We present an energy based approach to estimate a dense disparity map from a set of two weakly calibrated stereoscopic images while preserving its discontinuities resulting from image boundaries. We first derive a simplified expression for the disparity that allows us to estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the Nagel-Enkelmann operator. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method. The resulting parabolic problem has a unique solution. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scalespace. Experimental results on both synthetic and real images are presented to illustrate the capabilities of this PDE and scale-space based method.

This article describes an implementation of the optical flow estimation method introduced by Zach, Pock and Bischof in 2007. This method is based on the minimization of a functional containing a data term using the L 1 norm and a regularization term using the total variation of the flow. The main feature of this formulation is that it allows discontinuities in the flow field, while being more robust to noise than the classical approach by Horn and Schunck. The algorithm is an efficient numerical scheme, which solves a relaxed version of the problem by alternate minimization. Source CodeA C implementation of this algorithm is provided. The source code and an online demo are accessible at the web page of this article 1 .

Traditional techniques of dense optical flow estimation do not generally yield symmetrical solutions: the results will differ if they are applied between images I 1 and I 2 or between images I 2 and I 1 . In this work, we present a method to recover a dense optical flow field map from two images, while explicitely taking into account the symmetry across the images as well as possible occlusions in the flow field. The idea is to consider both displacements vectors from I 1 to I 2 and I 2 to I 1 and to minimise an energy functional that explicitely encodes all those properties. This variational problem is then solved using the gradient flow defined by the Euler-Lagrange equations associated to the energy. To prove the importance of the concepts of symmetry and occlusions for optical flow computation, we have extended a classical approach to handle those. Experiments clearly show the added value of these properties to improve the accuracy of the computed flows. Figures appear in color in the online version of this paper.

This paper presents an interpretation of a classic optical ow method by Nagel and Enkelmann as a tensor-driven anisotropic di usion approach in digital image analysis. We i n troduce an improvement i n to the model formulation, and we establish well-posedness results for the resulting system of parabolic partial di erential equations. Our method avoids linearizations in the optical ow constraint, and it can recover displacement elds which a r e f a r b e y ond the typical one-pixel limits that are characteristic for many di erential methods for optical ow recovery. A robust numerical scheme is presented in detail. We a void convergence to irrelevant local minima by e m bedding our method into a linear scalespace framework and using a focusing strategy from coarse to ne scales. The high accuracy of the proposed method is demonstrated by means of a s y n thetic and a real-world image sequence.

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We present an implementation of the inverse compositional algorithm for parametric motion estimation. It computes a global motion between two images using a non-linear least square technique. Our implementation allows computing several types of planar transformations, such as translations, similarities, affinities or homographies. The algorithm is iterative so it typically yields solutions with high accuracy. The use of robust error functions, different from the L 2 norm, improves the stability of the method under the presence of noise and occlusions, and allows it to detect the predominant motion, even if there are several types of displacements. The method works with multi-channel images and makes use of a coarse-to-fine strategy for dealing with large displacements. Source CodeThe reviewed source code and documentation for this algorithm are available from the web page of this article 1 . Compilation and usage instruction are included in the README.txt file of the archive.