Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate segmentation. To this end, we reformulate the problem by imposing piecewise constancy of the parameter field, and derive a specific proximal splitting optimization scheme. A key component of our framework is an efficient 1D piecewise-affine estimator for vector-valued signals. The first advantage of our approach over segmentation-based methods is its absence of initialization. The second advantage is its lower computational cost, which is independent of the complexity of the motion field. In addition to these features, we demonstrate competitive accuracy with other piecewise-parametric methods on standard evaluation benchmarks. Our new regularization scheme also outperforms the more standard use of total variation and total generalized variation.
Most of the computational effort is spent on the image-partitioning problem. The earliest works retain at most five regions to make the problem tractable . More recently, the layered approach handles a larger number of regions but requires several hours of computation, and the primal dual approach can take up to one hour despite a GPU implementation. The method proposed in @cite_36 achieves around fifteen minutes for @math image, with a graph cut minimization approach.
@cite_36
2063266501 2119213281 2147298660 2113197522
Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimum-cut using the maximum flow algorithm. We present a third major approach by generalizing the Swendsen-Wang method - a well celebrated algorithm in statistical mechanics. Our algorithm simulates ergodic, reversible Markov chain jumps in the space of graph partitions to sample a posterior probability. At each step, the algorithm splits, merges, or regroups a sizable subgraph, and achieves fast mixing at low temperature enabling a fast annealing procedure. Experiments show it converges in 2-30 seconds on a PC for image segmentation. This is 400 times faster than the single-site update Gibbs sampler, and 20-40 times faster than the DDMCMC algorithm. The algorithm can optimize over the number of models and works for general forms of posterior probabilities, so it is more general than the existing graph cut approaches. This paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimization using Graph-cuts. Our approach is to seek the optimal partitioning of 3D space into two regions labeled as "object" and "empty" under a cost functional consisting of the following two terms: 1) A term that forces the boundary between the two regions to pass through photo-consistent locations; and 2) a ballooning term that inflates the "object" region. To take account of the effect of occlusion on the first term, we use an occlusion robust photo-consistency metric based on normalized cross correlation, which does not assume any geometric knowledge about the reconstructed object. The globally optimal 3D partitioning can be obtained as the minimum cut solution of a weighted graph. The heavy-tailed distribution of gradients in natural scenes have proven effective priors for a range of problems such as denoising, deblurring and super-resolution. These distributions are well modeled by a hyper-Laplacian (p(x) ∝ e-k|x|α ), typically with 0.5 ≤ α ≤ 0.8. However, the use of sparse distributions makes the problem non-convex and impractically slow to solve for multi-megapixel images. In this paper we describe a deconvolution approach that is several orders of magnitude faster than existing techniques that use hyper-Laplacian priors. We adopt an alternating minimization scheme where one of the two phases is a non-convex problem that is separable over pixels. This per-pixel sub-problem may be solved with a lookup table (LUT). Alternatively, for two specific values of α, 1 2 and 2 3 an analytic solution can be found, by finding the roots of a cubic and quartic polynomial, respectively. Our approach (using either LUTs or analytic formulae) is able to deconvolve a 1 megapixel image in less than 3 seconds, achieving comparable quality to existing methods such as iteratively reweighted least squares (IRLS) that take 20 minutes. Furthermore, our method is quite general and can easily be extended to related image processing problems, beyond the deconvolution application demonstrated. This study explores the use of the graphics processing units (GPUs) for performing the two-dimensional discrete wavelet transform (DWT) of images. The study of fast wavelet transforms has been driven both by the enormous volumes of data produced by modern cameras and by the need for real-time processing of these data. With the emergence of general computing on GPUs, many time-consuming applications have started to reap the associated benefits. In the implementation of a GPU-based DWT, two approaches are used according to the published works, which are the row-column (RC) approach and the block-based (BB) approach. Most state-of-the-art techniques are based on the RC approach, which utilises the parallelism between different rows and columns; few works are based on the BB approach, which explores the parallelism between different blocks of the image. Although easy to implement, resource usage of the RC approach is usually related to the image size. Another shortcoming of the RC approach lies in the fact, according to the author's analysis, that more global memory access is required. The authors thus select the BB approach in this study. Experiment results show that the proposed BB approach outperforms the RC approach, being 99× faster than a native CPU implementation for 4096 × 4096 images.