text:
\section{Introduction}
\label{sec1}
Despite significant progress being made towards understanding the pathophysiology of cancer, its self-sustaining and highly dynamic nature poses several challenges pertaining to cancer detection and treatment monitoring.  While technological advancements hold promise in addressing those dilemmas, owing to its complexity, challenges remain in several stages of cancer management, including pre-cancerous lesion detection, tumor segmentation, tumor infiltration, tracing of tumor evolution, prediction of tumor aggressiveness, and recurrence.

Brain Tumors are among the most dangerous malignancies.  The unique genetic, epigenetic, and microenvironmental properties of neural tissues confer resistance to treatments \citep{mackay2017integrated, quail2017microenvironmental}, and thus, the clinical management of brain tumors remains a critical challenge. Among tumors arising from the brain, the most predominant are metastases from systemic cancers and gliomas \citep{bi2019artificial}.  Stage IV glioma, referred to as glioblastoma, develops from glial cells and infiltrates the surrounding cell tissues and is the most aggressive form of primary brain tumor, with a median survival of 15 months \citep{koshy2012improved}. Brain tumors are often complex in shape and vary greatly in size, texture, and location and thus, the clinical information related to tumors exhibits high spatial and structural variation from patient to patient. Neuroimaging is a pivotal diagnostic tool in disease assessment. While there exists a variety of diagnostic imaging techniques that are in use at present such as X-ray, computed tomography (CT), positron emission tomography (PET), and mammograms, magnetic resonance imaging (MRI) is the method of choice in neurology as it does not involve the risk of exposure to ionizing radiation. In brain tumor studies, the clinical information embedded in MRI data is vital for analyzing structural brain abnormalities, detecting pre-cancerous lesions, tumor segmentation, and diagnosis.

The segmentation of biomedical images entails delineating pathological regions and is a crucial first step in cancer diagnostic. In the case of glioblastoma multiforme brain tumor (GBM), segmentation involves separating different heterogeneous regions of tumor tissues as the necrotic core, enhancing tumor, and peritumoral edema (swelling in surrounding brain tissues). Different types of imaging modalities provide useful biological information related to tumor-induced neural tissue changes. The T1-weighted (T1), T1-weighted contrast-enhanced (T1ce), T2-weighted (T2), and T2 fluid-attenuated inversion recovery (FLAIR) modalities are the routinely used brain MRI image sequences. A 2D slice of each modality and the segmented scan is depicted in Fig. \ref{fig:gbm}. While segmentation aids in precise localization and diagnosis through objective quantification of tumor tissue composition and size, proper segmentation remains a key challenge due to the intra-tumoral heterogeneity of tumor cells.

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{images/glioma.png}
    \caption{On the left is an example of glioblastoma brain tumor in T1, T1-contrast, T2 and FLAIR modalities. On the right is the ground truth segmentation of the tumor which specifies the class of each voxel.}
    \label{fig:gbm}
\end{figure*}

Traditional methods of tumor evaluation depend upon qualitative features such as tumor density, intra-tumoral cellular composition, and anatomic relationship to surrounding tissues, which are also termed semantic features. Technological advancements have enabled quantitative assessment of neuropathology facilitating quantification of tumor size, shape, and textual patterns \citep{aerts2014decoding, bi2019artificial}. While early methods of diagnosis relied upon probabilistic tumor models, pivotal breakthroughs in computer vision led to a rapid rise in Artificial Intelligence (AI) research in medical imaging. Deep Learning \citep{lecun2015deep} is a subset of AI that holds great potential to support clinicians in gaining insight from complex, high-dimensional, and heterogeneous biomedical data. Traditional statistics and deep learning vary in their approach for brain tumor quantification, each with its own strengths and weaknesses. Although biomedical image segmentation with statistical modeling and deep learning methods are well-established as independent areas of research, hybridization of the two paradigms is an emerging trend. Going beyond recent retrospective reviews in tumor segmentation which are mostly concentrated on deep learning-based methods, we provide a comprehensive overview linking the two disciplines.

The key contribution of this study towards neuroimaging literature is to provide an integrated overview of statistical modeling and deep learning methodologies for biomedical image segmentation from both a theory-driven and application perspective. Through a comprehensive summary of statistical and deep learning literature, we provide a critical discussion related to the methodologies, limitations, key challenges, and future directions in the area of brain tumor segmentation.

The remainder of this paper is structured as follows: In section 2, we present conceptual bases pertaining to cortical segmentation. Section 3 is a statistical overview comprised of computational theories and recent studies in 3D MRI brain tumor segmentation. This is followed in section 4 by deep learning network architectures in medical imaging and their tumor segmentation applications. Section 5 is comprised of a concise overview of integrated statistical and probabilistic deep learning studies in neuroimaging. Section 6 provides a discussion on limitations, critical challenges, and future directions. Section 7 concludes the paper.

\section{Brain Tumor Segmentation Preliminaries}

Brain imaging analyses rely upon anatomical images of the brain generated by an MRI scanner. The basic concepts in biomedical image segmentation relating to two-dimensional (2D) and three-dimensional (3D) imaging, tumor segmentation process and MRI scan pre-processing are briefly described here.

\subsection{2D and 3D Medical Imaging}

A 2D image can be defined as a continuous function $f(s,t)$, such that $f \colon \mathbb{R}^2 \to \mathbb{R}$, where $f(s,t)\in \mathbb{R}$ represents the image intensity level at spatial coordinates $(s,t) \in \mathbb{R}^2$. In the case of a 3D image, the function is represented by $f \colon \mathbb{R}^3 \to \mathbb{R}$, with intensity level $f(s,t,u)\in \mathbb{R}$  and spatial coordinates  $(s,t,u) \in \mathbb{R}^3$. An image can be converted into a digital image by sampling the spatial coordinates and quantization of the corresponding intensity value. An image that has been discretized in both spatial coordinates and intensity values can be defined on the digital image domain $D \in \mathbb{Z}^n$, where $\mathbb{Z}^n$ represents the $n$-dimensional discrete space \citep{gonzalez2006digital, banik2009landmarking}. A digital image, $f(i,j)$ in 2D space and $f(i,j,k)$ in 3D space, therefore, is composed of a finite number of picture elements uniquely identified by its spatial coordinates and intensity values which are referred to as pixels in 2D space and voxels in 3D space. In a matrix arrangement of pixels, $i$ denotes the row number and $j$, the column number. The MRI scanner generates 3D volumetric brain imaging data as a stack of 2D slices, and $k$ in the 3D space denotes the slice number. In a standard neuroanatomical volume, isotropic voxel dimension is on the order of 1-2mm. In the 3D space, data is acquired from a series of MRI scans and the resolution of volume data depends upon the in-plane resolution of the 2D cross-sections generated by the MRI scanner. Pixels in 2D space and voxels in 3D space are depicted in Fig. \ref{fig:mri} \citep{despotovic2015mri}.

\begin{figure}
    \centering
    \includegraphics[width=\linewidth]{images/pixels.pdf}
    \caption{Image elements in the MRI of the brain. An image pixel $(i,j)$ in 2D space is depicted by the square and an image voxel $(i,j,k)$ in 3D space is represented by the cube \citep{despotovic2015mri}.}
    \label{fig:mri}
\end{figure}

\subsection{Tumor Segmentation}

Segmentation is the process of partitioning an image into a set of semantically (i.e., anatomically) meaningful and coherent regions, the result of which is either the contours that delineate the region boundaries or the homogeneous region of the structures of interest (e.g., tumors). Let the image domain be denoted by $\mathcal{I}$ and the segmentation classes by $k \in K$ where each voxel $i$ belongs to one of the $K$ possible classes such that the set $S_k \subset \mathcal{I}$. Then the segmentation task involves determining the sets $S_k$ that satisfies:
\begin{equation}
    \mathcal{I} = \bigcup_{k=1}^K S_k
\end{equation}
where $S_j \cap S_k = \emptyset$ for $j \neq k.$

In the context of medical imaging, segmentation involves identifying the pixels or voxels that represent organs, lesions, and other anatomical substructures. Thus, it enables identifying the extent of an abnormality which can range from the estimation of maximal tumor diameter in 2D measurements to whole tumor assessments and adjacent tissue evaluations in 3D volumetric segmentation. Such information can subsequently be applied in diagnosis, risk assessment, and therapeutic planning.

There are several cortical segmentation clinical applications \citep{suri2001advanced} some of which are summarized here. In neurosurgery, \textit{surgical planning} \citep{schad1987three, kikinis1996computer} is imperative, and segmentation is often the first and the most critical step conducted to identify the 3D coordinates of the tumor cells. Segmentation also aids in \textit{neuro-surgical navigation} \citep{kosugi1988articulated, grimson1997utilizing} to guide the neurosurgeon to move towards the anatomical targets such as tumors while avoiding critical regions of the brain. \textit{Quantitative assessment} \citep{decarli1992method} of pathology is vital for establishing treatment strategies and often necessitates segmentation as it allows to quantitatively assess the extent of tumor resection \citep{cordova2014quantitative} and tumor volume measurements \citep{wright1995voxel}. By separating image data in anatomical structures into spatially and structurally correlated regions, segmentation enables effective \textit{visualization} \citep{zeng1998segmentation} of complex biomedical images.

While Segmentation involves separating the image into regions based on homogeneity, classification assigns each voxel to a particular tissue class. For instance, in the case of non-diagnostic neuroimaging classification of brain anatomical structure, tissue classes are gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF). The tasks of segmentation and classification are interconnected on the grounds that segmentation indicates a classification, and a classifier indirectly segments the image. Current clinical practice in oncology is typically dependent upon manually traced segmentation which is time-consuming and subject to inter-observer variability \citep{warfield2008validation} that leads to inconsistent segmentation and poor reproducibility \citep{hong2012heterogeneity}. Thus, a time-efficient, generalizable, and reproducible automated segmentation process is highly desirable. There are several different segmentation techniques that have been proposed in the past literature, including intensity-based, atlas-based, and surface-based methods, but here we primarily focus on statistical and deep learning voxel-based segmentation.

\subsection{MRI preprocessing}

In structural brain MRI, certain pre-processing steps are required prior to automated segmentation which typically includes image registration, skull stripping, and bias field correction. \textit{Image registration} \citep{zitova2003image} involves spatially aligning images acquired by different sensors, at different times, from different viewpoints to a common anatomical space. Inter-patient registration aims at standardizing the images across subjects, whereas intra-patient registration aids in the alignment of imaging modalities (e.g., T1 and T2) within the same subject. \textit{Skull stripping} \citep{kalavathi2016methods} is the process of brain tissue extraction from extra-meningeal tissues such as skull, muscles, or fat and aims at classifying voxels as brain or non-brain. While there are several skull stripping methods available, the most common approach is to use tools such as the brain extraction tool (BET) \citep{smith2002fast}. The intensity inhomogeneity, also known as the \textit{bias field} \citep{landini2018advanced,song2017review} is an undesirable artifact that degrades the segmentation performance leading to quantitative and qualitative misinterpretations. The intensity non-uniformity can be characterized by intensity variation of the same tissue across the MR image. To eliminate the spatial inhomogeneities, several methods have been proposed \citep{arnold2001qualitative,belaroussi2006intensity,uwano2014intensity} and N4 bias field correction \citep{tustison2010n4itk} is one of the widely applied methods at present.

\section{Statistical model-based 3D MRI Segmentation}

Prior art in computational analysis of clinical imaging often relied upon statistical inference. Representative early work in brain tumor segmentation can be categorized into two broad categories: \textit{generative probabilistic models} such as Bayesian-based approaches, Markov random fields and hidden Markov models, and \textit{discriminative models} such as neural networks and conditional random fields (CRFs) \citep{menze2014multimodal}. Generative models incorporate domain-specific prior knowledge related to the anatomy, appearance, and spatial distribution of tissues. For instance, spatial distribution prior for a given set of 3D MRI images can be obtained via lesion-specific biomarkers or by applying a tumor growth model that can be used to deduce the most probable tumor localization. While these methods generalize well to the unseen images, encoding prior information for a tumor is challenging. On the contrary, discriminative models do not incorporate domain knowledge in the learning task but require manually annotated training images. These methods first extract voxel-wise features from the training images such as intensity distributions which are then fed to a classifier for voxel classification and are therefore sensitive to the image intensity profiles. A significant amount of data is required to ensure robustness to imaging artifacts and variations in shape and image intensity.

Three main categories of probabilistic models for cortical segmentation can be identified \citep{suri2001advanced}: the Bayesian approach, Markov random field (MRF) and expectation-maximization (EM) algorithm. Theoretical aspects of each method and their applications towards brain MRI segmentation are presented here. While the scope of this section is restricted to tumor segmentation, readers can refer to the study by \citet{van2015tissue} for a more comprehensive overview of brain tissue classification.

\subsection{The Bayesian Modeling Framework}

The Bayesian approach falls under the generative modeling framework and models the probabilistic relationship between segmentation labels and image features such as voxel intensity values. In the Bayesian framework, the model is fully specified by the prior and the likelihood distribution.

The prior indicates the current state of the knowledge with regard to likely configurations of anatomical structures in the image before the data is observed. Let the segmentation prior distribution be denoted by $p(\mathbf{y}|\bm{\theta}_y)$ where $\mathbf{y}=(y_1,\dots,y_I )^T$ are the labels in an image with $I$ voxels such that $y_i \in \{1,\dots,K\}$ represents one of the $K$ possible anatomical structures assigned to voxel $i$ and $\bm{\theta}_y$  is the set of parameters of prior. Likelihood is the conditional distribution $p(\mathbf{x}|\mathbf{y},\bm{\theta}_x)$ of the voxel intensities $\mathbf{x}=(x_1,\dots,x_I )^T$ given anatomical labels $\mathbf{y}$ where $\bm{\theta}_x$  is the set of parameters. The segmentation posterior can then be computed via the Bayes' rule with appropriate parameters $\hat{\bm{\theta}}$:

\begin{equation}
    p(\mathbf{y}|\mathbf{x}, \hat{\bm{\theta}}) = \frac{p(\mathbf{x}|\mathbf{y},\hat{\bm{\theta}}_x) \, p(\mathbf{y}|\hat{\bm{\theta}}_y)}{p(\mathbf{x}|\hat{\bm{\theta}})}
\end{equation}
where $p(\mathbf{x}|\mathbf{y},\hat{\bm{\theta}}_x)$ is the likelihood, $p(\mathbf{y}|\hat{\bm{\theta}}_y)$ is the prior probability distribution and $p(\mathbf{x}|\hat{\bm{\theta}})$ is the marginal distribution with $p(\mathbf{x}|\hat{\bm{\theta}})= p(\mathbf{x}|\mathbf{y},\hat{\bm{\theta}}_x) \, p(\mathbf{y}|\hat{\bm{\theta}}_y).$

Prior and likelihood parametric distributions depend on parameters $\bm{\theta}=({\bm{\theta}_y}^T,{\bm{\theta}_x}^T)^T$ that are either assumed a priori known or estimated from the image data. The segmentation map of a new image can be estimated via the maximum a posteriori (MAP) estimation which involves maximizing the posterior distribution $p(\mathbf{y}|\mathbf{x}, \hat{\bm{\theta}})$ of possible segmentations:
\begin{align} \label{eq1}
\hat{\mathbf{y}} & = \operatorname*{arg\,max}_\mathbf{y} p(\mathbf{y}|\mathbf{x}, \hat{\bm{\theta}}) \nonumber \\
 & = \operatorname*{arg\,max}_\mathbf{y} p(\mathbf{x}|\mathbf{y},\hat{\bm{\theta}}_x) \, p(\mathbf{y}|\hat{\bm{\theta}}_y)
\end{align}
where $p(\mathbf{x}|\hat{\bm{\theta}})$ is a constant that can be excluded.

\emph{Gaussian Mixture Model:} In the segmentation of brain MRI, voxel intensities are typically assumed as independent samples from a mixture of Gaussian distributions. Gaussian mixture model (GMM) presumes that there are similar intensities for voxels in the same tissue class. Based on the assumption that the occurrence of a certain anatomical label in a particular voxel does not depend on the labels in other voxels, the prior distribution is modeled as:

\begin{equation}
    p(\mathbf{y}|\bm{\theta}_y)= \prod_{i} p(y_i|\bm{\theta}_y) = \prod_{i} \pi_{y_i}
\end{equation}
where parameters $\bm{\theta}_y=(\pi_1,\dots,\pi_K )^T$ such that $\pi_k \geq 0,\forall k$ and $\Sigma_k \pi_k =1$. $\pi_k$ denotes the prior probability of a voxel belonging to class $k$ which is set equal to the relative frequency of each label.

Assuming that the intensity in each voxel is independent of the labels in other voxels and only dependent on the anatomical label in that voxel, the likelihood component of the model has the form:

\begin{equation}
    p(\mathbf{x}|\mathbf{y},\bm{\theta}_x)= \prod_{i} p(x_i|y_i,\bm{\theta}_x)
\end{equation}
where the product is over all voxels.

Voxel intensity distribution in each tissue class $k$ can be modeled by a Gaussian distribution characterized by mean $\mu_k$ and variance $\sigma_k^2$:
\begin{equation}
    p(x_i|y_i, \bm{\theta}_x)=\mathcal{N}(x_i|\mu_{y_i}, \sigma_{y_i}^2)
\end{equation}
where $\mathcal{N}(x|\mu , \sigma^2)= \frac{1}{\sqrt{2 \pi \sigma^2}} exp[-\frac{(x-\mu)^2}{2 \sigma^2}]$ and
$\bm{\theta}_x = (\mu_1,\dots,\mu_K,\sigma_1^2,\dots,\sigma_K^2)^T.$

It can be derived that:
\begin{equation}
    p(x|\bm{\theta}) = \Sigma_k \, \mathcal{N}(x|\mu_k, \sigma_k^2) \, \pi_k
\end{equation}
where $\pi_k, \, \mu_k$ and $\sigma_k^2$ are prior, mean and variance of class $k$, respectively. Thus, in the GMM, each voxel's intensity distribution is described by a linear superposition of $K$ Gaussians.

Early studies, as well as current work, investigated the applicability of Bayesian methods for MRI segmentation. For example, in the formative work of \citet{shattuck2002brainsuite}, authors presented a cortical surface identification process from MR images and applied a Bayesian strategy for voxel-based tissue classification. \citet{corso2008efficient} proposed a Bayesian formulation to calculate affinities in the segmentation of glioblastoma multiforme brain tumor and showed that the incorporation of model-aware affinities improves segmentation results. \citet{patenaude2011bayesian} modeled the probabilistic relationships between both shape and intensity using a Bayesian approach which exhibited improved performance in structural segmentation of brain images in terms of accuracy and robustness. A GMM based on variational Bayesian inference for brain MRI image segmentation was proposed by \citet{xia2016brain}. However, their approach requires training a large number of variational models which is computationally expensive. In a recent study by \citet{lipkova2019personalized}, authors integrated structural and metabolic scans and modeled the tumor density of glioblastoma patients using a tumor growth model under the Bayesian framework.

While Bayesian MRI segmentation is a well-studied problem, they necessitate the use of prior information and the analysis is sensitive to the choice of the prior. When encoding prior knowledge robustness of the prior must be ensured so that the conclusions are not affected by the form of the prior distribution. Further, assuming spatial independence between voxel intensities is not justifiable and may lead to voxel misclassifications. The probabilistic tumor model should therefore incorporate context and characterize the true shape of anatomical structures.

\subsection{Modeling spatial context with Markov Random Field}

A voxel intensity value is statistically dependent on  the  intensity of neighboring voxels. Markov random field (MRF) allows modeling the spatial context by integrating voxel dependencies in the image surface. An MRF can be characterized by a graph $\mathcal{G} \triangleq (\mathcal{H} ,\mathcal{N})$ with $\mathcal{H}$ representing a lattice containing nodes and $\mathcal{N}$ indicating the links between the nodes, such that the neighboring relationship of nodes is defined by  $\mathcal{N}=\{\mathcal{N}_i | \forall i \in \mathcal{H} \}$, where $\mathcal{N}_i$ is the neighborhood around a position $i$ \citep{li2009mathematical}. This graphical structure is comparable to a 3D image grid with nodes representing the voxels and edges, the spatial dependency between voxels. For example, each voxel in a 3D image has 6 direct neighbors.

Assuming that the voxels with the same labels are a part of the same cluster, the MRF model formulates the prior distribution $p(\mathbf{y}|\bm{\theta}_y)$  as \citep{van2015tissue}:
\begin{equation}
    p(\mathbf{y}|\bm{\theta}_y) = \frac{1}{Z(\bm{\theta}_y))} \exp (-E(\mathbf{y}|\bm{\theta}_y))
\end{equation}
where $E(\mathbf{y}|\bm{\theta}_y)$ is an energy function and $Z(\theta_y)= \sum_\mathbf{y} \exp (-E(\mathbf{y}|\bm{\theta}_y))$  is a normalizing constant that guarantees $\sum_\mathbf{y} p(\mathbf{y}|\bm{\theta}_y)=1$.

Energy function typically takes the form,
\begin{equation}
    E(\mathbf{y}|\bm{\theta}_y) = \beta \sum_{(i,j)} \delta(y_i \neq y_j)
\end{equation}
where the summation is over all the neighboring voxel pairs. $\beta$ is a parameter that regulates the amount of penalization for undesired configurations. If $k=y$ then $\delta(k \neq y) =0$ and $1$ otherwise. Thus, the energy function promotes spatially clustered labels.

The MRF model reduces the effect of statistical noise in highly noisy data and the potential number of misclassified voxels and has been successfully applied in many studies. \citet{capelle2000unsupervised}  presented an unsupervised MRF-based segmentation approach to detect the presence of tumors. Each homogeneous region, healthy and tumor brain tissues, can be considered as a single texture. The texture number in the segmentation field is unknown a priori, which motivates the use of an unsupervised approach. They applied MRF as it classifies each pixel by considering the neighborhood dependency of pixels, where they then estimated realization of the hidden Markov field via a maximum a posteriori estimator (MAP). \citet{gering2002recognizing} proposed a brain tumor segmentation framework where they first trained on healthy brains to diagnose brain tissue abnormalities and then used a multi-layer MRF framework combined with an extended EM-based segmentation. They incorporated contextual information on several layers in the segmentation process which included intensities of voxels, structural coherence, intra and inter-structure properties, and user input. However, this approach has certain limitations as high-level layer classification is sensitive to the noise in the lower layers. \citet{bauer2011segmentation} utilized an MRF-based tumor growth model together with atlas-registration for volumetric MRI brain tumor segmentation. To ensure atlas and patient MRI scan correspondence, the tumor growth model is devised as a mesh-free MRF Energy Minimization problem. Their method is non-parametric and can be applied for tumor mass-effect simulations which facilitate the atlas-based segmentation. More recently, \citet{rajinikanth2017firefly}, applied the MRF-EM combination in conjunction with a firefly-assisted algorithm for 2D MRI tumor segmentation. During the process of segmentation, MRF assigns the label of each pixel to one of the three categories: white matter, gray matter, and tumor mass. Their results suggest that the proposed approach is a better alternative compared with the other methods tested in their study.

While the MRF model allows integrating prior that incorporate spatial context, computing the posterior explicitly is computationally expensive and requires the use of approximation schemes. Thus, MRFs have shortcomings with respect to computational efficiency.

\subsection{Parameter optimization with Expectation Maximization Algorithm}

Obtaining reliable parameter estimates is crucial in statistical model-based segmentation. To estimate appropriate model parameters $\hat{\bm{\theta}}$, the maximum likelihood approach can be adopted which attempts to estimate the setting of the parameter vector $\bm{\theta}$ that maximizes $p(\mathbf{x}|\bm{\theta})$,
\begin{align}
    \hat{\bm{\theta}} & = \operatorname*{arg\,max}_{\bm{\theta}} [p(\mathbf{x}|\bm{\theta})] \nonumber\\
    & = \operatorname*{arg\,max}_{\bm{\theta}} [\log p(\mathbf{x}|\bm{\theta})]
\end{align}
where $p(\mathbf{x}|\bm{\theta})$ represents how likely is an image $\mathbf{x}$ for a given set of parameters $\bm{\theta}.$

The expectation-maximization (EM) framework allows obtaining maximum likelihood estimates of unknown parameters which is a common strategy in tumor segmentation when modeling MRI intensities of brain tissues as Gaussian mixtures. The parameters in brain tissue segmentation may include intensity, bias correction, and registration parameters. The EM algorithm iterates between two steps until convergence: the \emph{expectation step} (e-step) and the \emph{maximization step} (m-step). In brain tissue segmentation, the model parameter estimates are often initialized via a GMM. Then, in the E-step the model seeks to estimate the tumor segmentation where each pixel/voxel is assigned to a cluster under the current model parameter estimates of the posterior distribution and the M-step estimates the model parameters based on the current classification.

There exists a considerable body of literature on tumor segmentation where the EM algorithm was incorporated in conjunction with the hidden Markov random field (HMRF) Model \citep{zhang2001segmentation, nie2009automated, doyle2013fully}. For example, in the prominent work by \citet{zhang2001segmentation}, authors showed that a 3D fully automated brain MR image segmentation which is both accurate and robust can be achieved through an HMRF-EM framework. HMRF framework aids in encoding spatial information of neighboring sites and the model parameters are estimated via maximum likelihood estimation using the EM algorithm.  \citet{moon2002model} proposed a model-based approach for segmenting healthy and tumor brain tissues from 3D MRI, where they used a probabilistic geometric model coupled with the EM algorithm. They extended the spatial prior of a probabilistic normal human brain atlas with tumor information obtained from patient data to include spatial prior for tumor tissues. A generalized EM segmenter via a generative probabilistic modeling approach for brain lesion segmentation was introduced by \citet{menze2015generative} which demonstrated improved generalization.

The EM algorithm ensures that likelihood increases with each step and frequently used when the model depends on latent variables. Nevertheless, it exhibits slow convergence and may only converge to local optima.

\textit{Summary}: Justifying the underlying probability distribution that drives data is an important facet in statistical model-based methods of segmentation. These methods have the intrinsic limitations of requiring domain expertise and knowledge of prior distribution. Translating information about prior knowledge into a probabilistic model can be challenging and inference may involve extensive computations. These shortcomings restrict their deployment in large-scale and time-sensitive applications. However, model-based approaches are effective in terms of the model interpretability and the amount of data required for the analysis.

\section{Deep Learning based 3D MRI Brain Tumor Imaging}

Deep Learning (DL) excels at the extraction of complex feature representations that cannot be perceived by the human brain enabling quantifiable image interpretation. Previous studies have exploited different architectures of deep networks for biomedical image segmentation, varying from unique convolutional neural net based architectures to probabilistic deep generative models. In this section, we present widely adopted deep learning architectures in recent literature and their practical applications in 3D multi-modal MRI brain tumor segmentation.

\subsection{Convolutional Neural Networks}

Recent years have seen a proliferating use of convolutional neural networks (CNNs) \citep{lecun1999object} in medical image analysis owing to their ability to integrate structural information contained in adjacent pixels. CNNs are comprised of multiple convolutional and pooling layers stacked sequentially. By convolving a filter (also referred to as kernel) across the input and performing a convolution operation, a convolutional layer generates feature maps, which are then passed through an activation function such as Rectified Linear Unit (ReLU) for non-linear transformation. The output feature map is then fed to a pooling layer for down-sampling. The fully connected layer placed at the end of the network maps the features extracted by convolutional and pooling layers into the final output and make the final prediction.

In contrast to the conventional DL classifiers such as AlexNet \citep{krizhevsky2017imagenet}, VGGNet \citep{simonyan2014very} and GoogLeNet \citep{szegedy2015going}, which takes an image as the input and output a probability distribution over all classes with regard to the entire image, the task of segmentation requires a per-pixel classification of the input. This can be achieved by feeding the classifier with patches extracted around each pixel and adopting a sliding-window strategy (Fig. \ref{fig:cnn}). Semantic segmentation in the computer vision domain typically involves 2D images, consequently, the methods developed for segmentation are mainly based on 2D methods. Therefore, deep learning in 3D volumetric medical image segmentation calls for modifications on architectures that are developed for semantic segmentation. While some studies showed promising results when applying 2D CNN architectures to process 3D volumes in a slice-by-slice manner, for example in \citep{ciresan2012deep, zikic2014segmentation, pereira2016brain, havaei2017brain}, it is arguably a sub-optimal use of the 3D clinical image data as it is time-inefficient and fails to leverage contextual information from adjacent slices.

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{images/patch.png}
    \caption{Patch-wise segmentation with CNN architecture. The input to the CNN is an image patch and the output is the probabilities for each class where the prediction for center pixel is the class with the highest score.}
    \label{fig:cnn}
\end{figure*}

\emph{3D Convolutional Neural Networks:} 3D CNNs, as a generic extension of 2D CNNs capable of extracting volumetric representations with the use of 3D kernels have received significant attention in neuroimaging. In the seminal work of \citet{kamnitsas2017efficient}, a 3D CNN based architecture, termed \emph{DeepMedic}, was introduced for automated brain lesion segmentation of 3D volumetric brain scans and ranked at the top in the Ischemic Stroke Lesion Segmentation (ISLES 2015) challenge. They conducted a patch-based analysis using a dual pathway strategy which allows feeding the network a version of the image at multiple scales concurrently, facilitating the incorporation of both local and global contextual information. This process was further improved later with several architectural modifications \citep{kamnitsas2017ensembles}.

While patch-wise segmentation with CNNs does not require major architectural adaptations, it is computationally expensive and entails redundant operations since adjacent pixels in an image are similar in the vicinity of the pixel being processed and the input patches from adjacent pixels are overlapped. In addition, the smaller the patch size, the network has less possibility of learning the global context as the learning process is confined to visible features in each patch.

\subsection{Multi-stream architectures}

The integration of contextual 3D information can also be performed through multi-stream architectures. While the standard CNN can incorporate multiple sources of information through the channels in the input layer, multi-stream architectures enable merging the channels at intermediate points in the network. They enable fusing features extracted from multi-angled patches from the 3D space (three patches from the orthogonal views of an MRI volume), an approach known as 2.5D method \citep{roth2014new}, which incorporates (partial) 3D information from neighboring slices using 2D kernels that results in lower computational cost, but less powerful volumetric representations than in 3D CNN. The multi-path approach also facilitates combining patches of different scales (2D, 2.5D, 3D patches), where each branch contains a CNN corresponding to each patch type. \citet{farabet2012learning} introduced multi-stream multi-scale architecture in natural images, and later the idea was implemented by several authors in the context of medical imaging \citep{roth2015improving, setio2016pulmonary, kamnitsas2017efficient, moeskops2016automatic}. However, multi-stage training schemes can be susceptible to overfitting.

Despite the increased use of 3D CNNs and their 2D/3D hybrid variants, these methods are associated with limitations such as computational complexities due to increased number of parameters, significant memory consumption, and slow inference.

\subsection{Fully Convolutional Net}

\begin{figure*}[ht!]
    \centering
    \includegraphics{images/segnet.png}
    \caption{A schematic illustration of semantic-wise brain tumor segmentation with a SegNet-like architecture. The down-sampling through pooling layers in the encoder part of the network is compensated by the up-sampling layers in the decoder part that results in a segmentation output with dimensions same as the original input image.}
    \label{fig:seg}
\end{figure*}

To address limitations in CNNs, \citet{long2015fully} devised a fully convolutional network (FCN) by transforming fully connected layers in the default CNN with convolutional layers that enabled taking input of arbitrary size and generating correspondingly sized output. While the FCN can be efficiently applied to an image or volume, the use of convolution layers with filters larger than 1 x 1 and max-pooling layers or strided convolutions lead to a reduction in data dimension resulting in a very low resolution in the output than in the input. In order to circumvent this limitation, the authors in \citep{long2015fully} applied the concept of up-sampling path using deconvolution operations to restore the spatial size of the down-sampled feature maps to the original input dimensions. Inspired by FCN architecture, \citet{badrinarayanan2017segnet} proposed an encoder-decoder network architecture for semantic pixel-wise segmentation called \textit{SegNet}. Each max-pooling layer in the encoder part has a corresponding up-sampling layer in the decoder, which restores the feature maps to the original resolution. The softmax layer makes pixel-wise predictions and generates the final segmentation output which has dimensions same as the original input image. Recent successful segmentation networks are mostly based on convolutional encoder-decoder architectures. An illustration of semantic-wise brain tumor segmentation with a SegNet-like architecture is depicted in Fig. \ref{fig:seg}.

FCN and its variants have been extended to 3D for voxel classification, for instance, a 3D CNN consisting of two interconnected pathways, specifically, a convolutional and deconvolutional pathway, was proposed by \citet{brosch2016deep} for multiple sclerosis lesion segmentation in MRI. They connected the first convolution layer and the last deconvolution layer through a single skip connection as a joint learning strategy of the feature extraction and prediction pathways and achieved superior performance when compared with five publicly available methods for this task. In the study by \citet{dolz20183d}, a 3D FCN model capable of performing volume-to-volume learning to segment subcortical structure is proposed to combat the computational and memory requirements in regular 3D CNN. They investigated the effect of small kernels which enabled deeper architectures and achieved promising results.

\subsection{Biomedical Image Segmentation with U-Net}

\citet{ronneberger2015u} proposed U-Net architecture comprised of a contracting path and an expanding path, which has become the dominant approach for segmentation in most recent applications.  While it is similar to FCN, the architectural novelty in U-Net lies in the fact that the up-sampling and down-sampling layers  are combined by skip connections to connect the opposing convolution and deconvolution layers. Later several variants of U-Net capable of performing 3D volume-to-volume segmentation were proposed with significant improvements. For instance, \citet{cciccek20163d} proposed a 3D U-Net by replacing 2D operations in 2D U-Net with their 3D equivalents and \citet{milletari2016v} implemented a 3D-variant of U-Net architecture using residual blocks, called V-net. These architectures are trained on entire images or large image patches as opposed to small patches and hence affected by data scarcity, which is typically addressed through data transformations such as shifting, rotating, scaling, or through applications of random deformations.

Efficient DNN-based medical image segmentation is often driven by the recent progress in semantic segmentation. In \citep{kayalibay2017cnn}, authors employed a network architecture similar to 3D U-Net for bone and brain tumor segmentation. They combined multiple segmentation maps created at different scales which was shown to speed up convergence. However, this approach can be computationally expensive as they employed large receptive fields in convolutional layers. \citet{isensee2017brain} implemented a 3D U-Net that has been modified with respect to up-sampling pathways, normalization methods, number of filters, and the batch size, enabling training with large image patches and capturing contextual information that leads to segmentation performance improvements. In a more recent work \citep{chen2018s3d}, a separable 3D U-Net consisting of sparable 3D convolutions was proposed. Their S3D-UNet architecture fully utilizes the 3D volumes via the use of several 3D U-Net blocks. \citet{isensee2018no} argue that a well-designed U-Net architecture is competent in generating state-of-the-art segmentation maps without the need for significant architectural modifications and that enhancements proposed in prior literature provide no additional benefit. It should be highlighted that the winning contributions of Brain Tumor Segmentation (BRATS) challenge in 2019 \citep{jiang2019two} and 2020 \citep{isensee2020nnu} have also adopted U-Net-based architectures. \citet{jiang2019two} utilized a two-stage cascaded U-Net and \citet{isensee2020nnu} employed the nnU-Net architecture \citep{isensee2019automated} which was initially developed as a general-purpose network for segmentation following a U-Net.

\subsection{Deep Generative models}

Supervised learning methods require large manually annotated data sets and do not generalize well for previously unseen pathological appearances. Alternatively, deep generative models facilitate unsupervised training and provide a mathematically grounded framework for learning hidden structures and complex distributions from unlabeled data. Here we briefly discuss two main subsets of deep generative models, variational autoencoders (AEs) \citep{kingma2013auto} and generative adversarial networks (GANs) \citep{goodfellow2014generative} and their applications in the realm of biomedical imaging \citep{salakhutdinov2015learning, yi2019generative}.

\begin{figure*}[ht!]
    \centering
    \includegraphics{images/VAE.png}
    \caption{Reconstruction of a healthy brain MRI using a VAE model with Multivariate Gaussian assumption.}
    \label{fig:vae}
\end{figure*}

\subsubsection{Variational Auto-encoders}

An autoencoder (AE) is composed of an inference network (encoder) that learns a mapping from the high-dimensional input $\textbf{x} \in \mathcal{X}$ to a lower-dimensional latent representation $\textbf{z} \in \mathcal{Z}$, and a generator network (decoder) that reconstructs the data in latent space to a reconstruction $\textbf{x}^\prime$, where the input space is $\mathcal{X}=\mathbb{R}^D$ and the latent space is $\mathcal{Z}=\mathbb{R}^d$. VAEs provide a probabilistic interpretation for variables in latent space by projecting input data onto a distribution. The prior distribution in the latent representation is typically a multivariate Gaussian, denoted by $p_\theta (\mathbf{z}) = \mathcal{N}(0,\mathbb{I}_d)$. The conditional distribution $p_\theta (\mathbf{x} \, | \, \mathbf{z})$ parametrized by $\theta$ represents the likelihood of generating a true data sample, given the sampled latent vector, which is usually defined as $p_\theta (\mathbf{x} \, | \, \mathbf{z})=\mathcal{N}(\mathbf{x} \, | \, \mu_\theta (\mathbf{z}), \mathbb{I}_D \, \sigma^2_\theta (\mathbf{z}))$ . The corresponding posterior distribution $p_\theta(\mathbf{z} \, | \, \mathbf{x})$ is analytically intractable and hence it is approximated by a variational distribution $q_\phi(\textbf{z} \, | \, \mathbf{x})$, parametrized by $\phi$. In practice, the probabilistic encoder parameterizes the latent distribution and maps input data onto a mean $(\mu)$ and variance $(\sigma)$ vector which are the parameters of the multivariate Gaussian. Latent distribution is then randomly sampled to feed into the probabilistic decoder that parameterizes the likelihood distribution $p_\theta(\mathbf{x} \, | \, \mathbf{z})$ and projects the latent space attributes back to the original domain space.

Owing to their ability to model the distribution that characterizes data, these models enable density-based anomaly detection and have received significant attention in clinical imaging. In MRI analysis, VAEs typically address detection of brain pathology via an unsupervised abnormality detection approach, where the distribution of healthy brain anatomy $\mathbf{x} \in \mathcal{X}_{healthy}$ is modeled, which enables detection of pathologies as outliers of the distribution \citep{baur2021autoencoders, chen2018deep}. In \citep{chen2018unsupervised}, authors investigated the performance of VAEs and adversarial auto-encoders on unsupervised lesion segmentation where they used a prior distribution of healthy brain tissues to detect any abnormalities. They further proposed a latent constraint to improve latent space consistency.  \citet{baur2018deep}, presented a spatial VAE based deep generative model that captures the global context of MR slices instead of local patches. A schematic illustration of brain MRI reconstruction with VAE model based on multivariate Gaussian assumption is presented in Fig. \ref{fig:vae}.

\subsubsection{Generative adversarial networks}

Initially introduced for image synthesis from noise, GANs made a huge impact on computer vision. Composed of a generator that generates new data by learning a latent representation of the training data from a prior distribution, and a discriminator that discriminates between real and synthetic data, the network is designed to compete against the two components during training, which is referred to as adversarial training. The same notion can be applied in segmentation by devising a segmentation network in place of the generator such that the discriminator distinguishes the input segmentation mask between the manually annotated ground truth and the segmentation map predicted by the network (Fig. \ref{fig:gan}). This forces the segmentation network to generate segmentation maps that are more anatomically plausible. In the seminal work by \citet{luc2016semantic}, the authors applied an adversarial training approach for semantic segmentation, which is arguably the first study to utilize adversarial training to learn semantic segmentation models. They trained a convolutional net coupled with an adversarial network that can discriminate between a segmentation map from ground truth and model prediction, thus, facilitating the regularization of the segmentation and the results showed improved accuracy. In the case of tumor segmentation, \citet{kamnitsas2017unsupervised} explored the performance of adversarial networks on domain adaptation and showed that their approach is robust to domain shift and does not require manual annotation of labels when applied to new data in the testing phase. This strategy of employing GANs for brain tumor segmentation was later followed by many other studies \citep{yu20183d, nema2020rescuenet} incorporating several modifications. Notable is the \emph{Segan} \citep{xue2018segan} introduced for medical image segmentation where they show that single scalar output of real or fake in classic GANs is ineffective and proposed an adversarial critic network with a multi-scale $L_1$ loss function.

\begin{figure*}[t!]

    \includegraphics[width=\textwidth]{images/GANs.png}
    \caption{Adversarial training for tumor segmentation. Segmentation network generates segmentation maps and discriminator distinguishes between the manually annotated and predicted segmentation maps.}
    \label{fig:gan}
\end{figure*}

\textit{summary:} Despite the demand for a large amount of data and the lack of model interpretability, medical image segmentation has seen a massive influx of methods associated with deep learning methods. Different strategies have been proposed in past literature to optimize the task of segmentation which has led to significant improvements in the development of fully automated diagnosis systems.

\section{Integrated Statistical and Probabilistic Deep Learning methods for MRI Segmentation}
\label{PDL}

There has been a recent surge of interest in approaches that leverage deep probabilistic models in segmentation. These methods are a step toward bridging the gap between traditional statistical methods of segmentation and modern deep learning-based segmentation, which enables the implementation of models that significantly benefit from both streams. Deep and statistical learning based integrated methods have great utility in a multitude of tasks, some of which are briefly discussed here.

\textit{Data set Limitations/ Scarce Annotations}: Probabilistic deep learning has proved to be useful when training with limited data and sparse annotations. \citet{dalca2019unsupervised} combined probabilistic atlas-based segmentation with deep learning to develop an unsupervised brain MRI segmentation model. They showed that their approach achieves promising results in terms of accuracy without the need for annotated data at test time and thus computationally efficient. \citet{ito2019semi} modeled the tumor segmentation as a semi-supervised learning problem based on a CNN using a small number of labeled images and a large number of unlabeled images where they use image registration to attach a pseudo-label for every voxel.  Since the true labels of the unlabeled images were unknown, they merged a probabilistic framework in their CNN model using the EM algorithm. While E-step performs a maximum a posteriori estimation for the hidden true label of unlabeled images, the M-step updates the parameters of the CNN model based on the estimated true labels. Their experimental results suggested that their approach achieves accurate and stable segmentation than the models trained relying only on DNN-based methods.

\begin{figure*}[ht!]
    \centering
    \includegraphics{images/cnn_crfs.png}
    \caption{Schematic illustration of post segmentation refinement with a fully connected CRF that operates on the entire segmentation map generated by the deep network to refine coarse voxel-level predictions.}
    \label{fig:crf}
\end{figure*}

\textit{Segmentation Refinement}: Voxel-based classification methodologies sometimes result in spurious responses and therefore, graphical-based models such as MRFs \citep{shakeri2016sub} and CRFs \citep{kamnitsas2017efficient, lafferty2001conditional, chen2017deeplab, dou20173d, zhao2018deep} are often integrated into likelihood maps generated by CNNs as post-processing to refine the segmentation which acts as label regularizers (Fig. \ref{fig:crf}). CRFs are probabilistic models that consider the contextual information, which allows to model voxels neighborhoods that are arbitrarily large. More specifically, CRFs model the conditional probability distribution of target pixel labels given the prediction distribution for each pixel. There are several different variants of post-segmentation refinement strategies with CRF such as fully-connected CRF (FC-CRF) that operates over the whole segmentation map, locally connected CRF that smoothens local patches, and CRFs formulated as recurrent neural networks (RNN-CRF) \citep{zheng2015conditional} that allow end-to-end training with the segmentation network. In the realm of tumor segmentation,  \citet{kamnitsas2017efficient} used a 3D CNN model in conjunction with a 3D fully connected CRF for segmenting brain lesions from 3D medical scans. While the 3D CNN model generates soft segmentation maps, CRF acts as a post-processing step that produces final refined segmentation labels. Instead of applying CRFs as a post-processing step of FCNNs, \citet{zhao2018deep} suggested integration of FCNNs and CRFs as one deep network. They used 2D image patches and image slices in axial, coronal, and sagittal views, and trained three models, which were then combined for segmentation of brain tumors and their results indicated that FCNN-CRF combination improves segmentation robustness.

\textit{Uncertainty Quantification:} There are several other areas such as uncertainty estimation where the integration of traditional statistical learning methods with deep learning becomes beneficial. Quantifying deep network prediction uncertainty arising from data set limitations or intrinsic biological noise is often necessary. Prior studies have investigated uncertainty quantification with Bayesian neural networks \citep{kendall2015bayesian, gal2016dropout} and their applicability to biomedical imaging in the context of brain segmentation \citep{jena2019bayesian, roy2019bayesian, kwon2020uncertainty}. In \citep{jena2019bayesian} authors show that uncertainty can be estimated analytically at test time through a Bayesian DL framework. Their experimental results on multiple biomedical imaging data sets indicated improved segmentation and calibration performance. Thus, prior research suggests that employing Bayesian deep nets for brain  segmentation is a promising direction for obtaining uncertainty estimates and the robustness level required for clinically deployed automated systems.

\textit{Generalizability:} Some recent studies \citep{agn2019modality, cerri2021contrast} have indicated that integrated methods can successfully be applied to improve generalizability.  For example, \citet{cerri2021contrast} presented a method for simultaneous segmentation of whole-brain and lesions by utilizing both a generative model and a deep net and demonstrated their approach is contrast adaptive.

In summary, it could be argued that the future path for medical decisions with computer-aided systems lies in the merging of statistical methodologies with deep learning-based methods.

\section{ Limitations, challenges and future directions in biomedical image analysis}

\subsection{Limitations and challenges}

Medical image segmentation encompasses a broad set of challenges including complex and subtle surrounding boundaries of organs, lack of sufficient level of the region uniformity and similarity, low contrast and intensity inhomogeneity, image noise, partial volume effect, and other artifacts that impede precise identification of abrupt variations between organs of interest. Class imbalance, data acquisition, and 3D nature of data poses additional challenges, which are briefly described here.

\emph{Class imbalance} presents one of the biggest difficulties in segmentation. For example, the tumor region typically constitutes only up to 15\% of the brain, and tumor sub-regions are even smaller, and thus the class distribution is dominated by the background voxels when compared with the foreground voxels of tumor tissues. Prior work propose several strategies to address imbalanced distributions which include applying a weight map to the categorical cross-entropy loss function or incorporation of different loss functions such as focal loss \citep{lin2017focal}. A recently introduced dynamically weighted balanced loss \citep{fernando2021dynamically} focuses on dynamically adjusting class weights to address the class imbalance which also leads to improved calibration. In the context of tumor segmentation, weighted dice loss is a commonly adopted approach \citep{milletari2016v}. Devising algorithms that are adept at dealing with class imbalance is imperative in medical image analysis.

Another primary limitation in biomedical imaging is the \emph{acquisition of labeled data}. While computer-aided systems make the diagnosis process more efficient, supervised deep architectures require access to large, labeled data sets. Manual annotation requires domain expertise, and it is time-consuming. Since small data sets lack generalizability, deployment of semi or unsupervised architectures may be more effective.

\emph{3D neuroimaging data} are memory intensive. In order to utilize contextual information in brain volumetry on MR images, 3D deep networks are typically deployed, which uses extensive memory. Previous research adopts different techniques to address this issue which include training on 2D slices or image patches and employing multi-path models. However, regulating the trade-off between leveraging the spatial context of neighboring voxels and computational complexity continues to be a challenge.

\subsection{Future Directions}

The transition from scientific research to clinical practice depends on the trustworthiness of computer-aided diagnosis systems and raises profound questions about reliability, uncertainty, and robustness. For example, how to detect when the computational algorithms get it wrong? Can we predict when the machine learning model fails, and how to make the algorithm robust to changes in real-world conditions and clinical data? These research questions are of central interest in safety-critical medical applications where accuracy is integral. Here we briefly discuss some of the critical challenges and potential future directions in medical image analysis.

\begin{itemize}
\item Learning the right features: The performance of the diagnosis system should not be influenced by the variability across different scanners, settings of the image acquisition, or other clinical conditions of patients. Learning discriminative features which are generalizable representations across data sets is an active area of research, however, until substantial progress is made in robustness research, care should be taken when relying on these strategies where precision is vital.

\item Knowing when the model does not know: Quantifying uncertainty in tumor segmentation is indispensable in clinical decision making \citep{begoli2019need, jungo2019assessing}. While deep learning-based approaches have achieved remarkable success performance-wise, their practical applicability is limited as models do not produce a measure for prediction uncertainty. We expect the research on uncertainty estimation in neuroimaging to increase in the near future.

\item Detecting when an automated system fails: Deep network based methods are prone to overfitting and hence evaluating the level of accuracy on new clinical data in the absence of ground truth is crucial in automated diagnosis. Methods are required to identify when the system fails and to evaluate the actual performance after implementation when a reference segmentation by an expert is inaccessible. This has been previously evaluated only to a very limited extent \citep{valindria2017reverse}. Future efforts should further explore this issue before clinical adoption of automated systems.

\item Going beyond human-level performance: The ultimate goal in computer-aided medical screening is to surpass human-level performance. Cancer histopathology reads in biomedical imaging requires expert knowledge, and it may subject to annotation bias while leading to a lack of agreement among human experts and therefore identifying the exact ground truth segmentation could be challenging. Synthesis of ground truth via adversarial learning appears to be a promising research direction in this context.
\end{itemize}

\section{Conclusion}

Precise tumor delineation is imperative for accurate assessment of the relative volume of lesion sub-components. A comprehensive review is conducted  on the state-of-the-art brain tumor segmentation of 3D MRI ranging from traditional statistical approaches to modern deep learning. We covered the fundamentals, discussed the methodological foundations, and addressed their potentials and limitations. The review conducted leads to the following conclusions: deep learning, being capable of learning high-level feature representations automatically, has emerged as a powerful mechanism in automated volumetric medical image segmentation. Moreover, it has been observed that engrafting statistical methodologies in deep networks improve biomedical image segmentation. Thus, volumetric 3D MRI segmentation at the intersection of statistical modeling and deep learning can be considered as a more effective alternative to the methods which are purely statistical or deep learning based. While these automated methodologies improve the qualitative expertise of clinicians and facilitate accurate volumetric tumor delineation and outcome prediction, they mostly remain in the pre-clinical research domain. Although studies have been conducted by many researchers for 3D volumetric tumor segmentation, difficulties associated with biomedical imaging are still insufficiently studied and the deployment of robust automated systems is a challenge for future research to explore. Future studies could fruitfully investigate these issues further by more systematic and theoretical analysis.

\begingroup
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\bibliographystyle{model2-names.bst}\biboptions{authoryear}

redpajama_set_name: RedPajamaArXiv


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The Official Home of Westwood Regional High School Football - Donnie Cimino Jr.
Donnie Cimino Jr., Class of 2011 sheds light on the college selection process, how athletics has helped him standout in the classroom, and what he misses most about his playing days as Captain of the Cardinals football and baseball teams.
Q: With your excellent academic and athletic credentials at WWRHS you had many options for college – what made you select a top business school like Wesleyan University?
A: I had a long recruiting process and for a long time I didn't know where I was going to go and what I was looking for. Eventually I valued the academic level of a university as the deciding factor for my college decision which led me to Wesleyan. I also knew that I could continue to play two sports here which definitely influenced me. Sure, I had other opportunities to play either sport at bigger schools but, in the end, Wesleyan was where I felt most comfortable. Looking back, I'd say that ultimately it comes down to how you feel at the school: going there, meeting students and trying to picture yourself there – that's when you know.
Q: A recent study concluded that athletics serve as a positive motivational factor for students and that THERE IS a direct relationship between participation in athletics and academic success. Do you agree?
A: I definitely agree that athletics play a major part in academic success. In sports, we learn that vale of hard work, focus passion, etc. These values easily translate to the classroom. In today's culture, you have to fulfill the student part of student athlete in order to compete for scholarship money so there is a huge incentive in doing well in both school and athletics.
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A: At Westwood, most of my friends were two, some even three-sport athletes so my schedule was similar to the kids I was seeing every day. In college, however, I'm one of the few two-sport athletes, which makes me have to be very independent and self-motivated. I have to keep myself regimented in order to go to class, workout, go to practice and then do homework or study for whatever academic responsibilities I have. Westwood gave me a solid foundation for this discipline.
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More about Donnie Cimino Jr.


There is no danger in the projection of the Astral Body, because everybody is projected in their Astral Body during normal sleep. Therefore, whosoever wants to awaken their consciousness during normal sleep must know the clue of discernment.
During normal sleep, every human being wanders in the internal worlds with their consciousness asleep. During normal sleep, the Soul, enveloped by its Astral Body, abandons the physical body. This is how the Ethereal Body is able repair the dense physical body.
We awaken from our natural sleep when the Soul enters into the physical body. In the internal worlds, the Souls are occupied repeating their same daily chores; there, they buy and sell as in the physical world.
During normal sleep, the Souls of the living and the Souls of the dead coexist together. In the internal worlds, we see everything as in the physical world, i.e. the same sun, the same clouds, the same houses of the city: everything looks the same.
Now, our Gnostic disciples will understand why the souls of the dead do not accept that they are physically dead. Likewise, our disciples will comprehend why the Souls of the living buy and sell, work, etc., during their normal sleep.
By consciously projecting ourselves in the Astral Body, we can know about the mysteries of life and death, since every human being is unconsciously projected in the Astral Body during normal sleep. Therefore, if we awaken the consciousness during normal sleep, then we can know about the great mysteries of life and death.
If while walking on a given street you unexpectedly find a friend or see objects that attract your attention, then perform a little jump with the intention of floating; naturally, logic says that if you float, it is because you are wandering outside of your physical body. However, if you do not float, it is because you are doing the jump with your physical body.
During normal sleep, within the internal worlds, it so happens that we act the same way as we would within the body of flesh and bones, and if we add to this the fact that we see everything the same way as when we are in the physical world, then we will comprehend that it is only if we float or fly that we will be aware of the fact that we are in our Astral Body; we then achieve the awakening of our consciousness.
To that effect, this exercise must be practiced at every moment during the vigil state while in the presence of any intriguing matter, since what we perform during the vigil state we repeat during normal sleep. Thus, when through our subconsciousness we repeat this practice during normal sleep, then when performing the jump, the outcome will be that we will float in the Astral Body. This is how our consciousness will awaken and filled with happiness we will say: "I am in my Astral Body...!"
Thus, we can direct ourselves to the Holy Gnostic Church in order to converse with the Angels, Archangels, Seraphim, Prophets, Masters, etc. This is how we receive instruction from the great Masters of the White Lodge. This is how we can travel in the Astral Body throughout the infinite.
So, we do not need to destroy our minds with so many books and theories, since within the internal worlds we can receive the teachings from the Masters.
When awakening from normal sleep, disciples must exert themselves to remember everything that they saw and heard during their normal sleep.
It is also necessary that our disciples learn how to interpret their internal experiences. To that effect, study the book of Daniel in the Bible; there, you will learn how to interpret internal experiences.
The slumber state and memory are the powers that allow us to know the great mysteries of life and death.


text:
The Theft and Killing of Maya
nathanwinograd.substack.com
Today is the anniversary of PETA's notorious crime
Nathan J. Winograd
To listen to an audio version of Why PETA Kills, my book, which tells the story of Maya and those of over 30,000 other animals PETA has put to death, subscribe on Substack by clicking here.
On October 18, 2014, two PETA representatives backed their van up to a home in Parksley, VA, and threw biscuits to Maya, who was sitting on her porch. They were hoping to coax her off her property and give PETA the ability to claim she was a stray dog "at large" whom they could therefore legally impound.
Maya refused to stay off the property and after grabbing the biscuit, ran back to the safety of her porch. One of the PETA representatives went onto the property and took Maya. Within hours, Maya was dead, illegally killed with a lethal dose of poison.
A PETA spokesperson claimed Maya was killed by "mistake," and defying credulity, explained that the same PETA representative who had earlier sat on the porch with Maya's family talking to them about her care and who was filmed taking Maya from that same porch mistook her for a different dog. The "apology" was not only a devastating admission of guilt, but evidence that killing healthy animals was business as usual for PETA employees — so commonplace that the only excuse PETA could offer for Maya's death was that in taking her life, a PETA representative had mistaken her for another healthy animal they had decided to kill. Was it likewise a "mistake" that five other animals ended up dead from the same trailer park and on the same day, too?
Though PETA claimed to be "devastated" by Maya's death, the claim was contradicted by the facts, and, given its timing, motivated not by honesty, transparency, or genuine contrition, but political necessity as the Virginia Department of Agriculture had opened an investigation into Maya's killing and Virginia's governor was weighing whether to sign into law a bill overwhelmingly passed by the legislature aimed at protecting animals from PETA.
As public outrage over PETA's killing of Maya spread, a former PETA employee came forward, shedding even more light on how disingenuous PETA's claim of being devastated at the killing of Maya was. Explaining that killing healthy animals at PETA was not an anomaly but rather "standard operating procedure," Heather Harper-Troje, a one-time PETA field worker, publicly uncovered the inner workings at PETA as no former employee ever had. "I know from firsthand experience that the PETA leadership has no problem lying," she wrote. "I was told regularly to say whatever I had to say in order to get people to surrender animals to me, lying was not only acceptable, it was encouraged." The purpose of acquiring these animals, according to Harper-Troje, was "to euthanize the[m] immediately."
Maya's family would ultimately sue PETA, alleging conversion of their dog (theft), trespass, and intentional infliction of emotional distress. PETA, in turn, asked the court to throw out the lawsuit based on several questionable claims.
First, PETA argued that Maya was legally worthless because she was not licensed, citing an 1887 law that required a dog "to be properly licensed as a condition of being deemed personal property." Putting aside the irony of a supposed "animal rights" group arguing that Maya had no value, the statute they cited was repealed in 1966. It had not been the law in half a century.
Alternatively, PETA argued that Maya had no value beyond the cost of replacement for another dog. In other words, PETA's position was that Maya was like a toaster. If you break it, you just throw it away and get a new one.
Third, PETA argued that they had permission to enter the trailer park by the trailer park's owner to remove community cats so they cannot be guilty of trespass for entering a private residence in that trailer park to kill a family's dog.
Fourth, PETA argued that the theft and killing of Maya was not "outrageous," a prerequisite to the awarding of punitive damages.
Finally, in an argument reeking with racist overtones, PETA demanded to know if Maya's family was legally in the U.S.
After arguing and losing most of the pre-trial motions — including rulings that the family's immigration status was not relevant to the theft and killing of their dog and that such conduct was, indeed, "outrageous" — as well as facing the specter of being forced to turn over records and testify under oath about PETA's inner workings, and perhaps trying to put the publicity behind their killing of Maya behind them, PETA settled the case, paying Maya's family $49,000.
But the condemnation only grew following a series of articles I wrote about Maya's killing, which ultimately led to the publication of Why PETA Kills, my book. Why PETA Kills tells Maya's story and that of over 30,000 others who have also died at their hands, a number that continues to increase by the thousands every year. In 2020, for example, PETA put to death 1,119 out of 1,542 cats. Another 407 went to pounds that also kill animals. Historically, many of the kittens and cats PETA has taken to those pounds have been killed, often within minutes, despite being young (as young as six weeks old) and healthy.
Not only do those records prove the lie that all of the animals PETA rounds up to kill are "suffering" as they now claim, but if those cats and kittens were killed or displaced others who were killed, that puts the overall cat death rate as high as 99%. They only adopted out 16 cats, an adoption rate of 1% despite millions of supporters, a staff of hundreds, and revenues of $66,277,867.
A healthy mother cat and her two equally healthy kittens were given to PETA by a veterinarian who was trying to find them homes and was told by PETA employees that they would have no problem adopting them out. Instead, the PETA employees killed them within minutes in the back of a van.
While dogs fared a little better, 600 out of 1,052 were put to death. Less than 2% were adopted out. PETA staff also killed 83% of other animal companions.
Puppies killed by PETA in the back of a van — a donor funded slaughterhouse on wheels.
To date, PETA has killed 42,573 dogs and cats and sent thousands more to be killed at local pounds, that we know of. The number may be many times higher. According to Harper-Troje,
I was told regularly to not enter animals into the log, or to euthanize off-site in order to prevent animals from even entering the building. I was told regularly to greatly overestimate the weight of animals whose euthanasia we recorded, in order to account for what would have otherwise been missing 'blue juice' (the chemical used to euthanize); because that allowed us to euthanize animals off the books.
Following the release of Why PETA Kills, PETA filed a run-of-the-mill defamation lawsuit targeting The No Kill Advocacy Center (NKAC), my organization, and me in an attempt to intimidate me and others into silence. But they didn't sue me directly, as they knew it would ultimately fail: truth, after all, is a defense to defamation. More importantly, they were fearful of doing so as suing me would be dangerous for PETA. Not only would it allow me to force the deposition (e.g., testimony under penalty of perjury) of Ingrid Newkirk, the architect of PETA's killing, as well as others at PETA who do the actual killing, but it would allow me to seek documents from PETA that would augment what public records and the PETA employees I spoke with already revealed: that PETA intentionally seeks out animals to kill and that the majority of those animals are healthy and adoptable. Absent a court case, as a private organization, PETA is not required to release that information under state freedom of information laws and has ignored my requests to do so.
Instead, PETA named me as a "co-conspirator," but not as a defendant in the complaint, a procedural gimmick that gave PETA the ability to issue a subpoena in order to (try to) seek the names of PETA employees who, fearing retribution, spoke to me on condition of anonymity; information that was used to corroborate newspaper articles, on the record sources, government documents, testimony and information from civil and criminal cases against PETA, videotape evidence, and admissions of killing by PETA officials. At the same time, that procedural ploy would prevent me from demanding documents and depositions of PETA leadership and staff in return.
But PETA's legal tactic failed to take into account two important factors. First, I would never reveal my confidential informants. Second, I did not have to legally do so, given my First Amendment rights as a journalist. In an attempt to force me to, however, PETA filed a motion in court to compel the disclosure of the names, claiming that as an animal advocate, I was not entitled to the protection of the First Amendment, a point of view they hypocritically reject for themselves and which, the Reporters Committee for Freedom of the Press, the organization founded to protect the rights of journalists by legendary Washington Post editor Ben Bradlee of Pentagon Papers fame, called "alarming."
In assisting me with my legal defense, the Reporters Committee noted,
We're concerned about the legal efforts to require Nathan Winograd to reveal the confidential sources for his reporting on PETA's practices. Both the First Amendment and California's constitution protect those who engage in journalistic activity… and any efforts to limit these protections should be alarming for all newsgatherers.
Threatened with a fine and jail time if I refused to reveal my sources, my lawyer argued that California Courts have consistently ruled that the First Amendment protects "investigative reporting." And investigative reporting includes "authors such as Lincoln Steffens and Upton Sinclair [who] exposed widespread corruption and abuse in American life. More recently, social critics such as Rachel Carson, Ralph Nader, Jessica Mitford, and others have written books that have made significant contributions to the public discourse on major issues confronting the American people."
As my attorney argued,
Every crusading journalist in that pantheon of heroes cited by the court would have flunked PETA's putative 'journalism' test, for their journalism was inseparable from their advocacy. Indeed, Sinclair and Nader took their advocacy onto the campaign trail and sought public office. Winograd and NKAC's intertwined investigative and advocacy work are no different from that done by Nader and his nonprofit Public Citizen.
The court agreed. Despite PETA's hiring of one of the most expensive law firms in the world, the Court denied PETA's motion, not only providing me and, more importantly, the animals an important victory, but breaking new ground by extending First Amendment protections to new/non-traditional media, such as bloggers.
Following that ruling, another whistleblower from inside PETA openly came forward and confirmed what my sources had revealed: that PETA staff lie to people in order to acquire their animals to kill, kill despite adoption alternatives, and indoctrinate people to kill in a cult-like atmosphere she described as "terrifying."
[A]s most new PETA employees are blooming animal rights activists, freshly plucked from college and determined to do whatever it takes to succeed in this demanding, low-paying activist world, PETA's methodology of indoctrination is quite successful. These employees soak it all in like a sponge, as I did at the age of 21 when I started there, and begin to spout the organization's soundbites at every turn. They will start to do so so naturally that they can't see where they themselves end and the organization begins.
"Ultimately," wrote Laura Lee Cascada, a PETA field worker whose job included rounding up animals to kill, "the culture was terrifying and desensitizing — and I gradually felt that my view of death, of taking animals' lives, was being warped, my emotions being stripped away."
Like Heather Harper-Troje before her, Cascada's chilling account described the method whereby employees are intimidated and emotionally manipulated into participating in the killing of animals, an act that came to be euphemistically called to "take care of" an animal (the words "killing" and even "euthanasia" are not used). Employees "were forced to participate in euthanasias they didn't believe in" or "were fired because they refused to do so."
[I]f an employee, like many animal rights advocates who believe in the rights and autonomy of each individual animal, wanted to critically assess whether a euthanasia decision was truly the best thing for an individual animal in his or her unique circumstances, there was a real, true fear of being branded as an advocate for hoarding or a secret supporter of the enemy. Thus, speaking up could have meant being booted from the tribe.
Cascada also described numerous examples of healthy animals who were killed for the "good of all animals":
I rescued and cared for a pair of birds from a cruelty case for weeks, bonding with and growing to love them. When the decision was made to euthanize the boy because of a debilitating medical condition, the girl was also euthanized because it was thought that she would be lonely without him. She was one of those lumped into the 'unadoptable' category PETA brushes past as it explains its euthanasia statistics each year. I was expected and required to swallow my emotions for her for the good of all animals. I was expected to welcome her death as a positive outcome in order to maintain my employment.
Another time, I rescued an unloved dog whose body condition and personality were unremarkable, meaning there was no immediate indication for euthanasia. I quickly heard from my mom that she'd be interested in adopting him. I excitedly emailed the manager of the shelter to make this offer but never received a reply. A few days later, I checked in with her and was told that he had already been killed.
She recounted being told to lie to people to acquire animals to kill and getting chastised for trying to find them homes. For example, Cascada wrote that she,
[R]esponded to a call from a concerned woman who'd found an abandoned days-old kitten under her porch. When I came to pick up the kitten, I had her sign a generic give-up form that spelled out that euthanasia was a possibility. But I was instructed to repeatedly convey that we would do our absolute best, and so that's what I said, even as the woman described her careful search for an organization she knew would work around the clock to help this tiny being pull through. It was my job to make sure I did not leave without that cat — that I said whatever necessary for the woman not to change her mind.
The entire way back to PETA's Norfolk, Virginia, headquarters, I sobbed, petting the infant cat in my lap, telling her things would all be OK, even though in my gut I knew it wouldn't, that she never really had a chance. I even began plotting out how I might take a detour and deliver her to a rehabber instead. But how could I explain a missing kitten to the woman waiting with the needle? I couldn't, so I complied without a word.
As a result of coming forward, she reported that she was,
[C]ontacted by individuals from all over the country expressing their gratitude, and their own fear, about speaking out about their experiences. People who worked at PETA and were forced to lie about euthanasias, people who were forced to euthanize animals they loved as a condition of their employment, and people who were told by leadership that they were worthless. There are dozens, and maybe hundreds, of us. Most are still afraid to break their silence.
PETA's lawsuit would ultimately collapse, but four important things came out of my victory against them. First, as noted above, it extended First Amendment protections for investigative journalism to animal rights bloggers and other new media for the first time.
Second, it demonstrated that PETA may have deep pockets and has no qualms about misusing the court system in an attempt to intimidate people into silence, but their strategy will always be limited by the fact that depositions and the witness stand could compel employees, including Newkirk, to testify under penalty of perjury. Consistent with overwhelming evidence already available, such testimony would be damning, and PETA knows it. If people stand up to PETA's donor-funded intimidation tactics, rather than cower to them, PETA will invariably back down.
Third, their empty saber rattling may have led to another whistleblower openly coming forward.
Fourth and finally, it led me to Ralph.
As fate would have it, on the way to court in the case, my wife and I came upon a little dog who had been hit by a car, bleeding in the gutter. Wrapping him in a coat, we rushed him to the nearest emergency veterinary hospital where he was given the care he needed, including pain medication.
After recovering from his injuries at our house, we found him a loving, new home, consistent with our belief in the ethical treatment of animals. Were it not for PETA's meritless lawsuit, we would never have found him.
For obvious reasons, I am grateful that it was us and not PETA representatives who saw him on the way to the courthouse. If PETA had gotten to him and history is any guide, Ralph would no longer be alive, put to death with a lethal dose of poison.
Because despite all we may still not know about PETA, this much is certain: PETA is letting loose upon the world individuals who not only believe that killing is a good thing and that the living want to die, but who are legally armed with lethal drugs which they have already proven — over 42,000 times — that they are not averse to using.
Why PETA Kills is available on Amazon. Substack subscribers can listen to it as an audiobook for free by clicking here.
© 2023 Nathan J. Winograd

redpajama_set_name: RedPajamaCommonCrawl


Cnephalocotes nitidithorax Simon, 1915a: 479 (Dm).
Silometopus nitidithorax Simon, 1926: 355, 487, f. 624 (m).
Silometopus nitidithorax Bosmans et al., 2009: 23, f. 13-19 (m, Df).
Silometopus nitidithorax Déjean, Danflous & Bosmans, 2014: 5, f. 3 (m).


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Short hair, pony tails, blonde/light brown hair color.
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Google wants to be your food matchmaker to help you spend more time eating and less time searching. It uses artificial intelligence to predict the places you'll like.
"What do you want to eat?" One person says.
"I don't know, what do you want to eat?" The other replies.
The questions continue like a game of Pong until they both are starving. The development of food apps has saved dinner dates everywhere, but somehow it's still difficult to figure out where the best place is to grab a bite.
Google Maps has stepped up its game in 2018 with the Explore feature that uses artificial intelligence to help you find the best places to eat and drink no matter where you are in the world.
The features in Explore have been expanding recently on both the iOS and Android apps. One of the most interesting features is the percentage match icon to predict how likely you are to enjoy nearby restaurants, based on past searches and places you've frequented.
The Explore tab is also based on tastemaker choices, local expert info, Google algorithms, and trusted publishers like The Infatuation. And, the app compiles the Foodies List to show users what's trending where they are.
It can even keep track of your progress at restaurants. For example, if you're looking to try all the steakhouses in a certain area, the app will let you know how many you have left.
People joke about marrying food, but the app definitely wants users to find their perfect food match. Tapping a location will numerically score the venue and give users reasons why they might like it.
"Our new 'match' feature will help you find your one true love. And by love, we mean your next favorite cheeseburger. Tap on a food or drink spot to see how likely you are to enjoy it based on your unique preferences--so you can spend more time eating and less time searching for places to go," Google said.
Google gathers information about the business, user preferences, and if they've previously rated it or put it on a list. Don't worry if you decide to go vegan, paleo, or gluten-free, the features adapt to evolving tastes.
The only thing worse than finding a place to eat, is getting all your friends there at the same time. Venues that look interesting can be added to a shortlist and shared with a group of your friends to vote on. After a consensus is reached, reservations and rides can now be organized in the app as well. Restaurant wait times are also available.
Google Maps' new features can also keep you up to date on the latest developments at your favorite venues. The app now lets you follow neighborhoods, restaurants, or bars to get alerts.
Google Maps is rolling out a new feature that attempts to match users with the perfect restaurant.
The feature adapts to evolving tastes, helps organize friend groups, and keeps users up to date on the newest food and venue info.


text:
Cispius thorelli est une espèce d'araignées aranéomorphes de la famille des Pisauridae.

Distribution
Cette espèce est endémique du Congo-Kinshasa. Elle se rencontre au Katanga.

Description
Le mâle holotype mesure .

Étymologie
Cette espèce est nommée en l'honneur de Tord Tamerlan Teodor Thorell.

Publication originale
 Blandin, 1978 : Études sur les Pisauridae africaines IX. Mise au point sur les genres Cispius Simon, 1898 et Charminus Thorell, 1899 (Araneae - Pisauridae - Pisaurinae). Revue de Zoologie Africaine, ,  (texte intégral).

Liens externes

Notes et références

Pisauridae
Espèce d'araignées (nom scientifique)
Faune endémique de la république démocratique du Congo

redpajama_set_name: RedPajamaWikipedia


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It's been 1159 days since your murder.
—It's been 699 days since he murdered you.
me. Always remember your voice. Always love you the most.
~"How are you?" She asks.
"I'm waiting for the day you shout out Fantastic," she smiles.
I mean, how would she know?


text:
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/**
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  String location();

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  String name();

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   * Return the content as InputStream.
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  InputStream inputStream();

  /**
   * Return the content as lines.
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  List<String> loadAsLines(Charset charset);

  /**
   * Return the content of this resource as a string.
   */
  String loadAsString(Charset charset);

}

redpajama_set_name: RedPajamaGithub


BEIJING, June 10 -- The Chinese mainland holds a positive and open attitude toward cross-Strait intercity exchanges with Taiwan as long as there is correct understanding of the nature of cross-Strait relations and city-to-city exchanges.
Ma Xiaoguang, spokesperson for the State Council's Taiwan Affairs Office, made the remarks Saturday in response to questions about an interview with Taipei Mayor Ko Wen-je, who made remarks on the annual city forum between Shanghai and Taipei, as well as the mainland-Taiwan relations.
Ko had said he would work actively to facilitate the exchanges between Taipei and Shanghai as long as the exchanges benefit people on both sides of the Taiwan Strait and are conducive to peaceful development across the strait.
Ma said the mainland had taken note of the reports of the interview. He said Shanghai and Taipei will take care of detailed arrangements for the annual city forum.


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