Abdol-Reza Mansouri

Region tracking via level set PDEs without motion computation

We propose an approach to region tracking that is derived from a Bayesian formulation. The novelty of the approach is twofold. First, no motion field or motion parameters need to be computed. This removes a major burden since accurate motion computation has been and remains a challenging problem and the quality of region tracking algorithms based on motion critically depends on the computed motion fields and parameters. The second novelty of this approach, is that very little a priori information about the region being tracked is used in the algorithm. In particular, unlike numerous tracking algorithms, no assumption is made on the strength of the intensity edges of the boundary of the region being tracked, nor is its shape assumed to be of a certain parametric form. The problem of region tracking is formulated as a Bayesian estimation problem and the resulting tracking algorithm is expressed as a level set partial differential equation. We present further extensions to this partial differential equation, allowing the possibility of including additional information in the tracking process, such as priors on the regions intensity boundaries and we present the details of the numerical implementation. Very promising experimental results are provided.

Motion segmentation with level sets

Motion segmentation is an important problem in video processing and compression, and in computer vision. It is usually performed by either first estimating a field of motion parameters and then segmenting it, or by applying joint motion estimation and segmentation. Motion segmentation methods often constrain the set of possible solutions by forcing motion discontinuities to coincide with intensity discontinuities. In this paper, we propose an iterative method for joint motion estimation and segmentation that is based on level sets. The motion within individual segments is parametric and the method does not use the intensity discontinuity constraint, but is shown to be accurate for images with both synthetic and natural motion compliant with the assumed motion models.

Motion tracking as spatio-temporal motion boundary detection

Abstract The purpose of this study is to investigate tracking of moving objects in a sequence of images by detecting the surface generated by motion boundaries in the space–time domain. Estimation of this spatio-temporal surface is formulated as a Bayesian image partitioning problem. Minimization of the resulting energy functional seeks a solution biased toward smooth closed surfaces which coincide with motion boundaries, have small area, and partition the image into regions of contrasting motion activity. The Euler–Lagrange partial differential equations of minimization are expressed as level set evolution equations to obtain a topology independent and numerically stable algorithm. The formulation does not require estimation of the image motion field or assume a known background. It allows multiple non-simultaneous independent motions to occur and can account for camera motion without prior estimation of this motion. The analysis assumes short-range image motion. With moving cameras, it assumes that this short-range motion varies smoothly everywhere except across motion boundaries.

Bayesian winner-take-all reconstruction of intermediate views from stereoscopic images

This paper presents a new algorithm for the reconstruction of intermediate views from a pair of still stereoscopic images. The algorithm is designed to address the issue of blur caused by linear filtering often employed in such reconstruction. The proposed algorithm is block-based and to reconstruct the intermediate views employs nonlinear disparity-compensated filtering by means of a winner-take-all strategy. The reconstructed image is modeled as a tiling by fixed-size blocks coming from various positions (disparity compensation) of either the left or right images, while the tiling map itself is modeled by a binary decision field. In addition to that, an observation model relating the left and right images via a disparity field, and a disparity field model are used. All models are probabilistic and are combined into a maximum a posteriori probability criterion. The intermediate intensities, disparities and the binary decision field are estimated jointly using the expectation-maximization algorithm. The new approach is compared experimentally on complex natural images with a reference block-based algorithm employing linear filtering. Although the improvements are localized and often subtle, they demonstrate that a high-quality intermediate view reconstruction for complex scenes is feasible.

Selective image diffusion: application to disparity estimation

Inverse problems encountered in image processing and computer vision are often ill-posed. Whether set in a Bayesian or energy-based context, such problems require prior assumptions expressed through an a priori probability or a regularization term, respectively. In some cases, the prior term exhibits partial dependence on the observations (e.g., images) that is often ignored to simplify modeling and computations. We review methods that take this dependence into account and we propose a new formulation of the prior term that blends some other simple approaches. Similarly to others, we apply a linear transformation to the prior term but, in addition, we require that the eigenvalues of the transformation have specific properties. These properties are chosen so that diffusion is allowed only along the direction perpendicular to the local image gradient. If the gradient magnitude is small, isotropic diffusion is performed. We apply this formulation to stereoscopic disparity estimation and we show several experimental results; improvements over a standard approach are clear.

Image partioning by level set multiregion competition

The purpose of this study is to investigate a new representation of a partition of an image domain into a given number of regions and its use in the context of region competition to provide an extensional level set multiregion competition algorithm. In contrast with the standard region competition formulation, this multiregion competition formulation leads to a system of coupled curve evolution equations which is easily amenable to a level set implementation. Minimization of the functional guarantees an unambiguous segmentation. We provide a common statement of the multiregion competition algorithm for intensity, motion, and disparity based segmentation. Experimental results are shown.

A comparative evaluation of algorithms for fast computation of level set PDEs with applications to motion segmentation

We address the problem of fast computation of level set partial differential equations (PDEs) in the context of motion segmentation. Although several fast level set computation algorithms are known, some of them, such as the fast marching method, are not applicable to the video segmentation problem since the front being computed does not advance monotonically. We study narrow-banding, pyramidal and a pyramidal/narrow-banding schemes that leads to a 70-fold time gain over the single-resolution scheme.

Spatio-temporal motion segmentation via level set partial differential equations

Motion-based segmentation of image sequences is an important problem of image analysis, with numerous applications to image coding and image manipulation. We present a novel algorithm for segmenting image sequences into distinct motion trajectories. This algorithm is expressed as a system of level set partial differential equations which is solved using level set discretization schemes. We provide experimental results on real image sequences with natural and synthetic image motion.

Minimum description length region tracking with level sets

This paper addresses the problem of tracking an arbitrary region in a sequence of images, given a pre-computed velocity field. Such a problem is of importance in applications ranging from video surveillance to video database search. The algorithm presented here formulates tracking as an estimation problem. We propose, as our estimation criterion, a precise description length measure that quantifies tracking performance. In this context, tracking is naturally formulated as minimum description length estimation. The solution to this estimation problem is given by particular evolution equations for the region boundary. The implicit representation of the region boundary by the zero level set of a smooth function yields an equivalent set of partial differential equations and the added benefit of topology independence; regions may split (e.g., for divergent velocity fields) or merge (e.g. for convergent velocity fields) during tracking, clearly a desirable feature in real-world applications. We illustrate the performance of the proposed algorithm on a number of real images with natural motion.

Multiple motion segmentation with level sets

Motion segmentation of an image sequence belongs to the most difficult and important problems in video processing and compression, and in computer vision. In this paper, we consider the problem of segmenting an image into multiple regions possibly undergoing different motions. To this end we use level sets of functions evolving according to certain partial differential equations. Contrary to numerous other motion segmentation algorithms based on level sets, we compute accurate motion boundaries without relying on intensity boundaries as an accessory. This will be illustrated on examples where intensity boundaries are hardly visible and yet motion boundaries are accurately identified. The main benefit of the level set representation is in its ability to handle variations in the topology of the level sets. As a result, it is only necessary to know the total number of distinct motion classes and their parameters. We describe an automatic initialization procedure that is based on feature point correspondences and K-means clustering in a 6-parameter space of affine parameters. We illustrate the performance of the proposed algorithm on real images with both real and synthetic motion.