Learning Three-Dimensional Shape Models for Sketch Recognition

Artifacts made by humans, such as items of furniture and houses, exhibit an enormous amount of variability in shape. In this paper, we concentrate on models of the shapes of objects that are made up of fixed collections of sub-parts whose dimensions and spatial arrangement exhibit variation. Our goals are: to learn these models from data and to use them for recognition. Our emphasis is on learning and recognition from three-dimensional data, to test the basic shape-modeling methodology. In this paper we also demonstrate how to use models learned in three dimensions for recognition of two-dimensional sketches of objects.

Segmentation of Brain Tissue from Magnetic Resonance Images

Segmentation of medical imagery is a challenging problem due to the complexity of the images, as well as to the absence of models of the anatomy that fully capture the possible deformations in each structure. Brain tissue is a particularly complex structure, and its segmentation is an important step for studies in temporal change detection of morphology, as well as for 3D visualization in surgical planning. In this paper, we present a method for segmentation of brain tissue from magnetic resonance images that is a combination of three existing techniques from the Computer Vision literature: EM segmentation, binary morphology, and active contour models. Each of these techniques has been customized for the problem of brain tissue segmentation in a way that the resultant method is more robust than its components. Finally, we present the results of a parallel implementation of this method on IBM's supercomputer Power Visualization System for a database of 20 brain scans each with 256x256x124 voxels and validate those against segmentations generated by neuroanatomy experts.

Learning Shape Descriptions: Generating and Generalizing Models of Visual Objects

We present the results of an implemented system for learning structural prototypes from grey-scale images. We show how to divide an object into subparts and how to encode the properties of these subparts and the relations between them. We discuss the importance of hierarchy and grouping in representing objects and show how a notion of visual similarities can be embedded in the description language. Finally we exhibit a learning algorithm that forms class models from the descriptions produced and uses these models to recognize new members of the class.

Active Learning with Statistical Models

For many types of learners one can compute the statistically 'optimal' way to select data. We review how these techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate.

Models of Noise and Robust Estimates

Given n noisy observations g; of the same quantity f, it is common use to give an estimate of f by minimizing the function Eni=1(gi-f)2. From a statistical point of view this corresponds to computing the Maximum likelihood estimate, under the assumption of Gaussian noise. However, it is well known that this choice leads to results that are very sensitive to the presence of outliers in the data. For this reason it has been proposed to minimize the functions of the form Eni=1V(gi-f), where V is a function that increases less rapidly than the square. Several choices for V have been proposed and successfully used to obtain "robust" estimates. In this paper we show that, for a class of functions V, using these robust estimators corresponds to assuming that data are corrupted by Gaussian noise whose variance fluctuates according to some given probability distribution, that uniquely determines the shape of V.

Light Field Morphable Models

Statistical shape and texture appearance models are powerful image representations, but previously had been restricted to 2D or simple 3D shapes. In this paper we present a novel 3D morphable model based on image-based rendering techniques, which can represent complex lighting conditions, structures, and surfaces. We describe how to construct a manifold of the multi-view appearance of an object class using light fields and show how to match a 2D image of an object to a point on this manifold. In turn we use the reconstructed light field to render novel views of the object. Our technique overcomes the limitations of polygon based appearance models and uses light fields that are acquired in real-time.

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.

Shape from Contour

The problem of using image contours to infer the shapes and orientations of surfaces is treated as a problem of statistical estimation. The basis for solving this problem lies in an understanding of the geometry of contour formation, coupled with simple statistical models of the contour generating process. This approach is first applied to the special case of surfaces known to be planar. The distortion of contour shape imposed by projection is treated as a signal to be estimated, and variations of non-projective origin are treated as noise. The resulting method is then extended to the estimation of curved surfaces, and applied successfully to natural images. Next, the geometric treatment is further extended by relating countour curvature to surface curvature, using cast shadows as a model for contour generation. This geometric relation, combined with a statistical model, provides a measure of goodness-of-fit between a surface and an image contour. The goodness-of-fit measure is applied to the problem of establishing registration between an image and a surface model. Finally, the statistical estimation strategy is experimentally compared to human perception of orientation: human observers' judgements of tilt correspond closely to the estimates produced by the planar strategy.

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.

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.

Face processing in humans is compatible with a simple shape-based model of vision

Understanding how the human visual system recognizes objects is one of the key challenges in neuroscience. Inspired by a large body of physiological evidence (Felleman and Van Essen, 1991; Hubel and Wiesel, 1962; Livingstone and Hubel, 1988; Tso et al., 2001; Zeki, 1993), a general class of recognition models has emerged which is based on a hierarchical organization of visual processing, with succeeding stages being sensitive to image features of increasing complexity (Hummel and Biederman, 1992; Riesenhuber and Poggio, 1999; Selfridge, 1959). However, these models appear to be incompatible with some well-known psychophysical results. Prominent among these are experiments investigating recognition impairments caused by vertical inversion of images, especially those of faces. It has been reported that faces that differ "featurally" are much easier to distinguish when inverted than those that differ "configurally" (Freire et al., 2000; Le Grand et al., 2001; Mondloch et al., 2002) ??finding that is difficult to reconcile with the aforementioned models. Here we show that after controlling for subjects' expectations, there is no difference between "featurally" and "configurally" transformed faces in terms of inversion effect. This result reinforces the plausibility of simple hierarchical models of object representation and recognition in cortex.