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.

Image Chunking: Defining Spatial Building Blocks for Scene Analysis

Rapid judgments about the properties and spatial relations of objects are the crux of visually guided interaction with the world. Vision begins, however, with essentially pointwise representations of the scene, such as arrays of pixels or small edge fragments. For adequate time-performance in recognition, manipulation, navigation, and reasoning, the processes that extract meaningful entities from the pointwise representations must exploit parallelism. This report develops a framework for the fast extraction of scene entities, based on a simple, local model of parallel computation.sAn image chunk is a subset of an image that can act as a unit in the course of spatial analysis. A parallel preprocessing stage constructs a variety of simple chunks uniformly over the visual array. On the basis of these chunks, subsequent serial processes locate relevant scene components and assemble detailed descriptions of them rapidly. This thesis defines image chunks that facilitate the most potentially time-consuming operations of spatial analysis---boundary tracing, area coloring, and the selection of locations at which to apply detailed analysis. Fast parallel processes for computing these chunks from images, and chunk-based formulations of indexing, tracing, and coloring, are presented. These processes have been simulated and evaluated on the lisp machine and the connection machine.

The Computation of Color

This thesis takes an interdisciplinary approach to the study of color vision, focussing on the phenomenon of color constancy formulated as a computational problem. The primary contributions of the thesis are (1) the demonstration of a formal framework for lightness algorithms; (2) the derivation of a new lightness algorithm based on regularization theory; (3) the synthesis of an adaptive lightness algorithm using "learning" techniques; (4) the development of an image segmentation algorithm that uses luminance and color information to mark material boundaries; and (5) an experimental investigation into the cues that human observers use to judge the color of the illuminant. Other computational approaches to color are reviewed and some of their links to psychophysics and physiology are explored.

Analysis of Differential and Matching Methods for Optical Flow

Several algorithms for optical flow are studied theoretically and experimentally. Differential and matching methods are examined; these two methods have differing domains of application- differential methods are best when displacements in the image are small (<2 pixels) while matching methods work well for moderate displacements but do not handle sub-pixel motions. Both types of optical flow algorithm can use either local or global constraints, such as spatial smoothness. Local matching and differential techniques and global differential techniques will be examined. Most algorithms for optical flow utilize weak assumptions on the local variation of the flow and on the variation of image brightness. Strengthening these assumptions improves the flow computation. The computational consequence of this is a need for larger spatial and temporal support. Global differential approaches can be extended to local (patchwise) differential methods and local differential methods using higher derivatives. Using larger support is valid when constraint on the local shape of the flow are satisfied. We show that a simple constraint on the local shape of the optical flow, that there is slow spatial variation in the image plane, is often satisfied. We show how local differential methods imply the constraints for related methods using higher derivatives. Experiments show the behavior of these optical flow methods on velocity fields which so not obey the assumptions. Implementation of these methods highlights the importance of numerical differentiation. Numerical approximation of derivatives require care, in two respects: first, it is important that the temporal and spatial derivatives be matched, because of the significant scale differences in space and time, and, second, the derivative estimates improve with larger support.

Parallel Computation of Vernier Offsets, Curvature and Chevrons in Humans

A vernier offset is detected at once among straight lines, and reaction times are almost independent of the number of simultaneously presented stimuli (distractors), indicating parallel processing of vernier offsets. Reaction times for identifying a vernier offset to one side among verniers offset to the opposite side increase with the number of distractors, indicating serial processing. Even deviations below a photoreceptor diameter can be detected at once. The visual system thus attains positional accuracy below the photoreceptor diameter simultaneously at different positions. I conclude that deviation from straightness, or change of orientation, is detected in parallel over the visual field. Discontinuities or gradients in orientation may represent an elementary feature of vision.

Some Extensions of the K-Means Algorithm for Image Segmentation and Pattern Classification

In this paper we present some extensions to the k-means algorithm for vector quantization that permit its efficient use in image segmentation and pattern classification tasks. It is shown that by introducing state variables that correspond to certain statistics of the dynamic behavior of the algorithm, it is possible to find the representative centers fo the lower dimensional maniforlds that define the boundaries between classes, for clouds of multi-dimensional, mult-class data; this permits one, for example, to find class boundaries directly from sparse data (e.g., in image segmentation tasks) or to efficiently place centers for pattern classification (e.g., with local Gaussian classifiers). The same state variables can be used to define algorithms for determining adaptively the optimal number of centers for clouds of data with space-varying density. Some examples of the applicatin of these extensions are also given.

Towards an Example-Based Image Compression Architecture for Video-Conferencing

This paper consists of two major parts. First, we present the outline of a simple approach to very-low bandwidth video-conferencing system relying on an example-based hierarchical image compression scheme. In particular, we discuss the use of example images as a model, the number of required examples, faces as a class of semi-rigid objects, a hierarchical model based on decomposition into different time-scales, and the decomposition of face images into patches of interest. In the second part, we present several algorithms for image processing and animation as well as experimental evaluations. Among the original contributions of this paper is an automatic algorithm for pose estimation and normalization. We also review and compare different algorithms for finding the nearest neighbors in a database for a new input as well as a generalized algorithm for blending patches of interest in order to synthesize new images. Finally, we outline the possible integration of several algorithms to illustrate a simple model-based video-conference system.

Linear Object Classes and Image Synthesis from a Single Example Image

The need to generate new views of a 3D object from a single real image arises in several fields, including graphics and object recognition. While the traditional approach relies on the use of 3D models, we have recently introduced techniques that are applicable under restricted conditions but simpler. The approach exploits image transformations that are specific to the relevant object class and learnable from example views of other "prototypical" objects of the same class. In this paper, we introduce such a new technique by extending the notion of linear class first proposed by Poggio and Vetter. For linear object classes it is shown that linear transformations can be learned exactly from a basis set of 2D prototypical views. We demonstrate the approach on artificial objects and then show preliminary evidence that the technique can effectively "rotate" high- resolution face images from a single 2D view.

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.

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.

Direct Estimation of Motion and Extended Scene Structure from a Moving Stereo Rig

We describe a new method for motion estimation and 3D reconstruction from stereo image sequences obtained by a stereo rig moving through a rigid world. We show that given two stereo pairs one can compute the motion of the stereo rig directly from the image derivatives (spatial and temporal). Correspondences are not required. One can then use the images from both pairs combined to compute a dense depth map. The motion estimates between stereo pairs enable us to combine depth maps from all the pairs in the sequence to form an extended scene reconstruction and we show results from a real image sequence. The motion computation is a linear least squares computation using all the pixels in the image. Areas with little or no contrast are implicitly weighted less so one does not have to explicitly apply a confidence measure.

The Image Dissector "Eyes"

This is a collection of data on the construction operation and performance of the two image dissector cameras. Some of this data is useful in deciding whether certain shortcomings are significant for a given application and if so how to compensate for them.

Implementing Universal Computation in an Evolutionary System

Evolutionary algorithms are a common tool in engineering and in the study of natural evolution. Here we take their use in a new direction by showing how they can be made to implement a universal computer. We consider populations of individuals with genes whose values are the variables of interest. By allowing them to interact with one another in a specified environment with limited resources, we demonstrate the ability to construct any arbitrary logic circuit. We explore models based on the limits of small and large populations, and show examples of such a system in action, implementing a simple logic circuit.

Recovering Intrinsic Images from a Single Image

We present an algorithm that uses multiple cues to recover shading and reflectance intrinsic images from a single image. Using both color information and a classifier trained to recognize gray-scale patterns, each image derivative is classified as being caused by shading or a change in the surface's reflectance. Generalized Belief Propagation is then used to propagate information from areas where the correct classification is clear to areas where it is ambiguous. We also show results on real images.

Shape Recipes: Scene Representations that Refer to the Image

The goal of low-level vision is to estimate an underlying scene, given an observed image. Real-world scenes (e.g., albedos or shapes) can be very complex, conventionally requiring high dimensional representations which are hard to estimate and store. We propose a low-dimensional representation, called a scene recipe, that relies on the image itself to describe the complex scene configurations. Shape recipes are an example: these are the regression coefficients that predict the bandpassed shape from bandpassed image data. We describe the benefits of this representation, and show two uses illustrating their properties: (1) we improve stereo shape estimates by learning shape recipes at low resolution and applying them at full resolution; (2) Shape recipes implicitly contain information about lighting and materials and we use them for material segmentation.