Edge-enhancing Filters with Negative Weights

In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by projecting the noisy image to a lower dimensional Krylov subspace of the graph Laplacian, constructed using nonnegative weights determined by distances between image data corresponding to image pixels. We~extend the construction of the graph Laplacian to the case, where some graph weights can be negative. Removing the positivity constraint provides a more accurate inference of a graph model behind the data, and thus can improve quality of filters for graph-based signal processing, e.g., denoising, compared to the standard construction, without affecting the costs.Comment: 5 pages; 6 figures. Accepted to IEEE GlobalSIP 2015 conferenc

Accelerated graph-based spectral polynomial filters

Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop on Machine Learning for Signal Processin

Accelerated graph-based nonlinear denoising filters

Denoising filters, such as bilateral, guided, and total variation filters, applied to images on general graphs may require repeated application if noise is not small enough. We formulate two acceleration techniques of the resulted iterations: conjugate gradient method and Nesterov's acceleration. We numerically show efficiency of the accelerated nonlinear filters for image denoising and demonstrate 2-12 times speed-up, i.e., the acceleration techniques reduce the number of iterations required to reach a given peak signal-to-noise ratio (PSNR) by the above indicated factor of 2-12.Comment: 10 pages, 6 figures, to appear in Procedia Computer Science, vol.80, 2016, International Conference on Computational Science, San Diego, CA, USA, June 6-8, 201

Guided Filtering based Pyramidal Stereo Matching for Unrectified Images

Stereo matching deals with recovering quantitative depth information from a set of input images, based on the visual disparity between corresponding points. Generally most of the algorithms assume that the processed images are rectified. As robotics becomes popular, conducting stereo matching in the context of cloth manipulation, such as obtaining the disparity map of the garments from the two cameras of the cloth folding robot, is useful and challenging. This is resulted from the fact of the high efficiency, accuracy and low memory requirement under the usage of high resolution images in order to capture the details (e.g. cloth wrinkles) for the given application (e.g. cloth folding). Meanwhile, the images can be unrectified. Therefore, we propose to adapt guided filtering algorithm into the pyramidical stereo matching framework that works directly for unrectified images. To evaluate the proposed unrectified stereo matching in terms of accuracy, we present three datasets that are suited to especially the characteristics of the task of cloth manipulations. By com- paring the proposed algorithm with two baseline algorithms on those three datasets, we demonstrate that our proposed approach is accurate, efficient and requires low memory. This also shows that rather than relying on image rectification, directly applying stereo matching through the unrectified images can be also quite effective and meanwhile efficien