For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the structure, color and texture of object surfaces, from the two-dimensional image that is projected onto the eye or camera. This goal is not achieved in a single step; vision proceeds in stages, with each stage producing increasingly more useful descriptions of the image and then the scene. The first clue about the physical properties of the scene are provided by the changes of intensity in the image. The importance of intensity changes and edges in early visual processg has led to extensive research on their detection, description and .use, both in computer and biological vision systems. This article reviews some of the theory that underlies the detection of edges, and the methods used to carry out this analysis.

Abstract not found

We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Basis Functions approximation schemes. This paper shows that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular, we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions, som...

Abstract not found

The use of energy-minimizing curves, known as "snakes" to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos [23]. A balloon model was introduced in [12] as a way to generalize and solve some of the problems encountered with the original method. We present a 3D generalization of the balloon model as a 3D deformable surface, which evolves in 3D images. It is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential. We also show properties of energy-minimizing surfaces concerning their relationship with 3D edge points. To solve the minimization problem for a surface, two simplified approaches are shown first, defining a 3D surface as a series of 2D planar curves. Then, after comparing Finite Element Method and Finite Difference Method in the 2D problem, we solve the 3D model using the Finite Element Method yielding greater stability and faster convergence. We have a...

When we look at images, certain salient structures often attract our immediate attention, without requiring a systematic scan of the entire image. In subsequent stages, processing resources can be allocated preferentially to these salient structures. In many cases this saJiency is a property of the structure as a whole, i.e., parts of the structure are not salient in isolation. In this paper we present a saliency measure based on cur- vature and curvature variation. The structures this measure emphasizes are also salient in human perception, and they often correspond to objects of interest in the image. We present a method for computing the sallehey by a simple iterative scheme, using a uniform network of locally connected processing elements. The network uses an optimization approach to produce a "saliency map" which is a representation of the image emphasizing salient locations. The main.properties of the network are: (i) the computations are simple and local, (ii) globally salient structures emerge with a small number of iterations (iii) as a by-product of the computation contours are smoothed, and gaps are filled-in.

This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous B-spline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct B-spline transform). The reverse operation is the signal reconstruction from its spline coefficients with an optional zooming factor rn (indirect B-spline transform) . We derive general expressions for the z transforms and the equivalent continuous impulse responses of B-spline interpolators of order n. We present simple techniques for signal differentiation and filtering in the transformed domain. We then derive recursive filters that efficiently solve the problems of smoothing spline and least squares approximations. The smoothing spline technique approximates a signal with a complete set of coefficients subject to certain regularization or smoothness constraints. The least squares approach, on the other hand, uses a reduced number of B-spline coefficients with equally spaced nodes; this technique is in many ways analogous to the application of antialiasing low-pass filter prior to decimation in order to represent a signal correctly with a reduced number of samples.

In computer vision and image processing, edge detection concerns the localization of significant variations of the grey level image and the identification of the physical phenomena that originated them. This information is very useful for applications in 3D reconstruction, motion, recognition, image enhancement and restoration, image registration, image compression, and so on. Usually, edge detection requires smoothing and differentiation of the image. Differentiation is an ill-conditioned problem and smoothing results in a loss of information. It is difficult to design a general edge detection algorithm which performs well in many contexts and captures the requirements of subsequent processing stages. Consequently, over the history of digital image processing a variety of edge detectors have been devised which differ in their mathematical and algorithmic properties. This paper is an account of the current state of our understanding of edge detection. We propose an overview of research...

The goal of perception is to extract invariant properties of the underlying world. By computing contrast at edges, the retina reduces incident light intensities spanning twelve decades to a twentyfold variation. In one stroke, it solves the dynamic range problem and extracts relative reflectivity, bringing us a step closer to the goal. We have built a contrast-- sensitive silicon retina that models all major synaptic interactions in the outer--plexiform layer of the vertebrate retina using current--mode CMOS circuits: namely, reciprocal synapses between cones and horizontal cells, which produce the antagonistic center/surround receptive field, and cone and horizontal cell gap junctions, which determine its size. The chip has 90 \Theta 92 pixels on a 6:8 \Theta 6:9mm die in 2¯m n--well technology and is fully functional. 1 INTRODUCTION Retinal cones use both intracellular and extracellular mechanisms to adapt their gain to the input intensity level and hence remain sensitive over a la...

The use of energy-minimizing curves, known as "snakes" to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos [10]. A balloon model was introduced in [5] as a way to generalize and solve some of the problems encountered with the original method. We present a