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.

A face recognition system must recognize a face from a novel image despite the variations between images of the same face. A common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations. Examples of such representations are edge maps, image intensity derivatives, and images convolved with 2D Gabor-like filters. Here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination, as well as viewpoint and facial expression. Our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination. Similar results were obtained for changes due to viewpoint and expression. Image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination. However, systems...

Absfrucf- We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisifies several desirable analytical and computational properties for MAP estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global mini-mum of the U posteriori log-likeihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography. I.

When extracting features from image data, the type of information that can be extracted may be strongly dependent on the scales at which the feature detectors are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of scale levels when detecting one-dimensional features, such as edges and ridges. Anovel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An important property of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analysed in detail. It is shown that by expressing these in terms of γ-normalized derivatives, an immediate consequence of this definition is that fine scales are selected for sharp edges (so as to reduce the shape distortions due to scale-space smoothing), whereas coarse scales are selected for diffuse edges, such that an edge model constitutes a valid abstraction of the intensity profile across the edge. With slight modifications, this idea can be used for formulating a ridge detector with automatic scale selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge.

Abstract—We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating between a template matching and a maximum pooling operation. We demonstrate the strength of the approach on a range of recognition tasks: From invariant single object recognition in clutter to multiclass categorization problems and complex scene understanding tasks that rely on the recognition of both shape-based as well as texture-based objects. Given the biological constraints that the system had to satisfy, the approach performs surprisingly well: It has the capability of learning from only a few training examples and competes with state-of-the-art systems. We also discuss the existence of a universal, redundant dictionary of features that could handle the recognition of most object categories. In addition to its relevance for computer vision, the success of this approach suggests a plausibility proof for a class of feedforward models of object recognition in cortex.

Corners and vertices are strong and useful features in Computer Vision for scene analysis, stereo matching and motion analysis. This paper deals with the development of a computational approach to these important features. We consider first a corner model and study analytically its behavior once it has been smoothed using the well-known Gaussian filter. This allows us to clarify the behavior of some well known cornerness measure based approaches used to detect these points of interest. Most of these classical approaches appear to detect points that do not correspond to the exact position of the corner. A new scale-space based approach that combines useful properties from the Laplacian and Beaudet's measure [Bea78] is then proposed in order to correct and detect exactly the corner position. An extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection. In particular, it is shown that a trihedral vertex has two elliptic maxima on ...

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.

We propose a new definition of the total variation norm for vector valued functions which can be applied to restore color and other vector valued images. The new TV norm has the desirable properties of (i) not penalizing discontinuities (edges) in the image, (ii) rotationally invariant in the image space, and (iii) reduces to the usual TV norm in the scalar case. Some numerical experiments on denoising simple color images in RGB color space are presented. 1 Introduction During gathering and transfer of image data some noise and blur is usually introduced into the image. Several reconstruction methods based on the total variation (TV) norm have been proposed and studied for intensity (gray scale) images, see [9, 14, 21, 26, 29]. Since these methods have been successful in reducing noise and blur without smearing sharp edges for intensity images, it is natural to extend the TV norm to handle color and other vector valued images. Why do we need color restoration? It can be argued that si...

We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The absolute minimal Lipschitz extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range.

Standard edge detectors fail to nd most relevant edges, nding either too many or too few, because they lack a geometric model to guide their search. We present a technique that integrates both photometric and geometric models with an initial estimate of the boundary. The strength of this approach lies in the ability of the geometric model to overcome various photometric anomalies, thereby nding boundaries that could not otherwise be found. Furthermore, edges can be scored based on their goodness of t to the model, thus allowing one to use semantic model information to accept or reject the edges. 1