Efficient dense blur map estimation for automatic 2D-to-3D conversion

Focus is an important depth cue for 2D-to-3D conversion of low depth-of-field images and video. However, focus can be only reliably estimated on edges. Therefore, Bea et al. [1] first proposed an optimization based approach to propagate focus to non-edge image portions, for single image focus editing. While their approach produces accurate dense blur maps, the computational complexity and memory requirements for solving the resulting sparse linear system with standard multigrid or (multilevel) preconditioning techniques, are infeasible within the stringent requirements of the consumer electronics and broadcast industry. In this paper we propose fast, efficient, low latency, line scanning based focus propagation, which mitigates the need for complex multigrid or (multilevel) preconditioning techniques. In addition we propose facial blur compensation to compensate for false shading edges that cause incorrect blur estimates in people's faces. In general shading leads to incorrect focus estimates, which may lead to unnatural 3D and visual discomfort. Since visual attention mostly tends to faces, our solution solves the most distracting errors. A subjective assessment by paired comparison on a set of challenging low-depth-of-field images shows that the proposed approach achieves equal 3D image quality as optimization based approaches, and that facial blur compensation results in a significant improvemen

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

Multigrid Backprojection Super-Resolution and Deep Filter Visualization

We introduce a novel deep-learning architecture for image upscaling by large factors (e.g. 4x, 8x) based on examples of pristine high-resolution images. Our target is to reconstruct high-resolution images from their downscale versions. The proposed system performs a multi-level progressive upscaling, starting from small factors (2x) and updating for higher factors (4x and 8x). The system is recursive as it repeats the same procedure at each level. It is also residual since we use the network to update the outputs of a classic upscaler. The network residuals are improved by Iterative Back-Projections (IBP) computed in the features of a convolutional network. To work in multiple levels we extend the standard back-projection algorithm using a recursion analogous to Multi-Grid algorithms commonly used as solvers of large systems of linear equations. We finally show how the network can be interpreted as a standard upsampling-and-filter upscaler with a space-variant filter that adapts to the geometry. This approach allows us to visualize how the network learns to upscale. Finally, our system reaches state of the art quality for models with relatively few number of parameters.Comment: Spotlight paper in the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19

A discrete graph Laplacian for signal processing

In this thesis we exploit diffusion processes on graphs to effect two fundamental problems of image processing: denoising and segmentation. We treat these two low-level vision problems on the pixel-wise level under a unified framework: a graph embedding. Using this framework opens us up to the possibilities of exploiting recently introduced algorithms from the semi-supervised machine learning literature. We contribute two novel edge-preserving smoothing algorithms to the literature. Furthermore we apply these edge-preserving smoothing algorithms to some computational photography tasks. Many recent computational photography tasks require the decomposition of an image into a smooth base layer containing large scale intensity variations and a residual layer capturing fine details. Edge-preserving smoothing is the main computational mechanism in producing these multi-scale image representations. We, in effect, introduce a new approach to edge-preserving multi-scale image decompositions. Where as prior approaches such as the Bilateral filter and weighted-least squares methods require multiple parameters to tune the response of the filters our method only requires one. This parameter can be interpreted as a scale parameter. We demonstrate the utility of our approach by applying the method to computational photography tasks that utilise multi-scale image decompositions. With minimal modification to these edge-preserving smoothing algorithms we show that we can extend them to produce interactive image segmentation. As a result the operations of segmentation and denoising are conducted under a unified framework. Moreover we discuss how our method is related to region based active contours. We benchmark our proposed interactive segmentation algorithms against those based upon energy-minimisation, specifically graph-cut methods. We demonstrate that we achieve competitive performance

Preconditioning for time-harmonic Maxwell's equations using the Laguerre transform

A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential equations. However, solving large systems of linear algebraic equations with indefinite ill-conditioned matrices is a challenge. The high order of the matrices limits the capabilities of the Gaussian method to solve such systems, since this requires large RAM and much calculation. To reduce these requirements, an iterative preconditioned algorithm based on integral Laguerre transform in time is used. This approach allows using multigrid algorithms and, as a result, needs less RAM compared to the direct methods of solving systems of linear algebraic equations.Comment: 12 pages, 4 figure

Non-Iterative, Feature-Preserving Mesh Smoothing

With the increasing use of geometry scanners to create 3D models, there is a rising need for fast and robust mesh smoothing to remove inevitable noise in the measurements. While most previous work has favored diffusion-based iterative techniques for feature-preserving smoothing, we propose a radically different approach, based on robust statistics and local first-order predictors of the surface. The robustness of our local estimates allows us to derive a non-iterative feature-preserving filtering technique applicable to arbitrary "triangle soups". We demonstrate its simplicity of implementation and its efficiency, which make it an excellent solution for smoothing large, noisy, and non-manifold meshes.Singapore-MIT Alliance (SMA

Edge-preserving Multiscale Image Decomposition based on Local Extrema

We propose a new model for detail that inherently captures oscillations, a key property that distinguishes textures from individual edges. Inspired by techniques in empirical data analysis and morphological image analysis, we use the local extrema of the input image to extract information about oscillations: We define detail as oscillations between local minima and maxima. Building on the key observation that the spatial scale of oscillations are characterized by the density of local extrema, we develop an algorithm for decomposing images into multiple scales of superposed oscillations. Current edge-preserving image decompositions assume image detail to be low contrast variation. Consequently they apply filters that extract features with increasing contrast as successive layers of detail. As a result, they are unable to distinguish between high-contrast, fine-scale features and edges of similar contrast that are to be preserved. We compare our results with existing edge-preserving image decomposition algorithms and demonstrate exciting applications that are made possible by our new notion of detail