Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Multi Task Consistency Guided Source-Free Test-Time Domain Adaptation Medical Image Segmentation

Source-free test-time adaptation for medical image segmentation aims to enhance the adaptability of segmentation models to diverse and previously unseen test sets of the target domain, which contributes to the generalizability and robustness of medical image segmentation models without access to the source domain. Ensuring consistency between target edges and paired inputs is crucial for test-time adaptation. To improve the performance of test-time domain adaptation, we propose a multi task consistency guided source-free test-time domain adaptation medical image segmentation method which ensures the consistency of the local boundary predictions and the global prototype representation. Specifically, we introduce a local boundary consistency constraint method that explores the relationship between tissue region segmentation and tissue boundary localization tasks. Additionally, we propose a global feature consistency constraint toto enhance the intra-class compactness. We conduct extensive experiments on the segmentation of benchmark fundus images. Compared to prediction directly by the source domain model, the segmentation Dice score is improved by 6.27\% and 0.96\% in RIM-ONE-r3 and Drishti GS datasets, respectively. Additionally, the results of experiments demonstrate that our proposed method outperforms existing competitive domain adaptation segmentation algorithms.Comment: 31 pages,7 figure

Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D

We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups $SE(2)$ and $SE(3)$. In our distance approximations we consider homogeneous norms on nilpotent groups that locally approximate $SE(n)$, and which are obtained via the exponential and logarithmic map on $SE(n)$. In a qualitative validation we show that the norms provide accurate approximations of the true sub-Riemannian distances, and we discuss their relations to the fundamental solution of the sub-Laplacian on $SE(n)$. The quantitative experiments further confirm the accuracy of the approximations. Quantitative results are obtained by evaluating perceptual grouping performance of retinal blood vessels in 2D images and curves in challenging 3D synthetic volumes. The results show that 1) sub-Riemannian geometry is essential in achieving top performance and 2) that grouping via the fast analytic approximations performs almost equally, or better, than data-adaptive fast marching approaches on $\mathbb{R}^n$ and $SE(n)$.Comment: 18 pages, 9 figures, 3 tables, in review at JMI

Higher-Order Regularization in Computer Vision

At the core of many computer vision models lies the minimization of an objective function consisting of a sum of functions with few arguments. The order of the objective function is defined as the highest number of arguments of any summand. To reduce ambiguity and noise in the solution, regularization terms are included into the objective function, enforcing different properties of the solution. The most commonly used regularization is penalization of boundary length, which requires a second-order objective function. Most of this thesis is devoted to introducing higher-order regularization terms and presenting efficient minimization schemes. One of the topics of the thesis covers a reformulation of a large class of discrete functions into an equivalent form. The reformulation is shown, both in theory and practical experiments, to be advantageous for higher-order regularization models based on curvature and second-order derivatives. Another topic is the parametric max-flow problem. An analysis is given, showing its inherent limitations for large-scale problems which are common in computer vision. The thesis also introduces a segmentation approach for finding thin and elongated structures in 3D volumes. Using a line-graph formulation, it is shown how to efficiently regularize with respect to higher-order differential geometric properties such as curvature and torsion. Furthermore, an efficient optimization approach for a multi-region model is presented which, in addition to standard regularization, is able to enforce geometric constraints such as inclusion or exclusion of different regions. The final part of the thesis deals with dense stereo estimation. A new regularization model is introduced, penalizing the second-order derivatives of a depth or disparity map. Compared to previous second-order approaches to dense stereo estimation, the new regularization model is shown to be more easily optimized

Combinatorial Solutions for Shape Optimization in Computer Vision

This thesis aims at solving so-called shape optimization problems, i.e. problems where the shape of some real-world entity is sought, by applying combinatorial algorithms. I present several advances in this field, all of them based on energy minimization. The addressed problems will become more intricate in the course of the thesis, starting from problems that are solved globally, then turning to problems where so far no global solutions are known. The first two chapters treat segmentation problems where the considered grouping criterion is directly derived from the image data. That is, the respective data terms do not involve any parameters to estimate. These problems will be solved globally. The first of these chapters treats the problem of unsupervised image segmentation where apart from the image there is no other user input. Here I will focus on a contour-based method and show how to integrate curvature regularity into a ratio-based optimization framework. The arising optimization problem is reduced to optimizing over the cycles in a product graph. This problem can be solved globally in polynomial, effectively linear time. As a consequence, the method does not depend on initialization and translational invariance is achieved. This is joint work with Daniel Cremers and Simon Masnou. I will then proceed to the integration of shape knowledge into the framework, while keeping translational invariance. This problem is again reduced to cycle-finding in a product graph. Being based on the alignment of shape points, the method actually uses a more sophisticated shape measure than most local approaches and still provides global optima. It readily extends to tracking problems and allows to solve some of them in real-time. I will present an extension to highly deformable shape models which can be included in the global optimization framework. This method simultaneously allows to decompose a shape into a set of deformable parts, based only on the input images. This is joint work with Daniel Cremers. In the second part segmentation is combined with so-called correspondence problems, i.e. the underlying grouping criterion is now based on correspondences that have to be inferred simultaneously. That is, in addition to inferring the shapes of objects, one now also tries to put into correspondence the points in several images. The arising problems become more intricate and are no longer optimized globally. This part is divided into two chapters. The first chapter treats the topic of real-time motion segmentation where objects are identified based on the observations that the respective points in the video will move coherently. Rather than pre-estimating motion, a single energy functional is minimized via alternating optimization. The main novelty lies in the real-time capability, which is achieved by exploiting a fast combinatorial segmentation algorithm. The results are furthermore improved by employing a probabilistic data term. This is joint work with Daniel Cremers. The final chapter presents a method for high resolution motion layer decomposition and was developed in combination with Daniel Cremers and Thomas Pock. Layer decomposition methods support the notion of a scene model, which allows to model occlusion and enforce temporal consistency. The contributions are twofold: from a practical point of view the proposed method allows to recover fine-detailed layer images by minimizing a single energy. This is achieved by integrating a super-resolution method into the layer decomposition framework. From a theoretical viewpoint the proposed method introduces layer-based regularity terms as well as a graph cut-based scheme to solve for the layer domains. The latter is combined with powerful continuous convex optimization techniques into an alternating minimization scheme. Lastly I want to mention that a significant part of this thesis is devoted to the recent trend of exploiting parallel architectures, in particular graphics cards: many combinatorial algorithms are easily parallelized. In Chapter 3 we will see a case where the standard algorithm is hard to parallelize, but easy for the respective problem instances

The optimal connection model for blood vessels segmentation and the MEA-Net

Vascular diseases have long been regarded as a significant health concern. Accurately detecting the location, shape, and afflicted regions of blood vessels from a diverse range of medical images has proven to be a major challenge. Obtaining blood vessels that retain their correct topological structures is currently a crucial research issue. Numerous efforts have sought to reinforce neural networks' learning of vascular geometric features, including measures to ensure the correct topological structure of the segmentation result's vessel centerline. Typically, these methods extract topological features from the network's segmentation result and then apply regular constraints to reinforce the accuracy of critical components and the overall topological structure. However, as blood vessels are three-dimensional structures, it is essential to achieve complete local vessel segmentation, which necessitates enhancing the segmentation of vessel boundaries. Furthermore, current methods are limited to handling 2D blood vessel fragmentation cases. Our proposed boundary attention module directly extracts boundary voxels from the network's segmentation result. Additionally, we have established an optimal connection model based on minimal surfaces to determine the connection order between blood vessels. Our method achieves state-of-the-art performance in 3D multi-class vascular segmentation tasks, as evidenced by the high values of Dice Similarity Coefficient (DSC) and Normalized Surface Dice (NSD) metrics. Furthermore, our approach improves the Betti error, LR error, and BR error indicators of vessel richness and structural integrity by more than 10% compared to other methods, and effectively addresses vessel fragmentation and yields blood vessels with a more precise topological structure.Comment: 19 page

Computational models for image contour grouping

Contours are one dimensional curves which may correspond to meaningful entities such as object boundaries. Accurate contour detection will simplify many vision tasks such as object detection and image recognition. Due to the large variety of image content and contour topology, contours are often detected as edge fragments at first, followed by a second step known as {u0300}{u0300}contour grouping'' to connect them. Due to ambiguities in local image patches, contour grouping is essential for constructing globally coherent contour representation. This thesis aims to group contours so that they are consistent with human perception. We draw inspirations from Gestalt principles, which describe perceptual grouping ability of human vision system. In particular, our work is most relevant to the principles of closure, similarity, and past experiences. The first part of our contribution is a new computational model for contour closure. Most of existing contour grouping methods have focused on pixel-wise detection accuracy and ignored the psychological evidences for topological correctness. This chapter proposes a higher-order CRF model to achieve contour closure in the contour domain. We also propose an efficient inference method which is guaranteed to find integer solutions. Tested on the BSDS benchmark, our method achieves a superior contour grouping performance, comparable precision-recall curves, and more visually pleasant results. Our work makes progresses towards a better computational model of human perceptual grouping. The second part is an energy minimization framework for salient contour detection problem. Region cues such as color/texture homogeneity, and contour cues such as local contrast, are both useful for this task. In order to capture both kinds of cues in a joint energy function, topological consistency between both region and contour labels must be satisfied. Our technique makes use of the topological concept of winding numbers. By using a fast method for winding number computation, we find that a small number of linear constraints are sufficient for label consistency. Our method is instantiated by ratio-based energy functions. Due to cue integration, our method obtains improved results. User interaction can also be incorporated to further improve the results. The third part of our contribution is an efficient category-level image contour detector. The objective is to detect contours which most likely belong to a prescribed category. Our method, which is based on three levels of shape representation and non-parametric Bayesian learning, shows flexibility in learning from either human labeled edge images or unlabelled raw images. In both cases, our experiments obtain better contour detection results than competing methods. In addition, our training process is robust even with a considerable size of training samples. In contrast, state-of-the-art methods require more training samples, and often human interventions are required for new category training. Last but not least, in Chapter 7 we also show how to leverage contour information for symmetry detection. Our method is simple yet effective for detecting the symmetric axes of bilaterally symmetric objects in unsegmented natural scene images. Compared with methods based on feature points, our model can often produce better results for the images containing limited texture

Content based image retrieval for identification of plants using color, texture and shape features

In this thesis, an application of content-based image retrieval is proposed for plant identification, along with a preliminary implementation. The system takes a plant image as input and finds the matching plant from a plant image database and is intended to provide users a simple method to locate information about their plants. With a larger database, the system might be used by biologists, as an easy way to access to plant databases. Max-flow min-cut technique is used as the image segmentation method to separate the plant from the background of the image, so as to extract the general structure of the plant. Various color, texture and shape features extracted from the segmented plant region are used in matching images to the database. Color and texture analysis are based on commonly used features, namely color histograms in different color spaces, color co-occurrence matrices and Gabor texture maps. As for shape, we introduce some new descriptors to capture the outer contour characteristics of a plant. While color is very useful in many CBIR problems, in this particular problem, it introduces some challenges as well, since many plants just differ in the particular hue of the green color. As for shape and texture analysis, the difficulty stems from the fact that the plant is composed of many leaves, resulting in a complex and variable outer contour and texture. For texture analysis, we tried to capture leaf-level information using smaller shape regions or patches. Patch size is designed to contain a leaf structure approximately. Results show that for 54% of the queries, the correct plant image is retrieved among the top-15 results, using our database of 380 plants from 78 different plant types. Moreover, the tests are also performed on a clean database in which all the plant images have smooth shape descriptors and are among the 380 images. The test results obtained using this clean database increased the top-15 retrieval probability to 68%