Search

Saliency detection aims to highlight the most relevant objects in an image. Methods using conventional models struggle whenever salient objects are pictured on top of a cluttered background while deep neural nets suffer from excess complexity and slow evaluation speeds. In this paper, we propose a simplified convolutional neural network which combines local and global information through a multi-resolution 4×5 grid structure. Instead of enforcing spacial coherence with a CRF or superpixels as is usually the case, we implemented a loss function inspired by the Mumford-Shah functional which penalizes errors on the boundary. We trained our model on the MSRA-B dataset, and tested it on six different saliency benchmark datasets. Results show that our method is on par with the state-of-the-art while reducing computation time by a factor of 18 to 100 times, enabling near real-time, high performance saliency detection.

We propose to incorporate a weighted difference of anisotropic and isotropic total variation (TV) norms into a relaxed formulation of the two phase Mumford-Shah (MS) model for image segmentation. We show results exceeding those obtained by the MS model when using the standard TV norm to regularize partition boundaries. In particular, examples illustrating the qualitative differences between the proposed model and the standard MS one are shown. A fast numerical method is introduced to minimize the proposed model utilizing the difference-of-convex algorithm (DCA) and the primal dual hybrid gradient (PDHG) method.

A novel shape prior segmentation model is proposed that utilizes the cliques invariant signature along with a polygonal piecewise constant implementation of the Mumford-Shah Functional. The model will be shown to be useful in the context of difficult segmentation problems including and not limited to segmenting objects amidst clutter, or recognizing objects that contain components with largely varying non-uniform image intensities. In addition, the model will also be shown to be effective for image disocclusion. Lastly, the proposed model can accomplish all the aforementioned tasks both efficiently and with near automation.

International audience; We consider the Chan and Vese multiphase segmentationbased on the partition of an image minimizing an energyinvolving a region-based data fidelity term and a regularization term. The common implementation of the continuousoptimization of this segmentation framework, with multiplelevel set functions, raises some numerical issues which leadto poor performance of the method when handling more thantwo phases. We propose a general formulation of the multi-phase model, and a permutation method, incorporated in thelevel-set based implementation of the multi-phase approachto handle in an original way the so-called hidden phase problem.

In this paper, we revisit the phase-field approximation of Ambrosio and Tortorelli for the Mumford -- Shah functional. We then propose a convex relaxation for it to attempt to compute globally optimal solutions rather than solving the nonconvex functional directly, which is the main contribution of this paper. Inspired by McCormick's seminal work on factorable nonconvex problems, we split a nonconvex product term that appears in the Ambrosio -- Tortorelli elliptic functionals in a way that a typical alternating gradient method guarantees a globally optimal solution without completely removing coupling effects. Furthermore, not only do we provide a fruitful analysis of the proposed relaxation but also demonstrate the capacity of our relaxation in numerous experiments that show convincing results compared to a naive extension of the McCormick relaxation and its quadratic variant. Indeed, we believe the proposed relaxation and the idea behind would open up a possibility for convexifying a new class of functions in the context of energy minimization for computer vision.

Image segmentation is intended to group perceptually similar pixels into 2D regions, and the corresponding border is gained at the same time. Video segmentation generalizes this concept to the grouping of pixels into spatio-temporal regions that exhibit coherence in both appearance and motion, but this generalization pose the complexity of spatio-temporal grouping, and in order to overcome this complexity, the existing video segmentation methods have extended the image segmentation methods to 3D domain. In these volumetric approaches, it is not known a priori, which regions to track, what frames contain those regions, or the time-direction for tracking (forward or backward). In this paper we present an efficient and scalable method for spatio-temporal segmentation obtained by minimizing a 2D+time extension of the simplified Mumford-Shah functional. The 2D+time extension permits to write the Mumford-Shah functional as an a multiscale energy, which is minimized on a hierarchy of video domain. The construction of this hierarchy based on the 2D-shapes of video images, and Scale-invariant feature transform (SIFT).

Segmentation of brain lesions in Magnetic Resonance Imaging (MRI) is a difficult task to be mastered by the specialist. This is due to the presence of noise, partial volume effects and susceptibility artifacts in the images and on the borders of the regions of interest. These problems can interfere with the results when manual segmentation is used. Manual segmentation uses local anatomic information based on the user's background; that implies the necessity of constant human intervention. Deformable model approaches attempt to minimize these drawbacks by outlining the region of interest semi-automatically. These methods have been shown to be effective in the extraction of the lesion boundaries in brain MR images. The proposed method employs the multi-channel version of the Mumford-Shah model via level set methods in order to segment multi-sequence brain magnetic resonance (MR) images: FLAIR (Fluid attenuated inversion recovery), T 1 and T 2 - weighted images. Results showed that segmentation of multi-sequence images using this methodology yielded superior results than using each sequence alone. As a consequence, medical doctors can exploit the segmentation results to follow up their patients' status by controlling the evolution or involution of brain lesions.

In this work we revisit the Mumford-Shah functional, one of the most studied variational approaches to image segmentation. The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the Mumford-Shah functional obtained by functional lifting. The algorithm is an efficient primal-dual projection algorithm for which we prove convergence. In contrast to existing algorithms for minimizing the full Mumford-Shah this is the first one which is based on a convex relaxation. As a consequence the computed solutions are independent of the initialization. Experimental results confirm that the proposed algorithm determines smooth approximations while preserving discontinuities of the underlying signal.

A top-down image segmentation method is proposed in this paper, utilizing level set image representation and the piecewise-constant Mumford-Shah functional. The method achieves top-down hierarchical segmentation by taking advantage of the tree structure provided by level set image representation. The piecewise-constant Mumford-Shah functional is utilized in the proposed method to determine if each node in the tree segments the image. Experimental results show that this method is able to segment complicated real images.

Partial matching is probably one of the most challenging problems in nonrigid shape analysis. The problem consists of matching similar parts of shapes that are dissimilar on the whole and can assume different forms by undergoing nonrigid deformations. Conceptually, two shapes can be considered partially matching if they have significant similar parts, with the simplest definition of significance being the size of the parts. Thus, partial matching can be defined as a multicriterion optimization problem trying to simultaneously maximize the similarity and the size of these parts. In this paper, we propose a different definition of significance, taking into account the regularity of parts besides their size. The regularity term proposed here is similar to the spirit of the Mumford-Shah functional. Numerical experiments show that the regularized partial matching produces semantically better results compared to the non-regularized one.

One of the more successful approaches to image segmentation involves formulating the problem as the minimisation of a Mumford-Shah functional and then applying region merging algorithms to approximate the minimiser. Moreover, it can be proved mathematically that such segmentations have desirable properties, and further, fast implementations are available. In this paper, we describe improvements to one such algorithm, the full lambda-schedule segmentation algorithm (FLSA). The FLSA maintains a list of merge costs (as measured by the Mumford-Shah functional) for all relevant pairs of neighbouring regions and at each step selects the best pair to merge from the list. This is done quickly and efficiently through the use sophisticated data structures. We present significant improvements to those data structures which further simplify the maintenance of the merge cost list. The new algorithm makes use of a new list, the edge list, which allows the regions neighbouring a newly merged pair to be searched more efficiently. Owing to a change in the way "multiple boundaries'' are handled, the new segmentations may differ slightly from the old ones but we argue that they are equally valid. We refer to the new algorithm as the FLSA Edge List (FLSA-EL) algorithm.

Curve evolution implementations [3][23] [25] of the Mumford-Shah functional [16] are of broad interest in image segmentation. These implementations, however, have initialization problems [6] [25]. A mathematical analysis of the initialization problem for the Chan-Vese implementation [3] [25] is provided in this paper. The initialization problem is a result of the non-convexity of the Mumford- Shah functional and the top-down hierarchy of the model?s use of global region information in the image. Based on the analysis, efficient implementation methods are proposed for the Chan-Vese models [3] [25]. The proposed methods do not have to solve PDEs and thus work fast. The advantages of level set methods, such as automatic handling of topological changes, are preserved. These methods work well for images without strong noise. Initialization problems, however, still exist. A bottom-up image segmentation method is proposed that alleviates the initialization problem, based on region competition and the Mumford Shah functional [16]. This algorithm extends the method in [15], and is able to automatically and efficiently segment objects in complicated images. Using a bottom-up hierarchy, the method avoids the initialization problem in the Chan-Vese model and works for images with multiple junctions and color images. It is then extended to textured images using Gabor filters and fractal methods. Experimental results show that the proposed method works well and is robust to the effects of noise.

Curve evolution implementations [3][17] [18] of the Mumford-Shah functional [11] are of broad interest in image segmentation. These implementations, however, have initialization problems [4]. A mathematical analysis of the initialization problem for the bi-modal Chan-Vese model [3] is provided in this paper. The initialization problem is a result of the non-convexity of the Mumford-Shah functional and the top-down hierarchy of the model's use of global region information in the image. An efficient image segmentation method is proposed that alleviates the initialization problem, based on region growing, region competition and the Mumford Shah functional [11]. This algorithm is able to automatically and efficiently segment objects in complicated images. Using a bottom-up hierarchy, the method avoids the initialization problem in the Chan-Vese model and works for images with multiple junctions and color images. It can be extended to textured images. Experimental results show that the proposed method is robust to the effects of noise.

This paper generalizes the methods in a previous paper in Pan, Y. et al, (2006) in two ways. First, a more comprehensive analysis of the initialization problem of the Chan-Vese models is given. Second, the image segmentation method proposed in Pan, Y. et al. (2006) is improved by applying bimodal curve evolution with region competition. The improved method maintains the advantages of the previous method. It is efficient, stable in the presence of strong noise and able to handle complicated images. It outperforms the previous method for images with weak edges. Experimental results in this paper demonstrate these improvements

This paper presents a level set technique to extract the vascular structures in coronary angiography. It makes use of the Mumford-Shah functional to extract contours that are not necessary defined by gradient. A shape artery simulator was implemented to test and evaluate the detection method. Experimental results are presented on simulated data and real images successively.

In this paper, we propose a variational method to segment image objects, which have a given parametric shape based on a level-set formulation of the Mumford-Shah functional, and the shape parameters. We define an energy functional composed by two complementary terms. The first one detects object boundaries using a Chan-Vese-like method. The second term constrains the contour to find a shape compatible with the parametric shape. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variation and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We focus in this paper on the parametric category of image linear objects. Applications of the proposed model are presented on synthetic and real images

In this paper, we propose a joint despeckling and edge detection algorithm based on the Mumford-Shah functional, which accomplishes the image filtering and segmentation as a result of an analytical variational problem. This approach turns out to be well suited to jointly despeckle and segment SAR image data; the experimental results demonstrate that the proposed technique yields high quality despeckling without impairing critical image features and with the additional advantage to provide a detailed edge map

We first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah (1989) paradigm from a curve evolution perspective. In particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Next, we generalize the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty. This more general model leads us to a novel partial differential equation (PDE) based approach for simultaneous image magnification, segmentation, and smoothing.

We present an estimation-theoretic approach to curve evolution for the Mumford-Shah problem. By viewing an active contour as the set of discontinuities in the Mumford-Shah problem, we may use the corresponding functional to determine gradient descent evolution equations to deform the active contour. In each gradient descent step, we solve a corresponding optimal estimation problem, connecting the Mumford-Shah functional and curve evolution with the theory of boundary-value stochastic processes. In employing the Mumford-Shah functional, our active contour model inherits its attractive ability to generate, in a coupled manner, both a smooth reconstruction and a segmentation of the image. Next, by generalizing the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty, we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing. This more general model leads us to a novel PDE-based approach for simultaneous image magnification, segmentation, and smoothing, thereby extending the traditional applications of the Mumford-Shah functional which only considers simultaneous segmentation and smoothing.