Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. The first algorithm, called Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image super-resolution, deblurring and denoising applications and shown to outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings.Comment: 15 pages, 10 figures and 5 table

Exact asymptotics of the uniform error of interpolation by multilinear splines

The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others. In this paper we will investigate the questions regarding adaptive approximation of C2 functions with arbitrary but fixed throughout the domain signature by multilinear splines. In particular, we will study the asymptotic behavior of the optimal error of the weighted uniform approximation by interpolating and quasi-interpolating multilinear splines

Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

Bags of Affine Subspaces for Robust Object Tracking

We propose an adaptive tracking algorithm where the object is modelled as a continuously updated bag of affine subspaces, with each subspace constructed from the object's appearance over several consecutive frames. In contrast to linear subspaces, affine subspaces explicitly model the origin of subspaces. Furthermore, instead of using a brittle point-to-subspace distance during the search for the object in a new frame, we propose to use a subspace-to-subspace distance by representing candidate image areas also as affine subspaces. Distances between subspaces are then obtained by exploiting the non-Euclidean geometry of Grassmann manifolds. Experiments on challenging videos (containing object occlusions, deformations, as well as variations in pose and illumination) indicate that the proposed method achieves higher tracking accuracy than several recent discriminative trackers.Comment: in International Conference on Digital Image Computing: Techniques and Applications, 201

Effects of Intraframe Distortion on Measures of Cone Mosaic Geometry from Adaptive Optics Scanning Light Ophthalmoscopy

Purpose: To characterize the effects of intraframe distortion due to involuntary eye motion on measures of cone mosaic geometry derived from adaptive optics scanning light ophthalmoscope (AOSLO) images. Methods: We acquired AOSLO image sequences from 20 subjects at 1.0, 2.0, and 5.08 temporal from fixation. An expert grader manually selected 10 minimally distorted reference frames from each 150-frame sequence for subsequent registration. Cone mosaic geometry was measured in all registered images (n ¼ 600) using multiple metrics, and the repeatability of these metrics was used to assess the impact of the distortions from each reference frame. In nine additional subjects, we compared AOSLO-derived measurements to those from adaptive optics (AO)-fundus images, which do not contain system-imposed intraframe distortions. Results: We observed substantial variation across subjects in the repeatability of density (1.2%–8.7%), inter-cell distance (0.8%–4.6%), percentage of six-sided Voronoi cells (0.8%–10.6%), and Voronoi cell area regularity (VCAR) (1.2%–13.2%). The average of all metrics extracted from AOSLO images (with the exception of VCAR) was not significantly different than those derived from AO-fundus images, though there was variability between individual images. Conclusions: Our data demonstrate that the intraframe distortion found in AOSLO images can affect the accuracy and repeatability of cone mosaic metrics. It may be possible to use multiple images from the same retinal area to approximate a ‘‘distortionless’’ image, though more work is needed to evaluate the feasibility of this approach. Translational Relevance: Even in subjects with good fixation, images from AOSLOs contain intraframe distortions due to eye motion during scanning. The existence of these artifacts emphasizes the need for caution when interpreting results derived from scanning instruments

Integral Geometry and General Adaptive Neighborhoods for Multiscale Image Analysis

International audienceIn quantitative image analysis, Minkowski functionals are becoming standard parameters for topological and geometrical measurements. Nevertheless, they are limited to binary images or to sections of gray-tone images and are achieved in a global and monoscale way. The use of General Adaptive Neighborhoods (GANs) enables to overcome these limitations. The GANs are spatial neighborhoods defined around each point of the spatial support of a gray-tone image, according to three (GAN) axiomatic criteria: a criterion function (luminance, contrast, ...), an homogeneity tolerance with respect to this criterion, and an algebraic model for the image space. Thus, the GANs are simultaneously adaptive with the analyzing scales, the spatial structures and the image intensities. This paper aims to introduce the GAN-based Minkowski functionals, which allow a gray-tone image analysis to be realized in a local, adaptive and multiscale way. The Minkowski functionals are computed on the GAN of each point of the spatial support of a gray-tone image, enabling to define the so-called Minkowski maps by assigning the Minkowski functional value to each point. The histograms of these maps provide a statistical distribution of the topology and geometry of the gray-tone image structures, and not only of the image intensities. The impact of the GAN characteristics, as well as the impact of multiscale transformations, are analyzed in a qualitative global and local way through these GAN-based Minkowski maps and histograms. This multiscale image analysis is illustrated on the test image 'Lena' and also applied in both the biomedical and materials areas

Adaptive Optimisation of Illumination Beam Profiles in Fluorescence Microscopy

Wide-field fluorescence microscope techniques such as single/selective plane illumination microscope (SPIM) are typically configured to image large regions of a sample at once. Here the illumination beam provides uniform excitation of several biological features across the region, `sliced' to a thickness of between 5-10 microns. In this paper we propose a simple alteration to the optical configuration of a SPIM by switching the light-sheet- forming cylindrical lens with a spatial light modulator. This has the potential to adaptively reconfigure the light sheet geometry to improve the optical sectioning of specific biological features, rather than the thicker sectioning of several features at once across a larger observation field-of-view. We present a prototype version of such a system, referred to as an Adaptive-SPIM (A-SPIM) system. We then suggest that the direct recording of illumination beam shapes within the working microscope system can better facilitate the analysis and subsequent re-configuration of the illumination beam to a specific geometry, and summarise the design and operation of a device that we have developed specifically for this purpose. We finally present reconstructed quantitative three dimensional flux maps of illumination beams from three microscope configurations taken using this miniature high-dynamic range beam profiling device, comparing the beam geometry of a regular SPIM system with our prototype A-SPIM system, and suggesting future improvements

A Data Cube Extraction Pipeline for a Coronagraphic Integral Field Spectrograph

Project 1640 is a high contrast near-infrared instrument probing the vicinities of nearby stars through the unique combination of an integral field spectrograph with a Lyot coronagraph and a high-order adaptive optics system. The extraordinary data reduction demands, similar those which several new exoplanet imaging instruments will face in the near future, have been met by the novel software algorithms described herein. The Project 1640 Data Cube Extraction Pipeline (PCXP) automates the translation of 3.8*10^4 closely packed, coarsely sampled spectra to a data cube. We implement a robust empirical model of the spectrograph focal plane geometry to register the detector image at sub-pixel precision, and map the cube extraction. We demonstrate our ability to accurately retrieve source spectra based on an observation of Saturn's moon Titan.Comment: 35 pages, 15 figures; accepted for publication in PAS