A threshold selection method from gray level histograms

This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.

A Computational Approach to Edge Detection

Texture is one of the important characteristics used in identifying objects or regions of interest in an image, whether the image be a photomicrograph, an aerial photograph, or a satellite image. This paper describes some easily computable textural features based on gray-tone spatial dependancies, and illustrates their application in category-identification tasks of three different kinds of image data: photomicrographs of five kinds of sandstones, 1:20 000 panchromatic aerial photographs of eight land-use categories, and Earth Resources Technology Satellite (ERTS) multispecial imagery containing seven land-use categories. We use two kinds of decision rules: one for which the decision regions are convex polyhedra (a piecewise linear decision rule), and one for which the decision regions are rectangular parallelpipeds (a min-max decision rule). In each experiment the data set was divided into two parts, a training set and a test set. Test set identification accuracy is 89 percent for the photomicrographs, 82 percent for the aerial photographic imagery, and 83 percent for the satellite imagery. These results indicate that the easily computable textural features probably have a general applicability for a wide variety of image-classification applications.

Textural Features for Image Classification

Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >

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A theory for multiresolution signal decomposition: the wavelet representation

We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.

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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

This paper describes an approach to interpreting line drawings under assumptions which are ubiquitous in natural scenes. The assumptions are that many identical, essentially two-dimensional features are depicted and they are arranged in random orientations. We assume that at least one of the many features is paralled to the image plane, and thus gives the real dimensions of a feature. From this, the orientations of the other features can be easily recovered. Four examples of this approach are shown to give quite natural results.

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Shape from random planar features

Elementary Problems: E2629, E2630-E2634

Parallel string acceptance using lattice graphs

Most previous theoretical work on motion planning has addressed the problem of path planning for geometrically simple robots in geometrically simple regions of Euclidean space (e.g., a planar region containing polygonal obstacles). In this paper we define a natural version of the motion planning problem in a graph theoretic setting. We establish conditions under which a “robot” or team of robots having a particular graph structure can move from any start location to any goal destination in a graph-structured space.

Graphbots: Mobility in Discrete Spaces

The perception of luminance transparency for superimposed patterns depends on how luminance, figural, and topological conditions are simultaneously satisfied. Motion transparency or coherence for two superimposed patterns, which correspond to the perception of both patterns moving across one another or to the perception of compound motion of the regions of pattern intersection, depends on the relation between the local velocity, luminance, and shape information. This study analyzes how luminance, shape, and local velocity interact in the perception of motion transparency and coherence. Psychophysical experiments done with sinusoidally modulated bar patterns are presented which show that the perception of motion transparency or coherence can be described as the result of the interaction of two integration modules: the velocity-luminance and the velocity-shape processes. The velocity-luminance process describes the integration of the local velocity with luminance information. When the luminance transparency rules are satisfied this process always generates the perception of motion transparency independently of the shape or contour information. On the other hand, when the luminance transparency rules are violated one can either perceive motion coherence or non-rigid motion; one perceives motion coherence when the patterns have small or zero amplitude, and non-rigid motion when the patterns have large amplitude. The velocity-shape process describes the integration of local velocity with shape information, and this depends on the relation between the error in the extraction of the local velocity and the magnitude of the contour amplitude. As a result of these experiments it is conjectured that the velocity-luminance and the velocity-shape processes do interact constructively or destructively. The constructive interaction occurs when the luminance transparency rules are satisfied. The destructive interaction occurs when the luminance transparency rules are violated, and such that, although the patterns contain sufficient shape information to solve the aperture problem and therefore generate the perception of motion transparency, one perceives non-rigid motion. This shows that global information describing the stratification of superimposed patterns can affect the integration of local velocity information with, for example, shape information, and this is not described by current motion theories.

Azriel Rosenfeld

Papers

Shape from random planar features

Elementary Problems: E2629, E2630-E2634

Parallel string acceptance using lattice graphs

Graphbots: Mobility in Discrete Spaces

The interaction of luminance, velocity, and shape information in the perception of motion transparency, coherence, and non-rigid motion