Direct Computation of 3D Shape Invariants and the Focus of Expansion

Structure from motion often refers to the computation of 3D structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images, I will first show that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line-segments in one image. Using this result, local surface patches can be classified as convex, concave, parabolic (cylindrical), hyperbolic (saddle point) or planar. At the same time the translational component of the optical flow is obtained, from which the focus of expansion can be computed.

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.

Inferring 3D Structure with a Statistical Image-Based Shape Model

We present an image-based approach to infer 3D structure parameters using a probabilistic "shape+structure'' model. The 3D shape of a class of objects may be represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras. Bayesian reconstructions of new shapes can then be estimated using a prior density constructed with a mixture model and probabilistic principal components analysis. We augment the shape model to incorporate structural features of interest; novel examples with missing structure parameters may then be reconstructed to obtain estimates of these parameters. 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 dataset of thousands of pedestrian images generated from a synthetic model, we can perform accurate inference of the 3D locations of 19 joints on the body based on observed silhouette contours from real 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.

Structure from Stereo and Motion

Stereopsis and motion parallax are two methods for recovering three dimensional shape. Theoretical analyses of each method show that neither alone can recover rigid 3D shapes correctly unless other information, such as perspective, is included. The solutions for recovering rigid structure from motion have a reflection ambiguity; the depth scale of the stereoscopic solution will not be known unless the fixation distance is specified in units of interpupil separation. (Hence the configuration will appear distorted.) However, the correct configuration and the disposition of a rigid 3D shape can be recovered if stereopsis and motion are integrated, for then a unique solution follows from a set of linear equations. The correct interpretation requires only three points and two stereo views.

Vectorizing Face Images by Interpreting Shape and Texture Computations

The correspondence problem in computer vision is basically a matching task between two or more sets of features. In this paper, we introduce a vectorized image representation, which is a feature-based representation where correspondence has been established with respect to a reference image. This representation has two components: (1) shape, or (x, y) feature locations, and (2) texture, defined as the image grey levels mapped onto the standard reference image. This paper explores an automatic technique for "vectorizing" face images. Our face vectorizer alternates back and forth between computation steps for shape and texture, and a key idea is to structure the two computations so that each one uses the output of the other. A hierarchical coarse-to-fine implementation is discussed, and applications are presented to the problems of facial feature detection and registration of two arbitrary faces.

Feature Extraction Without Edge Detection

Information representation is a critical issue in machine vision. The representation strategy in the primitive stages of a vision system has enormous implications for the performance in subsequent stages. Existing feature extraction paradigms, like edge detection, provide sparse and unreliable representations of the image information. In this thesis, we propose a novel feature extraction paradigm. The features consist of salient, simple parts of regions bounded by zero-crossings. The features are dense, stable, and robust. The primary advantage of the features is that they have abstract geometric attributes pertaining to their size and shape. To demonstrate the utility of the feature extraction paradigm, we apply it to passive navigation. We argue that the paradigm is applicable to other early vision problems.

Implementation of a Theory of Edge Detection

This report describes the implementation of a theory of edge detection, proposed by Marr and Hildreth (1979). According to this theory, the image is first processed independently through a set of different size filters, whose shape is the Laplacian of a Gaussian, ***. Zero-crossings in the output of these filters mark the positions of intensity changes at different resolutions. Information about these zero-crossings is then used for deriving a full symbolic description of changes in intensity in the image, called the raw primal sketch. The theory is closely tied with early processing in the human visual systems. In this report, we first examine the critical properties of the initial filters used in the edge detection process, both from a theoretical and practical standpoint. The implementation is then used as a test bed for exploring aspects of the human visual system; in particular, acuity and hyperacuity. Finally, we present some preliminary results concerning the relationship between zero-crossings detected at different resolutions, and some observations relevant to the process by which the human visual system integrates descriptions of intensity changes obtained at different resolutions.

Region-Based Feature Interpretation for Recognizing 3D Models in 2D Images

In model-based vision, there are a huge number of possible ways to match model features to image features. In addition to model shape constraints, there are important match-independent constraints that can efficiently reduce the search without the combinatorics of matching. I demonstrate two specific modules in the context of a complete recognition system, Reggie. The first is a region-based grouping mechanism to find groups of image features that are likely to come from a single object. The second is an interpretive matching scheme to make explicit hypotheses about occlusion and instabilities in the image features.

Stereo-Based Head Pose Tracking Using Iterative Closest Point and Normal Flow Constraint

In this text, we present two stereo-based head tracking techniques along with a fast 3D model acquisition system. The first tracking technique is a robust implementation of stereo-based head tracking designed for interactive environments with uncontrolled lighting. We integrate fast face detection and drift reduction algorithms with a gradient-based stereo rigid motion tracking technique. Our system can automatically segment and track a user's head under large rotation and illumination variations. Precision and usability of this approach are compared with previous tracking methods for cursor control and target selection in both desktop and interactive room environments. The second tracking technique is designed to improve the robustness of head pose tracking for fast movements. Our iterative hybrid tracker combines constraints from the ICP (Iterative Closest Point) algorithm and normal flow constraint. This new technique is more precise for small movements and noisy depth than ICP alone, and more robust for large movements than the normal flow constraint alone. We present experiments which test the accuracy of our approach on sequences of real and synthetic stereo images. The 3D model acquisition system we present quickly aligns intensity and depth images, and reconstructs a textured 3D mesh. 3D views are registered with shape alignment based on our iterative hybrid tracker. We reconstruct the 3D model using a new Cubic Ray Projection merging algorithm which takes advantage of a novel data structure: the linked voxel space. We present experiments to test the accuracy of our approach on 3D face modelling using real-time stereo images.

Representation and Detection of Shapes in Images

We present a set of techniques that can be used to represent and detect shapes in images. Our methods revolve around a particular shape representation based on the description of objects using triangulated polygons. This representation is similar to the medial axis transform and has important properties from a computational perspective. The first problem we consider is the detection of non-rigid objects in images using deformable models. We present an efficient algorithm to solve this problem in a wide range of situations, and show examples in both natural and medical images. We also consider the problem of learning an accurate non-rigid shape model for a class of objects from examples. We show how to learn good models while constraining them to the form required by the detection algorithm. Finally, we consider the problem of low-level image segmentation and grouping. We describe a stochastic grammar that generates arbitrary triangulated polygons while capturing Gestalt principles of shape regularity. This grammar is used as a prior model over random shapes in a low level algorithm that detects objects in images.

Global Depth Perception from Familiar Scene Structure

In the absence of cues for absolute depth measurements as binocular disparity, motion, or defocus, the absolute distance between the observer and a scene cannot be measured. The interpretation of shading, edges and junctions may provide a 3D model of the scene but it will not inform about the actual "size" of the space. One possible source of information for absolute depth estimation is the image size of known objects. However, this is computationally complex due to the difficulty of the object recognition process. Here we propose a source of information for absolute depth estimation that does not rely on specific objects: we introduce a procedure for absolute depth estimation based on the recognition of the whole scene. The shape of the space of the scene and the structures present in the scene are strongly related to the scale of observation. We demonstrate that, by recognizing the properties of the structures present in the image, we can infer the scale of the scene, and therefore its absolute mean depth. We illustrate the interest in computing the mean depth of the scene with application to scene recognition and object detection.