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

Optimal O

A number of acceleration schemes for speeding up the time-consuming bilateral filter have been proposed in the literature. Among these techniques, the histogram-based bilateral filter trades the flexibility for achieving O(1) computational complexity using box spatial kernel. A recent study shows that this technique can be leveraged for O(1) bilateral filter with arbitrary spatial and range kernels by linearly combining the results of multiple-box bilateral filters. However, this method requires many box bilateral filters to obtain sufficient accuracy when approximating the bilateral filter with a large spatial kernel. In this paper, we propose approximating arbitrary spatial kernel using a fixed number of boxes. It turns out that the multiple-box spatial kernel can be applied in many O(1) acceleration schemes in addition to the histogram-based one. Experiments on the application to the histogram-based acceleration are presented in this paper. Results show that the proposed method has better accuracy in approximating the bilateral filter with Gaussian spatial kernel, compared with the previous histogram-based methods. Furthermore, the performance of the proposed histogram-based bilateral filter is robust with respect to the parameters of the filter kernel

Machine Learning And Image Processing For Noise Removal And Robust Edge Detection In The Presence Of Mixed Noise

The central goal of this dissertation is to design and model a smoothing filter based on the random single and mixed noise distribution that would attenuate the effect of noise while preserving edge details. Only then could robust, integrated and resilient edge detection methods be deployed to overcome the ubiquitous presence of random noise in images. Random noise effects are modeled as those that could emanate from impulse noise, Gaussian noise and speckle noise. In the first step, evaluation of methods is performed based on an exhaustive review on the different types of denoising methods which focus on impulse noise, Gaussian noise and their related denoising filters. These include spatial filters (linear, non-linear and a combination of them), transform domain filters, neural network-based filters, numerical-based filters, fuzzy based filters, morphological filters, statistical filters, and supervised learning-based filters. In the second step, switching adaptive median and fixed weighted mean filter (SAMFWMF) which is a combination of linear and non-linear filters, is introduced in order to detect and remove impulse noise. Then, a robust edge detection method is applied which relies on an integrated process including non-maximum suppression, maximum sequence, thresholding and morphological operations. The results are obtained on MRI and natural images. In the third step, a combination of transform domain-based filter which is a combination of dual tree – complex wavelet transform (DT-CWT) and total variation, is introduced in order to detect and remove Gaussian noise as well as mixed Gaussian and Speckle noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on medical ultrasound and natural images. In the fourth step, a smoothing filter, which is a feed-forward convolutional network (CNN) is introduced to assume a deep architecture, and supported through a specific learning algorithm, l2 loss function minimization, a regularization method, and batch normalization all integrated in order to detect and remove impulse noise as well as mixed impulse and Gaussian noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on natural images for both specific and non-specific noise-level

Automatic 2D-to-3D conversion of single low depth-of-field images

This research presents a novel approach to the automatic rendering of 3D stereoscopic disparity image pairs from single 2D low depth-of-field (LDOF) images. Initially a depth map is produced through the assignment of depth to every delineated object and region in the image. Subsequently the left and right disparity images are produced through depth imagebased rendering (DIBR). The objects and regions in the image are initially assigned to one of six proposed groups or labels. Labelling is performed in two stages. The first involves the delineation of the dominant object-of-interest (OOI). The second involves the global object and region grouping of the non-OOI regions. The matting of the OOI is also performed in two stages. Initially the in focus foreground or region-of-interest (ROI) is separated from the out of focus background. This is achieved through the correlation of edge, gradient and higher-order statistics (HOS) saliencies. Refinement of the ROI is performed using k-means segmentation and CIEDE2000 colour-difference matching. Subsequently the OOI is extracted from within the ROI through analysis of the dominant gradients and edge saliencies together with k-means segmentation. Depth is assigned to each of the six labels by correlating Gestalt-based principles with vanishing point estimation, gradient plane approximation and depth from defocus (DfD). To minimise some of the dis-occlusions that are generated through the 3D warping sub-process within the DIBR process the depth map is pre-smoothed using an asymmetric bilateral filter. Hole-filling of the remaining dis-occlusions is performed through nearest-neighbour horizontal interpolation, which incorporates depth as well as direction of warp. To minimising the effects of the lateral striations, specific directional Gaussian and circular averaging smoothing is applied independently to each view, with additional average filtering applied to the border transitions. Each stage of the proposed model is benchmarked against data from several significant publications. Novel contributions are made in the sub-speciality fields of ROI estimation, OOI matting, LDOF image classification, Gestalt-based region categorisation, vanishing point detection, relative depth assignment and hole-filling or inpainting. An important contribution is made towards the overall knowledge base of automatic 2D-to-3D conversion techniques, through the collation of existing information, expansion of existing methods and development of newer concepts