Segmentation of Vectorial Image Features Using Shape Gradients and Information Measures

Abstract

Abstract. In this paper, we propose to focus on the segmentation of vectorial features (e.g. vector fields or color intensity) using region-based active contours. We search for a domain that minimizes a criterion based on homogeneity measures of the vectorial features. We choose to evaluate, within each region to be segmented, the average quantity of information carried out by the vectorial features, namely the joint entropy of vector components. We do not make any assumption on the underlying distribution of joint probability density functions of vector components, and so we evaluate the entropy using non parametric probability density functions. A local shape minimizer is then obtained through the evolution of a deformable domain in the direction of the shape gradient. The first contribution of this paper lies in the methodological approach used to differentiate such a criterion. This approach is mainly based on shape optimization tools. The second one is the extension of this method to vectorial data. We apply this segmentation method on color images for the segmentation of color homogeneous regions. We then focus on the segmentation of synthetic vector fields and show interesting results where motion vector fields may be separated using both their length and their direction. Then, optical flow is estimated in real video sequences and segmented using the proposed technique. This leads to promising results for the segmentation of moving video objects.

Surface-driven registration method for the structure-informed segmentation of diffusion MR images

“…They also propose a multiphase level-set function initialized from a labeled atlas to implement the active contours that drive the atlas registration. Alternatively, regseg implements the active contours with a hierarchical set of explicit surfaces (triangular meshes) instead of the multiphase level sets, and registration is driven by shape-gradients (Herbulot et al, 2006). As an advantage, the use of explicit surfaces enables segmenting dMRI images with accuracy below voxel size.…”

“…Tlw) to a bivariate target-volume comprehending the FA and ADC maps. The evolution of the surfaces is supported by a B-spline basis, optimized iteratively using a descent approach driven by shape-gradients (Jehan-Besson et al, 2003;Herbulot et al, 2006). Therefore, regseg establishes a registration framework that actually deals with the nonlinear warping induced by EPI distortions.…”

Texture Segmentation via Non-local Non-parametric Active Contours

“…These approaches are quite effective for many natural images or textures that contain complicated random fluctuations. The resulting statistical region-based active contours make use of pointwise similarity measures among distributions (such as the Kullback-Leibler divergence) to compare the distributions, in a parametric or non-parametric (using Parzen windows) fashion, see for instance [16][17][18][19]. In this paper, we also consider the setting of statistical segmentation, and we propose to use a fully non-parametric estimator that does not require to compute histograms.…”

“…A mathematically more rigorous way to derive the corresponding PDE is to make use of the shape derivative machinery, which is formally equivalent to letting ε tend to 0, see for instance [18,19]. Using such a shape gradient would make the evolution PDE well defined only on the boundary of Ω, and this evolution is then extended to the whole domain by preserving some distance function property on φ.…”

“…This is different from the more traditional Eulerian discretization, that makes use of a fixed set of points (usually a rectangular grid) but where the points are equipped with a weight to reflect the local density of the distribution. These histogram-based (Eulerian) discretizations are at the heart of previous statistical region-based active contours such as [20,18,19].…”