Salient Level Lines Selection Using the Mumford-Shah Functional

International audienceMany methods relying on the morphological notion of shapes, (i.e., connected components of level sets) have been proved to be very useful for pattern analysis and recognition. Selecting meaningful level lines (boundaries of level sets) yields to simplify images while preserving salient structures. Many image simplification and/or segmentation methods are driven by the optimization of an energy functional, for instance the Mumford-Shah functional. In this article, we propose an efficient shape-based morphological filtering that very quickly compute to a locally (subordinated to the tree of shapes) optimal solution of the piecewise-constant Mumford- Shah functional. Experimental results demonstrate the efficiency, usefulness, and robustness of our method, when applied to image simplification, pre-segmentation, and detection of affine regions with viewpoint changes

Hierarchical image simplification and segmentation based on Mumford-Shah-salient level line selection

Hierarchies, such as the tree of shapes, are popular representations for image simplification and segmentation thanks to their multiscale structures. Selecting meaningful level lines (boundaries of shapes) yields to simplify image while preserving intact salient structures. Many image simplification and segmentation methods are driven by the optimization of an energy functional, for instance the celebrated Mumford-Shah functional. In this paper, we propose an efficient approach to hierarchical image simplification and segmentation based on the minimization of the piecewise-constant Mumford-Shah functional. This method conforms to the current trend that consists in producing hierarchical results rather than a unique partition. Contrary to classical approaches which compute optimal hierarchical segmentations from an input hierarchy of segmentations, we rely on the tree of shapes, a unique and well-defined representation equivalent to the image. Simply put, we compute for each level line of the image an attribute function that characterizes its persistence under the energy minimization. Then we stack the level lines from meaningless ones to salient ones through a saliency map based on extinction values defined on the tree-based shape space. Qualitative illustrations and quantitative evaluation on Weizmann segmentation evaluation database demonstrate the state-of-the-art performance of our method.Comment: Pattern Recognition Letters, Elsevier, 201

Piecewise smooth reconstruction of normal vector field on digital data

International audienceWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio-Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state-of- the-art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12]

A Novel Euler's Elastica based Segmentation Approach for Noisy Images via using the Progressive Hedging Algorithm

Euler's Elastica based unsupervised segmentation models have strong capability of completing the missing boundaries for existing objects in a clean image, but they are not working well for noisy images. This paper aims to establish a Euler's Elastica based approach that properly deals with random noises to improve the segmentation performance for noisy images. We solve the corresponding optimization problem via using the progressive hedging algorithm (PHA) with a step length suggested by the alternating direction method of multipliers (ADMM). Technically, all the simplified convex versions of the subproblems derived from the major framework of PHA can be obtained by using the curvature weighted approach and the convex relaxation method. Then an alternating optimization strategy is applied with the merits of using some powerful accelerating techniques including the fast Fourier transform (FFT) and generalized soft threshold formulas. Extensive experiments have been conducted on both synthetic and real images, which validated some significant gains of the proposed segmentation models and demonstrated the advantages of the developed algorithm

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Image Segmentation by Energy and Related Functional Minimization Methods

Effective and efficient methods for partitioning a digital image into image segments, called ¿image segmentation,¿ have a wide range of applications that include pattern recognition, classification, editing, rendering, and compressed data for image search. In general, image segments are described by their geometry and similarity measures that identify them. For example, the well-known optimization model proposed and studied in depth by David Mumford and Jayant Shah is based on an L2 total energy functional that consists of three terms that govern the geometry of the image segments, the image fidelity (or closeness to the observed image), and the prior (or image smoothness). Recent work in the field of image restoration suggests that a more suitable choice for the fidelity measure is, perhaps, the l1 norm. This thesis explores that idea applied to the study of image segmentation along the line of the Mumford and Shah optimization model, but eliminating the need of variational calculus and regularization schemes to derive the approximating Euler-Lagrange equations. The main contribution of this thesis is a formulation of the problem that avoids the need for the calculus of variation. The energy functional represents a global property of an image. It turns out to be possible, however, to predict how localized changes to the segmentation will affect its value. This has been shown previously in the case of the l2 norm, but no similar method is available for other norms. The method described here solves the problem for the l1 norm, and suggests how it would apply to other forms of the fidelity measure. Existing methods rely on a fixed initial condition. This can lead to an algorithm finding local instead of global optimizations. The solution given here shows how to specify the initial condition based on the content of the image and avoid finding local minima

A local Rayleigh model with spatial scale selection for ultrasound image segmentation

12 pagesInternational audienceUltrasound images are very noisy, with poor contrast and the attenuation of the acoustic wave in the depth of the observed medium leads to strong inhomogeneities in the image. Segmentation methods using global image statistics give unsatisfactory results. The use of local image statistics can solve effectively the problem of attenuation. The contribution of this paper is two folds. First, we propose the study of the adaptation of the global model proposed by Sarti et al. We kept the variational framework and the Rayleigh model of the observed image statistics. Second, we propose an interesting and generic adaptive scale selection algorithm based on the Intersection of Confidence Interval rule. The latter is also applied to the local Gaussian segmentation model of Brox and Cremers. Results on realistic simulations of ultrasound images show the robustness and the superiority of the local Rayleigh model. The efficiency and the genericity of the proposed scale selection strategy is also demonstrated

Decreasing predictability of visual motion enhances feed-forward processing in visual cortex when stimuli are behaviorally relevant

Recent views of information processing in the (human) brain emphasize the hierarchical structure of the central nervous system, which is assumed to form the basis of a functional hierarchy. Hierarchical predictive processing refers to the notion that higher levels try to predict activity in lower areas, while lower levels transmit a prediction error up the hierarchy whenever the predictions fail. The present study aims at testing hypothetical modulatory effects of unpredictable visual motion on forward connectivities within the visual cortex. Functional magnetic resonance imaging was acquired from 35 healthy volunteers while viewing a moving ball under three different levels of predictability. In two different runs subjects were asked to attend to direction changes in the ball’s motion, where a button-press was required in one of these runs only. Dynamic causal modeling was applied to a network comprising V1, V5 and posterior parietal cortex in the right hemisphere. The winning model of a Bayesian model selection indicated an enhanced strength in the forward connection from V1 to V5 with decreasing predictability for the run requiring motor response. These results support the notion of hierarchical predictive processing in the sense of an augmented bottom-up transmission of prediction error with increasing uncertainty about motion direction. This finding may be of importance for promoting our understanding of trait characteristics in psychiatric disorders, as an increased forward propagation of prediction error is assumed to underlie schizophrenia and may be observable at early stages of the disease