Publications

Abstract: With emerging of next generation of digital cameras offering a 3D reconstruction of a viewed scene, Depth from Defocus (DFD) presents an attractive option. In this approach the depth profile of the scene is recovered from two views captured in different focus setting. The DFD is well known as a computationally-intensive method due to the shift-variant filtering involved with its estimation. In this paper we present a parallel GPGPU implementation of DFD based on the variational framework, enabling computation up to 15 frames/sec for a SVGA sequence. This constitutes the first GPU application and the fastest implementation known for passive DFD. The speed-up is obtained by using the novel Fast Explicit Diffusion approach and the fine grain data parallelism in an explicit scheme. We evaluate our method on publicly available real data and compare its results to a recently published PDE based method. The proposed method outperforms previous DFD techniques in terms of accuracy/runtime, suggesting the DFD as an alternative for 3D reconstruction in real-time.

Abstract: We present a kernel based approach for image de-noising in the spatial domain. The crux of evaluation for the kernel weights is addressed by a Bayesian regression. This approach introduces an adaptive filter, well preserving edges and thin structures in the image. The hyper-parameters in the model as well as the predictive distribution functions are estimated through an efficient iterative scheme. We evaluate our method on common test images, contaminated by white Gaussian noise. Qualitative results show the capability of our method to smooth out the noise while preserving the edges and fine texture. Quantitative comparison with the celebrated total variation (TV) and several wavelet methods ranks our approach among state-of-the-art denoising algorithms. Further advantages of our method include the capability of direct and simple integration of the noise PDF into the de-noising framework. The suggested method is fully automatic and can equally be applied to other regression problems.

Abstract: This paper addresses the problem of correspondence establishment in binocular stereo vision. We suggest a novel spatially continuous approach for stereo matching based on the variational framework. The proposed method suggests a unique regularization term based on Mumford-Shah functional for discontinuity preserving, combined with a new energy functional for occlusion handling. The evaluation process is based on concurrent minimization of two coupled energy functionals, one for domain segmentation (occluded vs. visible) and the other for disparity evaluation. In addition to a dense disparity map, our method also provides estimation for the half-occlusion domain, and a discontinuity function allocating the disparity/depth boundaries. Two new constraints are introduced improving the revealed discontinuity map. The experimental tests include a wide range of real data sets from Middlebury stereo database. The results demonstrate the capability of our method in calculating an accurate disparity function with sharp discontinuities and occlusion map recovery. Significant improvements are shown comparing to a recently published variational stereo approach. A comparison on the Middlebury stereo benchmark with sub-pixel accuracies shows that our method is currently among the top-ranked stereo matching algorithms.

Abstract: We evaluate the dense optical flow between two frames via variational approach. In this paper, a new framework for deriving the regularization term is introduced giving a geometric insight into the action of a smoothing term. The framework is based on the Beltrami paradigm in image denoising. It includes a general formulation that unifies several previous methods. Using the proposed framework we also derive two novel anisotropic regularizers incorporating a new criterion that requires co-linearity between the gradients of optical flow components and possibly the intensity gradient. We call this criterion ``alignment" and reveal its existence also in the celebrated Nagel and Enkelmann's formulation. It is shown that the physical model of rotational motion of a rigid body, pure divergent/convergent flow and irrotational fluid flow, satisfy the alignment criterion in the flow field. Experimental tests in comparison to a recently published method show the capability of the new criterion in improving the optical flow estimations.

Abstract: Every stereovision application must cope with the correspondence problem. The space of the matching variables, often consisting of spatial coordinates, intensity and disparity, is commonly referred as the data term (space). Since the data is often noisy a-priori preference is required constraining the evaluated disparity to be smooth (or piecewise smooth). It is shown that in the early local methods (e.g. window correlation techniques) a regularization is conducted on the data space. In the other hand, recent global methods consider a non-regularized data term with an added smoothing constraint implemented directly on the disparity. In this paper, we propose a new idea combining between the two latter approaches. To this end a novel geometric method for regularization of the data space is presented. The idea is then implemented on the state of the art variational method. Experimental results on the Middlebury real images demonstrate the qualitative and quantitative potential of the proposed approach.

Abstract: We present a new object segmentation method that is based on geodesic active contours with combined shape and appearance priors. It is known that using shape priors can significantly improve object segmentation in cluttered scenes and occlusions. Within this context, we add a new prior, based on the appearance of the object, (i.e., an image) to be segmented. This method enables the appearance pattern to be incorporated within the geodesic active contour framework with shape priors, seeking for the object whose boundaries lie on high image gradients and that best fits the shape and appearance of a reference model. The output contour results from minimizing an energy functional built of these three main terms. We show that appearance is a powerful term that distinguishes between objects with similar shapes and capable of successfully segment an object in a very cluttered environment where standard active contours (even those with shape priors) tend to fail.

Abstract: This paper addresses the problem of correspondence establishment in binocular stereo vision. We suggest a novel variational approach that considers both the discontinuities and occlusions. It deals with color images as well as gray levels. The proposed method divides the image domain into the visible and occluded regions where each region is handled differently. The depth discontinuities in the visible domain are preserved by use of the total variation term in conjunction with the Mumford-Shah framework. In addition to the dense disparity and the occlusion maps, our method also provides a discontinuity function revealing the location of the boundaries in the disparity map. We evaluate our method on data sets from Middlebury site showing superior performance in comparison to the state of the art variational technique.

Abstract: The problem of dense optical flow computation is addressed from a variational viewpoint. A new geometric framework is introduced. It unifies previous art and yields new efficient methods. Along with the framework a new alignment criterion suggests itself. It is shown that the alignment between the gradients of the optical flow components and between the latter and the intensity gradients is an important measure of the flow's quality. Adding this criterion as a requirement in the optimization process improves the resulting flow. This is demonstrated in synthetic and real sequences.

Abstract: The correspondence problem in stereo vision is notoriously difficult. In many approaches a noisy solution is extracted from the correspondence space. Various sophisticated regularization techniques are applied then on this noisy solution. We study here the possibility to denoise the correspondence/correlation space before extracting the solution, by a non-linear and non-isotropic scheme. We show that this methods preserves edges (depth discontinuities) well and overcomes some of the problems encountered in previous approaches.