arXiv subjects

Ron Kimmel

Publications and source records attributed to Ron Kimmel.

71 records · Page 4Linked to original sources

arXiv2016

3D Face Reconstruction by Learning from Synthetic Data

Fast and robust three-dimensional reconstruction of facial geometric structure from a single image is a challenging task with numerous applications. Here, we introduce a learning-based approach for reconstructing a three-dimensional face from a single image. Recent face recovery methods rely on accurate localization of key characteristic points. In contrast, the proposed approach is based on a Convolutional-Neural-Network (CNN) which extracts the face geometry directly from its image. Although such deep architectures outperform other models in complex computer vision problems, training them properly requires a large dataset of annotated examples. In the case of three-dimensional faces, currently, there are no large volume data sets, while acquiring such big-data is a tedious task. As an alternative, we propose to generate random, yet nearly photo-realistic, facial images for which the geometric form is known. The suggested model successfully recovers facial shapes from real images, even for faces with extreme expressions and under various lighting conditions.

cs.CV↗

arXiv2016

Fast Blended Transformations for Partial Shape Registration

Automatic estimation of skinning transformations is a popular way to deform a single reference shape into a new pose by providing a small number of control parameters. We generalize this approach by efficiently enabling the use of multiple exemplar shapes. Using a small set of representative natural poses, we propose to express an unseen appearance by a low-dimensional linear subspace, specified by a redundant dictionary of weighted vertex positions. Minimizing a nonlinear functional that regulates the example manifold, the suggested approach supports local-rigid deformations of articulated objects, as well as nearly isometric embeddings of smooth shapes. A real-time non-rigid deformation system is demonstrated, and a shape completion and partial registration framework is introduced. These applications can recover a target pose and implicit inverse kinematics from a small number of examples and just a few vertex positions. The result reconstruction is more accurate compared to state-of-the-art reduced deformable models.

cs.GR↗

arXiv2016

Randomized Independent Component Analysis

Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual Information, a measure of statistical independence of random vectors. Two such approximations are the Kernel Generalized Variance or the Kernel Canonical Correlation which has been shown to reach the highest performance of ICA methods. However, the computational effort necessary just for computing these measures is cubic in the sample size. Hence, optimizing them becomes even more computationally demanding, in terms of both space and time. Here, we propose a couple of alternative novel measures based on randomized features of the samples - the Randomized Generalized Variance and the Randomized Canonical Correlation. The computational complexity of calculating the proposed alternatives is linear in the sample size and provide a controllable approximation of their Kernel-based non-random versions. We also show that optimization of the proposed statistical properties yields a comparable separation error at an order of magnitude faster compared to Kernel-based measures.

stat.ML↗

arXiv2016

Customized Facial Constant Positive Air Pressure (CPAP) Masks

Sleep apnea is a syndrome that is characterized by sudden breathing halts while sleeping. One of the common treatments involves wearing a mask that delivers continuous air flow into the nostrils so as to maintain a steady air pressure. These masks are designed for an average facial model and are often difficult to adjust due to poor fit to the actual patient. The incompatibility is characterized by gaps between the mask and the face, which deteriorates the impermeability of the mask and leads to air leakage. We suggest a fully automatic approach for designing a personalized nasal mask interface using a facial depth scan. The interfaces generated by the proposed method accurately fit the geometry of the scanned face, and are easy to manufacture. The proposed method utilizes cheap commodity depth sensors and 3D printing technologies to efficiently design and manufacture customized masks for patients suffering from sleep apnea.

cs.GR↗

arXiv2016

Consistent Discretization and Minimization of the L1 Norm on Manifolds

The L1 norm has been tremendously popular in signal and image processing in the past two decades due to its sparsity-promoting properties. More recently, its generalization to non-Euclidean domains has been found useful in shape analysis applications. For example, in conjunction with the minimization of the Dirichlet energy, it was shown to produce a compactly supported quasi-harmonic orthonormal basis, dubbed as compressed manifold modes. The continuous L1 norm on the manifold is often replaced by the vector l1 norm applied to sampled functions. We show that such an approach is incorrect in the sense that it does not consistently discretize the continuous norm and warn against its sensitivity to the specific sampling. We propose two alternative discretizations resulting in an iteratively-reweighed l2 norm. We demonstrate the proposed strategy on the compressed modes problem, which reduces to a sequence of simple eigendecomposition problems not requiring non-convex optimization on Stiefel manifolds and producing more stable and accurate results.

math.NA↗

arXiv2016

Real-Time Depth Refinement for Specular Objects

The introduction of consumer RGB-D scanners set off a major boost in 3D computer vision research. Yet, the precision of existing depth scanners is not accurate enough to recover fine details of a scanned object. While modern shading based depth refinement methods have been proven to work well with Lambertian objects, they break down in the presence of specularities. We present a novel shape from shading framework that addresses this issue and enhances both diffuse and specular objects' depth profiles. We take advantage of the built-in monochromatic IR projector and IR images of the RGB-D scanners and present a lighting model that accounts for the specular regions in the input image. Using this model, we reconstruct the depth map in real-time. Both quantitative tests and visual evaluations prove that the proposed method produces state of the art depth reconstruction results.

cs.CV↗

arXiv2015

Rule Of Thumb: Deep derotation for improved fingertip detection

We investigate a novel global orientation regression approach for articulated objects using a deep convolutional neural network. This is integrated with an in-plane image derotation scheme, DeROT, to tackle the problem of per-frame fingertip detection in depth images. The method reduces the complexity of learning in the space of articulated poses which is demonstrated by using two distinct state-of-the-art learning based hand pose estimation methods applied to fingertip detection. Significant classification improvements are shown over the baseline implementation. Our framework involves no tracking, kinematic constraints or explicit prior model of the articulated object in hand. To support our approach we also describe a new pipeline for high accuracy magnetic annotation and labeling of objects imaged by a depth camera.

cs.CV↗

arXiv2014

Graph matching: relax or not?

We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly-stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n^2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic.

cs.DS↗

arXiv2014

On the optimality of shape and data representation in the spectral domain

A proof of the optimality of the eigenfunctions of the Laplace-Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied shape and data analysis. It is based on the Courant-Fischer min-max principle adapted to our case. % The theorem we present supports the new trend in geometry processing of treating geometric structures by using their projection onto the leading eigenfunctions of the decomposition of the LBO. Utilisation of this result can be used for constructing numerically efficient algorithms to process shapes in their spectrum. We review a couple of applications as possible practical usage cases of the proposed optimality criteria. % We refer to a scale invariant metric, which is also invariant to bending of the manifold. This novel pseudo-metric allows constructing an LBO by which a scale invariant eigenspace on the surface is defined. We demonstrate the efficiency of an intermediate metric, defined as an interpolation between the scale invariant and the regular one, in representing geometric structures while capturing both coarse and fine details. Next, we review a numerical acceleration technique for classical scaling, a member of a family of flattening methods known as multidimensional scaling (MDS). There, the optimality is exploited to efficiently approximate all geodesic distances between pairs of points on a given surface, and thereby match and compare between almost isometric surfaces. Finally, we revisit the classical principal component analysis (PCA) definition by coupling its variational form with a Dirichlet energy on the data manifold. By pairing the PCA with the LBO we can handle cases that go beyond the scope defined by the observation set that is handled by regular PCA.

cs.CV↗

arXiv2013

On Nonrigid Shape Similarity and Correspondence

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks.

cs.CV↗

arXiv2013

Spectral Generalized Multi-Dimensional Scaling

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances between each pair of points in the set. Distances in the target space can be computed analytically in this setting. Generalized MDS is an extension that allows mapping one metric space into another, that is, multidimensional scaling into target spaces in which distances are evaluated numerically rather than analytically. Here, we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition, where the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS procedure enables efficient embedding by implicitly incorporating smoothness of the mapping into the problem, thereby substantially reducing the complexity involved in its solution while practically overcoming its non-convex nature. The method is compared to existing techniques that compute dense correspondence between shapes. Numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state-of-the-art approaches.

cs.CG↗

arXiv2013

Matching LBO eigenspace of non-rigid shapes via high order statistics

A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes in flat domains while preserving distances measured on the manifold. Recently, attention has been given to embedding shapes into the eigenspace of the Lapalce-Beltrami operator. The Laplace-Beltrami eigenspace preserves the diffusion distance, and is invariant under isometric transformations. However, Laplace-Beltrami eigenfunctions computed independently for different shapes are often incompatible with each other. Applications involving multiple shapes, such as pointwise correspondence, would greatly benefit if their respective eigenfunctions were somehow matched. Here, we introduce a statistical approach for matching eigenfunctions. We consider the values of the eigenfunctions over the manifold as sampling of random variables, and try to match their multivariate distributions. Comparing distributions is done indirectly, using high order statistics. We show that the permutation and sign ambiguities of low order eigenfunctions, can be inferred by minimizing the difference of their third order moments. The sign ambiguities of antisymmetric eigenfunctions can be resolved by exploiting isometric invariant relations between the gradients of the eigenfunctions and the surface normal. We present experiments demonstrating the success of the proposed method applied to feature point correspondence.

cs.GR↗

arXiv2012

Schrödinger Diffusion for Shape Analysis with Texture

In recent years, quantities derived from the heat equation have become popular in shape processing and analysis of triangulated surfaces. Such measures are often robust with respect to different kinds of perturbations, including near-isometries, topological noise and partialities. Here, we propose to exploit the semigroup of a Schrödinger operator in order to deal with texture data, while maintaining the desirable properties of the heat kernel. We define a family of Schrödinger diffusion distances analogous to the ones associated to the heat kernels, and show that they are continuous under perturbations of the data. As an application, we introduce a method for retrieval of textured shapes through comparison of Schrödinger diffusion distance histograms with the earth's mover distance, and present some numerical experiments showing superior performance compared to an analogous method that ignores the texture.

cs.CV↗

arXiv2011

Diffusion framework for geometric and photometric data fusion in non-rigid shape analysis

In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail.

cs.CV↗

arXiv2010

Affine-invariant diffusion geometry for the analysis of deformable 3D shapes

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant Laplacian from which local and global geometric structures are extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.

cs.CV↗

arXiv2010

Affine-invariant geodesic geometry of deformable 3D shapes

Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing non-rigid shape analysis tools. In fact, we show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.

cs.CV↗

arXiv2010

The Video Genome

Fast evolution of Internet technologies has led to an explosive growth of video data available in the public domain and created unprecedented challenges in the analysis, organization, management, and control of such content. The problems encountered in video analysis such as identifying a video in a large database (e.g. detecting pirated content in YouTube), putting together video fragments, finding similarities and common ancestry between different versions of a video, have analogous counterpart problems in genetic research and analysis of DNA and protein sequences. In this paper, we exploit the analogy between genetic sequences and videos and propose an approach to video analysis motivated by genomic research. Representing video information as video DNA sequences and applying bioinformatic algorithms allows to search, match, and compare videos in large-scale databases. We show an application for content-based metadata mapping between versions of annotated video.

cs.CV↗