Air and iPad are clearly designed for business markets as well as for consumers, and Apple continues to display its mastery in smoothly morphing customer experience and brand preference from one product category to another.
As we say; no one in Apple will currently admit to such ambitions, but Apple's branding strategy is clearly expanding to include business and corporate markets once again.
After Halos - Clouds
The next step in Apple's marketing strategy is the Apple iCloud, which delivers a seamless experience for using and sharing content across all your Apple devices (iPhone, iPod, iPad, or Mac). iCloud enables a common "it just works" experience for using content across all of Apple's mainstream products. iCloud positions the company for a future where customers experiences and their digtal lives transcend the hardware devices which they use, and enables Apple to extend the brand experience well beyond individual products.
Apple has invested in a 500,000 (soon to be one million) square foot Apple data center in rural North Carolina. This data centre this will be used as the core of a data repository for Apple's iCloud services, which will enable Apple to leverage it's customer franchise into an even broader market space. Apple iCloud is one of many ways in which Apple and Google are fast becoming arch rivals.
iKnow Siri?
Once Apple hand-held device users have become acustomed to this style of interactivity, presumably natural language speech interaction will also be extended to the Mac - in whatever form-factor Apple's full-function computers have evolved into by then. Perhaps longer-term, it can also be assumed that a user's Siri personal assistant will be used to embody and create a feeling of continuous experience across different devices, with Siri seemingly moving with us from device to device.
This continuity across devices will be possible because Apple is using iCloud to offer customers device-independence and multi-device synchronisation - so that whichever Apple device you move to the experience continues because the new one will "know" what you were doing on the last one and can pick up dialogues such as chat messages where you left off.
Apple's Original Apple Macintosh Marketing Strategy
Stanford University has published contemporary records and original documents of the marketing strategy for the Apple Macintosh launch in 1984, including the original Apple marketing strategy and the Apple Macintosh product introduction plan written by Regis McKenna.
It is now nearly 3 decades since the launch of the Apple Macintosh (on January 24, 1984). Having proven itself and already gained considerable popularity with the Apple II, Apple chose to announce the Apple Mac in one of the most famous-ever commercials, aired during the third quarter of Super Bowl XVIII on 22 January 1984.
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(2) Time cards with recorded time must be signed by the employee and the designated supervisor.
a. Each employee and his/her supervisor must sign the time sheet or time card (from time clocks) to verify that the recorded time is the time actually worked.
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Conservation of historic buildings and monuments
New savings measures for listed places of worship
Grant scheme to be revised in line with government efficiency savings.
Published 7 October 2010
Department for Digital, Culture, Media & Sport and John Penrose MP
John Penrose, Minister for Tourism and Heritage has announced today that the Listed Places of Worship grant scheme is to be amended.
Currently listed places of worship, of any faith or denomination, can claim a grant equal to the VAT paid on eligible maintenance and building works. The new measures will see the scheme return to its original scope of eligibility which will exclude works on clocks, pews, bells, organs and professional services such as architects' fees, for the rest of this financial year.
"Everyone is being asked to make savings so I'm afraid we cannot exclude this scheme, however much I would like to," said Mr Penrose. "We asked representatives of the major denominations how they would prefer the savings to be made, and it was agreed that reducing the scope was the least damaging option for making savings, whilst still allowing claims for all other sorts of work."
The future of the scheme - which has given over £111 million since it began in 2001 - is currently under review as part of the Comprehensive Spending Review (CSR).
"The Listed Places of Worship scheme has helped around nine thousand communities to repair their historic places of worship," said Crispin Truman, Chair of Places of Worship at Heritage Alliance. "Any loss of scope under the scheme is to be regretted, but we appreciate that the Department needs to contribute to the savings needed, and are pleased that denominations had a chance to comment on the proposals."
Listed Places of Worship Grant Scheme
Memorials Grant Scheme
2010 Spending Review


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Home > Journals > Earth & Environmental Sciences > AJCC
AJCC> Vol.3 No.5, December 2014
Evaluation of the Eta Simulations Nested in Three Global Climate Models
Abstract Full-Text HTML XML Download as PDF (Size:11769KB) PP. 438-454
DOI: 10.4236/ajcc.2014.35039 4,935 Downloads 6,501 Views Citations
Sin Chan Chou1*, André Lyra1, Caroline Mourão1, Claudine Dereczynski2, Isabel Pilotto1, Jorge Gomes1, Josiane Bustamante1, Priscila Tavares1, Adan Silva1, Daniela Rodrigues1, Diego Campos1, Diego Chagas1, Gustavo Sueiro1, Gracielle Siqueira1, Paulo Nobre1, José Marengo3
1National Institute for Space Research, Cachoeira Paulista, Brazil.
2Department of Meteorology, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.
3Centre for Monitoring and Warning of Natural Disasters, Cachoeira Paulista, Brazil.
To provide long-term simulations of climate change at higher resolution, Regional Climate Models (RCMs) are nested in global climate models (GCMs). The objective of this work is to evaluate the Eta RCM simulations driven by three global models, the HadGEM2-ES, BESM, and MIROC5, for the present period, 1961-1990. The RCM domain covers South America, Central America, and Caribbean. These simulations will be used for assessment of climate change projections in the region. Maximum temperatures are generally underestimated in the domain, in particular by MIROC5 driven simulations, in summer and winter seasons. Larger spread among the simulations was found in the minimum temperatures, which showed mixed signs of errors. The spatial correlations of temperature simulations against the CRU observations show better agreement for the MIROC5 driven simulations. The nested simulations underestimate precipitation in large areas over the continent in austral summer, whereas in winter overestimate occurs in southern Amazonia, and underestimate in southern Brazil and eastern coast of Northeast Brazil. The annual cycle of the near-surface temperature is underestimated in all model simulations, in all regions in Brazil, and in most of the year. The temperature and precipitation frequency distributions reveal that the RCM and GCM simulations contain more extreme values than the CRU observations. Evaluations of the climatic extreme indicators show that in general hot days, warm nights, and heat waves are increasing in the period, in agreement with observations. The Eta simulations driven by HadGEM2-ES show wet trends in the period, whereas the Eta driven by BESM and by MIROC5 show trends for drier conditions.
South America, Climate Downscaling, Model Evaluation, Climatic Extreme Indicators, Eta Model
Chou, S. , Lyra, A. , Mourão, C. , Dereczynski, C. , Pilotto, I. , Gomes, J. , Bustamante, J. , Tavares, P. , Silva, A. , Rodrigues, D. , Campos, D. , Chagas, D. , Sueiro, G. , Siqueira, G. , Nobre, P. and Marengo, J. (2014) Evaluation of the Eta Simulations Nested in Three Global Climate Models. American Journal of Climate Change, 3, 438-454. doi: 10.4236/ajcc.2014.35039.
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