Virtual Visual Hulls: Example-Based 3D Shape Estimation from a Single Silhouette

Recovering a volumetric model of a person, car, or other object of interest from a single snapshot would be useful for many computer graphics applications. 3D model estimation in general is hard, and currently requires active sensors, multiple views, or integration over time. For a known object class, however, 3D shape can be successfully inferred from a single snapshot. We present a method for generating a ``virtual visual hull''-- an estimate of the 3D shape of an object from a known class, given a single silhouette observed from an unknown viewpoint. For a given class, a large database of multi-view silhouette examples from calibrated, though possibly varied, camera rigs are collected. To infer a novel single view input silhouette's virtual visual hull, we search for 3D shapes in the database which are most consistent with the observed contour. The input is matched to component single views of the multi-view training examples. A set of viewpoint-aligned virtual views are generated from the visual hulls corresponding to these examples. The 3D shape estimate for the input is then found by interpolating between the contours of these aligned views. When the underlying shape is ambiguous given a single view silhouette, we produce multiple visual hull hypotheses; if a sequence of input images is available, a dynamic programming approach is applied to find the maximum likelihood path through the feasible hypotheses over time. We show results of our algorithm on real and synthetic images of people.

Surface Reflectance Estimation and Natural Illumination Statistics

Humans recognize optical reflectance properties of surfaces such as metal, plastic, or paper from a single image without knowledge of illumination. We develop a machine vision system to perform similar recognition tasks automatically. Reflectance estimation under unknown, arbitrary illumination proves highly underconstrained due to the variety of potential illumination distributions and surface reflectance properties. We have found that the spatial structure of real-world illumination possesses some of the statistical regularities observed in the natural image statistics literature. A human or computer vision system may be able to exploit this prior information to determine the most likely surface reflectance given an observed image. We develop an algorithm for reflectance classification under unknown real-world illumination, which learns relationships between surface reflectance and certain features (statistics) computed from a single observed image. We also develop an automatic feature selection method.

Recognition of Surface Reflectance Properties from a Single Image under Unknown Real-World Illumination

This paper describes a machine vision system that classifies reflectance properties of surfaces such as metal, plastic, or paper, under unknown real-world illumination. We demonstrate performance of our algorithm for surfaces of arbitrary geometry. Reflectance estimation under arbitrary omnidirectional illumination proves highly underconstrained. Our reflectance estimation algorithm succeeds by learning relationships between surface reflectance and certain statistics computed from an observed image, which depend on statistical regularities in the spatial structure of real-world illumination. Although the algorithm assumes known geometry, its statistical nature makes it robust to inaccurate geometry estimates.

Fast Pose Estimation with Parameter Sensitive Hashing

Example-based methods are effective for parameter estimation problems when the underlying system is simple or the dimensionality of the input is low. For complex and high-dimensional problems such as pose estimation, the number of required examples and the computational complexity rapidly becme prohibitively high. We introduce a new algorithm that learns a set of hashing functions that efficiently index examples relevant to a particular estimation task. Our algorithm extends a recently developed method for locality-sensitive hashing, which finds approximate neighbors in time sublinear in the number of examples. This method depends critically on the choice of hash functions; we show how to find the set of hash functions that are optimally relevant to a particular estimation problem. Experiments demonstrate that the resulting algorithm, which we call Parameter-Sensitive Hashing, can rapidly and accurately estimate the articulated pose of human figures from a large database of example images.

A Statistical Image-Based Shape Model for Visual Hull Reconstruction and 3D Structure Inference

We present a statistical image-based shape + structure model for Bayesian visual hull reconstruction and 3D structure inference. The 3D shape of a class of objects is represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras. Bayesian reconstructions of new shapes are then estimated using a prior density constructed with a mixture model and probabilistic principal components analysis. We show how the use of a class-specific prior in a visual hull reconstruction can reduce the effect of segmentation errors from the silhouette extraction process. The proposed method is applied to a data set of pedestrian images, and improvements in the approximate 3D models under various noise conditions are shown. We further augment the shape model to incorporate structural features of interest; unknown structural parameters for a novel set of contours are then inferred via the Bayesian reconstruction process. Model matching and parameter inference are done entirely in the image domain and require no explicit 3D construction. Our shape model enables accurate estimation of structure despite segmentation errors or missing views in the input silhouettes, and works even with only a single input view. Using a data set of thousands of pedestrian images generated from a synthetic model, we can accurately infer the 3D locations of 19 joints on the body based on observed silhouette contours from real images.

Image Based Rendering Using Algebraic Techniques

This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.