Mikael Rousson

A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape

Since their introduction as a means of front propagation and their first application to edge-based segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework.Region-based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edge-based schemes such as the classical Snakes, region-based methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly well-suited for local optimization methods such as the level set method.We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals. We point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.

Shape Priors for Level Set Representations

Level Set Representations, the pioneering framework introduced by Osher and Sethian [14] is the most common choice for the implementation of variational frameworks in Computer Vision since it is implicit, intrinsic, parameter and topology free. However, many Computer vision applications refer to entities with physical meanings that follow a shape form with a certain degree of variability. In this paper, we propose a novel energetic form to introduce shape constraints to level set representations. This formulation exploits all advantages of these representations resulting on a very elegant approach that can deal with a large number of parametric as well as continuous transformations. Furthermore, it can be combined with existing well known level set-based segmentation approaches leading to paradigms that can deal with noisy, occluded and missing or physically corrupted data. Encouraging experimental results are obtained using synthetic and real images.

A variational framework for active and adaptative segmentation of vector valued images

Much effort has been made in integrating different information in a variational framework to segment images. Recent works on curve propagation were able to incorporate stochastic information (see Paragios, N. and Deriche, R., J. Visual Commun. and Image Representation, 2002; Zhu, S. and Yuille, A., 1996) and prior knowledge on shapes (see Cremers, D. et al., 2002; Rousson M. and Paragios, N., 2002). The information inserted in these studies is most of the time extracted offline. Meanwhile, other approaches have proposed to extract region information during the segmentation process itself (see Chan, T. et al., 2000; Jehan-Besson, S. et al., 2002; Yezzi, A. et al., 1999). Following these new approaches and extending the work of Paragios and Deriche to vector-valued images, we propose an entirely variational framework to approach the segmentation problem. Both the image partition and the statistical parameters for each region are unknown. After a brief reminder on recent segmenting methods, we present a variational formulation obtained from a Bayesian model. After that, we show two different differentiations driving to the same evolution equations. Detailed studies on gray and color images of the 2-phase case follow. We finish with an application to tracking which shows the benefits of our dynamic framework.

Active unsupervised texture segmentation on a diffusion based feature space

We propose a novel and efficient approach for active unsupervised texture segmentation. First, we show how we can extract a small set of good features for texture segmentation based on the structure tensor and nonlinear diffusion. Then, we propose a variational framework that incorporates these features in a level set based unsupervised segmentation process that adaptively takes into account their estimated statistical information inside and outside the region to segment. The approach has been tested on various textured images, and its performance is favorably compared to recent studies.

Statistics on the Manifold of Multivariate Normal Distributions: Theory and Application to Diffusion Tensor MRI Processing

This paper is dedicated to the statistical analysis of the space of multivariate normal distributions with an application to the processing of Diffusion Tensor Images (DTI). It relies on the differential geometrical properties of the underlying parameters space, endowed with a Riemannian metric, as well as on recent works that led to the generalization of the normal law on Riemannian manifolds. We review the geometrical properties of the space of multivariate normal distributions with zero mean vector and focus on an original characterization of the mean, covariance matrix and generalized normal law on that manifold. We extensively address the derivation of accurate and efficient numerical schemes to estimate these statistical parameters. A major application of the present work is related to the analysis and processing of DTI datasets and we show promising results on synthetic and real examples.

Non-rigid registration using distance functions

Abstract This paper deals with the registration of geometric shapes. Our primary contribution is the use of a simple and robust shape representation (distance functions) for global-to-local alignment. We propose a rigid-invariant variational framework that can deal as well with local non-rigid transformations. To this end, the registration map consists of a linear motion model and a local deformations field, incrementally recovered. In order to demonstrate the performance of the selected representation a simple criterion is considered, the sum of square differences. Empirical validation and promising results were obtained on examples that exhibit large global motion as well as important local deformations and arbitrary topological changes.

Prior Knowledge, Level Set Representations & Visual Grouping

Abstract In this paper, we propose a level set method for shape-driven object extraction. We introduce a voxel-wise probabilistic level set formulation to account for prior knowledge. To this end, objects are represented in an implicit form. Constraints on the segmentation process are imposed by seeking a projection to the image plane of the prior model modulo a similarity transformation. The optimization of a statistical metric between the evolving contour and the model leads to motion equations that evolve the contour toward the desired image properties while recovering the pose of the object in the new image. Upon convergence, a solution that is similarity invariant with respect to the model and the corresponding transformation are recovered. Promising experimental results demonstrate the potential of such an approach.

Matching Distance Functions: A Shape-to-Area Variational Approach for Global-to-Local Registration

This paper deals with the matching of geometric shapes. Our primary contribution is the use of a simple, robust, rich and efficient way to represent shapes, the level set representations according to singed distance transforms. Based on these representations we propose a variational framework for global as well as local shape registration that can be extended to deal with structures of higher dimension. The optimization criterion is invariant to rotation, translation and scale and combines efficiently a global motion model with local pixel-wise deformations. Promising results are obtained on examples showing small and large global deformations as well as arbitrary topological changes.

Implicit Active Shape Models for 3D Segmentation in MR Imaging

Extraction of structures of interest in medical images is often an arduous task because of noisy or incomplete data. However, hand-segmented data are often available and most of the structures to be extracted have a similar shape from one subject to an other. Then, the possibility of modeling a family of shapes and restricting the new structure to be extracted within this class is of particular interest. This approach is commonly implemented using active shape models [2] and the definition of the image term is the most challenging component of such an approach. In parallel, level set methods [8] define a powerful optimization framework, that can be used to recover objects of interest by the propagation of curves or surfaces. They can support complex topologies, considered in higher dimensions, are implicit, intrinsic and parameter free. In this paper we re-visit active shape models and introduce a level set variant of them. Such an approach can account for prior shape knowledge quite efficiently as well as use data/image terms of various form and complexity. Promising results on the extraction of brain ventricles in MR images demonstrate the potential of our approach.

Unsupervised Segmentation Incorporating Colour, Texture, and Motion

In this paper we integrate colour, texture, and motion into a segmentation process. The segmentation consists of two steps, which both combine the given information: a pre-segmentation step based on nonlinear diffusion for improving the quality of the features, and a variational framework for vector-valued data using a level set approach and a statistical model to describe the interior and the complement of a region. For the nonlinear diffusion we apply a novel diffusivity closely related to the total variation diffusivity, but being strictly edge enhancing. A multi-scale implementation is used in order to obtain more robust results. In several experiments we demonstrate the usefulness of integrating many kinds of information. Good results are obtained for both object segmentation and tracking of multiple objects.