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.

/pdf/stochastic-relaxation-gibbs-distributions-and-the-bayesian-4c0mbkv82j.pdf

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

Grammars whose languages consist of cycles (“necklaces”) rather than strings are considered. If G is context free, and we regard G as generating cycles instead of strings, the resulting language is just what we would get if we “bent” the strings of L ( G ) into cycles. This is no longer true if G is context sensitive. However, in this case too, the context-sensitive cycle languages are just the “bendings” of the context-sensitive string languages. Automata on cyclic tapes are also discussed.

A note on cycle grammars

Arc colorings, partial path groups, and parallel graph contractions

Linear feature compatibility for pattern-matching relaxation

It is shown that the “intrinsic diameter” of a connected digital object C—i.e., the maximum distance in C between any two points of C—never exceeds half of C's total perimeter (counting all of C's borders, including hole borders). As a preliminary result, it is shown that a simply connected digital object is a simple arc if and only if it has at most two “end” or “corner” points (and, in fact, it can then only have two “end” points).

A note on perimeter and diameter in digital pictures

: This paper examines an approach to image segmentation based on using a quadtree approximation image to identify regions in the image. The advantages of this approach are firstly that noise points are not present in the quadtree approximation of an image and secondly that by traversal of the tree it is possible to find the approximate location of the regions within an image. It is thus possible to extract a region by applying thresholds in the vicinity of the region and to identify the best threshold by correlating the extracted region with an edge map of the original image. Since thresholds to extract regions are applied locally, noise points which may be present elsewhere in the edge map have no effect on the correlation of extracted regions to the edge map of the original image.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA090243&Location=U2&doc=GetTRDoc.pdf

Azriel Rosenfeld

Papers

A note on cycle grammars

Arc colorings, partial path groups, and parallel graph contractions

Linear feature compatibility for pattern-matching relaxation

A note on perimeter and diameter in digital pictures

Use of Quadtrees for Image Segmentation