Laurent D. Cohen

Thomas Dagès, Laurent D. Cohen, Alfred M. Bruckstein

Traditional signal processing methods relying on mathematical data generation models have been cast aside in favour of deep neural networks, which require vast amounts of data. Since the theoretical sample complexity is nearly impossible to evaluate, these amounts of examples are usually estimated with crude rules of thumb. However, these rules only suggest when the networks should work, but do not relate to the traditional methods. In particular, an interesting question is: how much data is required for neural networks to be on par or outperform, if possible, the traditional model-based methods? In this work, we empirically investigate this question in two simple examples, where the data is generated according to precisely defined mathematical models, and where well-understood optimal or state-of-the-art mathematical data-agnostic solutions are known. A first problem is deconvolving one-dimensional Gaussian signals and a second one is estimating a circle's radius and location in random grayscale images of disks. By training various networks, either naive custom designed or well-established ones, with various amounts of training data, we find that networks require tens of thousands of examples in comparison to the traditional methods, whether the networks are trained from scratch or even with transfer-learning or finetuning.

Nicolas Makaroff, Laurent D. Cohen

When studying the results of a segmentation algorithm using convolutional neural networks, one wonders about the reliability and consistency of the results. This leads to questioning the possibility of using such an algorithm in applications where there is little room for doubt. We propose in this paper a new attention gate based on the use of Chan-Vese energy minimization to control more precisely the segmentation masks given by a standard CNN architecture such as the U-Net model. This mechanism allows to obtain a constraint on the segmentation based on the resolution of a PDE. The study of the results allows us to observe the spatial information retained by the neural network on the region of interest and obtains competitive results on the binary segmentation. We illustrate the efficiency of this approach for medical image segmentation on a database of MRI brain images.

Nicolas Makaroff, Théo Bertrand, Laurent D. Cohen

Leveraging geodesic distances and the geometrical information they convey is key for many data-oriented applications in imaging. Geodesic distance computation has been used for long for image segmentation using Image based metrics. We introduce a new method by generating isotropic Riemannian metrics adapted to a problem using CNN and give as illustrations an example of application. We then apply this idea to the segmentation of brain tumours as unit balls for the geodesic distance computed with the metric potential output by a CNN, thus imposing geometrical and topological constraints on the output mask. We show that geodesic distance modules work well in machine learning frameworks and can be used to achieve state-of-the-art performances while ensuring geometrical and/or topological properties.

Li Liu, Da Chen, Minglei Shu et al.

Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries. However, such a segmentation strategy cannot take into account the connectivity of the image edge features, increasing the risk of shortcut problem, especially in the case of complicated scenario. In this work, we introduce a new image segmentation model based on the minimal geodesic framework in conjunction with an adaptive cut-based circular optimal path computation scheme and a graph-based boundary proposals grouping scheme. Specifically, the adaptive cut can disconnect the image domain such that the target contours are imposed to pass through this cut only once. The boundary proposals are comprised of precomputed image edge segments, providing the connectivity information for our segmentation model. These boundary proposals are then incorporated into the proposed image segmentation model, such that the target segmentation contours are made up of a set of selected boundary proposals and the corresponding geodesic paths linking them. Experimental results show that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches.

Tao Chen, Dan Zhang, Da Chen et al.

Choroidal neovascularization (CNV), a primary characteristic of wet age-related macular degeneration (wet AMD), represents a leading cause of blindness worldwide. In clinical practice, optical coherence tomography angiography (OCTA) is commonly used for studying CNV-related pathological changes, due to its micron-level resolution and non-invasive nature. Thus, accurate segmentation of CNV regions and vessels in OCTA images is crucial for clinical assessment of wet AMD. However, challenges existed due to irregular CNV shapes and imaging limitations like projection artifacts, noises and boundary blurring. Moreover, the lack of publicly available datasets constraints the CNV analysis. To address these challenges, this paper constructs the first publicly accessible CNV dataset (CNVSeg), and proposes a novel multilateral graph convolutional interaction-enhanced CNV segmentation network (MTG-Net). This network integrates both region and vessel morphological information, exploring semantic and geometric duality constraints within the graph domain. Specifically, MTG-Net consists of a multi-task framework and two graph-based cross-task modules: Multilateral Interaction Graph Reasoning (MIGR) and Multilateral Reinforcement Graph Reasoning (MRGR). The multi-task framework encodes rich geometric features of lesion shapes and surfaces, decoupling the image into three task-specific feature maps. MIGR and MRGR iteratively reason about higher-order relationships across tasks through a graph mechanism, enabling complementary optimization for task-specific objectives. Additionally, an uncertainty-weighted loss is proposed to mitigate the impact of artifacts and noise on segmentation accuracy. Experimental results demonstrate that MTG-Net outperforms existing methods, achieving a Dice socre of 87.21\% for region segmentation and 88.12\% for vessel segmentation.

Chong Di, Shuwang Zhou, Da Chen et al.

The computation of minimal paths for the applications in tracking tubular structures such as blood vessels and roads is challenged by complex morphologies and environmental variations. Existing approaches can be roughly categorized into two research lines: the point-wise based models and the segment-wise based models. Although segment-wise approaches have obtained promising results in many scenarios, they often suffer from computational inefficiency and heavily rely on a prescribed prior to fit the target elongated shapes. We propose a novel framework that casts segment-wise tracking as a Markov Decision Process (MDP), enabling a reinforcement learning approach. Our method leverages Q-Learning to dynamically explore a graph of segments, computing edge weights on-demand and adaptively expanding the search space. This strategy avoids the high cost of a pre-computed graph and proves robust to incomplete initial information. Experimental reuslts on typical tubular structure datasets demonstrate that our method significantly outperforms state-of-the-art point-wise and segment-wise approaches. The proposed method effectively handles complex topologies and maintains global path coherence without depending on extensive prior structural knowledge.

Da Chen, Jean-Marie Mirebeau, Minglei Shu et al.

The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as Euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.

Da Chen, Jack Spencer, Jean-Marie Mirebeau et al.

The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the basic formulation of the dual-front models, the evolving contours can be considered as the interfaces of adjacent Voronoi regions. Among these dual-front models, a crucial ingredient is regarded as the geodesic metrics by which the geodesic distances and the corresponding Voronoi diagram can be estimated. In this paper, we introduce a type of asymmetric quadratic metrics dual-front model. The metrics considered are built by the integration of the image features and a vector field derived from the evolving contours. The use of the asymmetry enhancement can reduce the risk of contour shortcut or leakage problems especially when the initial contours are far away from the target boundaries or the images have complicated intensity distributions. Moreover, the proposed dual-front model can be applied for image segmentation in conjunction with various region-based homogeneity terms. The numerical experiments on both synthetic and real images show that the proposed dual-front model indeed achieves encouraging results.

Da Chen, Jean-Marie Mirebeau, Huazhong Shu et al.

The geodesic model based on the eikonal partial differential equation (PDE) has served as a fundamental tool for the applications of image segmentation and boundary detection in the past two decades. However, the existing approaches commonly only exploit the image edge-based features for computing minimal geodesic paths, potentially limiting their performance in complicated segmentation situations. In this paper, we introduce a new variational image segmentation model based on the minimal geodesic path framework and the eikonal PDE, where the region-based appearance term that defines then regional homogeneity features can be taken into account for estimating the associated minimal geodesic paths. This is done by constructing a Randers geodesic metric interpretation of the region-based active contour energy functional. As a result, the minimization of the active contour energy functional is transformed into finding the solution to the Randers eikonal PDE. We also suggest a practical interactive image segmentation strategy, where the target boundary can be delineated by the concatenation of several piecewise geodesic paths. We invoke the Finsler variant of the fast marching method to estimate the geodesic distance map, yielding an efficient implementation of the proposed region-based Randers geodesic model for image segmentation. Experimental results on both synthetic and real images exhibit that our model indeed achieves encouraging segmentation performance.