Early vision algorithms often have a first stage of linear-filtering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. This discretization produces anisotropies due to a loss of traslation-, rotation-, scaling-invariance that makes early vision algorithms less precise and more difficult to design. This need not be so: one can compute and store efficiently the response of families of linear filters defined on a continuum of orientations and scales. A technique is presented that allows (1) to compute the best approximation of a given family using linear combinations of a small number of `basis' functions; (2) to describe all finite-dimensional families, i.e. the families of filters for which a finite dimensional representation is p...

Families of kernels that are useful in a variety of early vision algorithms may be obtained by rotating and scaling in a continuum a `template' kernel. These multi-scale multi-orientation family may be approximated by linear interpolation of a discrete finite set of appropriate `basis' kernels. A scheme for generating such a basis together with the appropriate interpolation weights is described. Unlike previous schemes by Perona, and Simoncelli et al. it is guaranteed to generate the most parsimonious one. Additionally, it is shown how to exploit two symmetries in edge-detection kernels for reducing storage and computational costs and generating simultaneously endstop- and junction-tuned filters for free.

This paper describes a representation for pen-and-ink illustrations that allows the creation of high-fidelity illustrations at any scale or resolution. We represent a pen-and-ink illustration as a low-resolution grey-scale image, augmented by a set of discontinuity segments, along with a stroke texture. To render an illustration at a particular scale, we first rescale the grey-scale image to the desired size and then hatch the resulting image with pen-and-ink strokes. The main technical contribution of the paper is a new reconstruction algorithm that magnifies the low-resolution image while keeping the resulting image sharp along discontinuities.

xi 1 Introduction 1 1.1 Problem Statement : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2 The Neuron : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.2.1 Biological Model : : : : : : : : : : : : : : : : : : : : : : 7 1.2.2 Computational Model : : : : : : : : : : : : : : : : : : : 9 1.3 Implementation Technologies : : : : : : : : : : : : : : : : : : : : 11 1.4 State of the Art : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 1.5 Summary of Results : : : : : : : : : : : : : : : : : : : : : : : : 16 2 Implementation of Neural Models with Static Links 19 2.1 ANN Models with Static Links : : : : : : : : : : : : : : : : : : 20 2.1.1 The Hopfield Model : : : : : : : : : : : : : : : : : : : : : 21 2.1.2 The Perceptron Model : : : : : : : : : : : : : : : : : : : 23 2.1.3 The Multi-Layer Model : : : : : : : : : : : : : : : : : : : 24 2.2 Basic Computational Requirements : : : : : : : : : : : : : : : : 25 2.2.1 Search Phase Computations : : : : : : : : : : : : : : ...

: We present a novel ridge detector that finds ridges on vector fields. It is designed to automatically find the right scale of a ridge even in the presence of noise, multiple steps and narrow valleys. One of the key features of such ridge detector is that it has a zero response at discontinuities. The ridge detector can be applied both to scalar and vector quantities such as color. We also present a parallel perceptual organization scheme based on such ridge detector that works without edges; in addition to perceptual groups, the scheme computes potential focus of attention points at which to direct future processing. The relation to human perception and several theoretical findings supporting the scheme are presented. We also show results of a Connection Machine implementation of the scheme for perceptual organization (without edges) using color. Acknowledgements: This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technolo...

In this dissertation I address the problem of visual recognition of non-rigid objects. I introduce the frame alignment approach to recognition and illustrate it in two types of non-rigid objects: contour textures and elongated flexible objects. Frame alignment is based on matching stored models to images and has three stages: first, a "frame curve" and a corresponding object are computed in the image. Second, the object is brought into correspondence with the model by aligning the model axis with the object axis; if the object is not rigid it is "unbent" achieving a canonical description for recognition. Finally, object and model are matched against each other. Rigid and elongated flexible objects are matched using all contour information. Contour textures are matched using filter outputs around the frame curve. The central contribution of this thesis is Curved Inertia Frames (C.I.F.), a scheme for computing frame curves directly on the image. C.I.F. is the first algorithm which can c...

We study the problem of image segmentation in the presence of texture information at several scales. We propose to model homogeneous textured regions as ergodic random functions and to model images as piecewise ergodic random functions. Image properties can then be retrieved by filtering the image at all scale of resolution with a bunch of image descriptors and then averaging this description over regions of different sizes. The result is a representation embedded in a "scale-scale-space" which is an extension of the usual scale-space obtained by adding to it a statistical scale dimension. The ergodicity assumption then is equivalent to assume that the representation becomes deterministic as the statistical scale goes to infinity. Each type of texture can then be characterized by a deterministic "signature" which can be approximately retrieved from the image by using large enough averaging windows. We propose a method of segmentation based on evaluating the dishomogeneity at all statis...

An important step in image processing tasks is the identification of certain desired attributes in an image. Traditionally, this is done by transforming the image into a domain where the desired attributes or features are easily identifiable. One class of image transforms that have found great applicability in artificial vision systems are those that transform the image from the spatial to the frequency domain (the most popular of these is the Fourier Transform). It is desirable to use a member of this class that yields good resolution in both the spatial as well as the frequency domains. In this paper, we consider a transform called the 2-D Gabor Wavelet Transform that achieves the best possible conjoint resolution in space and frequency. This transform is based on families of functions that are translated, rotated or dilated versions of each other. In addition to their desirable mathematical properties, research in psychophysics has shown that the responses of simple cells in mammali...