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

A definition of convexity of digital solids is introduced. Then it is proved that a digital solid is convex if and only if it has the chordal triangle property. Other geometric properties which characterize convex digital regions are shown to be only necessary, but not sufficient, conditions for a digital solid to be convex. An efficient algorithm that determines whether or not a digital solid is convex is presented.

Convex Digital Solids

A method is described for automatic detection of a large class of industrial parts, whch is faster and more reliable than current methods. Many industrial parts have visible outlines which are either circular or elliptical or contain segments of these. Circles are seen as ellipses unless viewed head-on. Thus the ability to detect ellipses in an image of an industrial part, quickly and reliably, can be of great help in identification of this part by a robotic assembly process. In our method one first scans the image electronically by a video camera. When a scan line goes through an image of some object one can detect the edges of this image by detecting changes in the light intensity at these edges. For an object of the shape of a conic section (e.g. an ellipse), generally two edges will appear on each scan line and the midpoints between them will all lie on one straight line. This straight line can be detected with Hough's method.

Automatic detection of elliptical shapes

Perceptual motion transparency occurs whenever two or more patterns are seen moving at different depth levels, such that we can see one pattern move across the others, and perceptual motion coherence occurs when we see a single motion. We present here a model of perceptual motion transparency and coherence that consists of three stages: (i) measure the normal velocity along contours or the velocity of features such as corners or line end points; (ii) take the intersection, in velocity space, of all possible pairs of constraint lines associated with the normal velocity components; and (iii) combine the results of steps (i) and (ii) in the velocity histogram, which is the plot of the total number of votes for each velocity in velocity space. For two patterns we perceive motion coherence, transparency, or a mixture of both types of motion depending on whether the velocity histogram is unimodal, bimodal, or trimodal. According to our model we perceive motion transparency or coherence depending on the total number of prominent peaks of the velocity histogram, where each peak is located at the position corresponding to the velocity of one of the patterns or of coherent motion. We show that the number of prominent peaks in the velocity histogram depends on the error in the measurement of the local velocity and on the relative orientation of the local velocities along contours; this relative orientation encodes contour shape. Our model differs from current motion theories in that it describes the perception of motion not as a result of local velocity extraction but instead as the result of the integration of local velocity and geometrical shape information across different points of the image and across superimposed patterns. This model allows for the occurrence of mixed motion perception, which arises from the combination of the velocity information associated with motion transparency and coherence. We have tested this model through computational and psychophysical experiments done with line patterns. As a result of these experiments we conjecture that the human visual system may use at least three stages to process image velocity.

Azriel Rosenfeld

Papers

Convex Digital Solids

Automatic detection of elliptical shapes

Perceptual motion transparency : the role of geometrical information

Point-to-line mappings as Hough transforms

From pixels to features: J C Simon (ed). Published by Nort-Holland, Netherlands. 1989. 416 pp. $94.75