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 introduces a generalization of cellular automata in which each celi is a tape-bounded Turing machine rather than a finite-state machine. Fast algorithms are given for performing various basic image processing tasks by such automata. It is suggested that this model of parallel computation is a very suitable one for studying the advantages of parallelism in this domain.

Parallel Image Processing by Memory-Augmented Cellular Automata

Construction of image pyramids is described as a two-di-mensional decimation process Frequently employed generating kernels are compared to the optimal kernel that assures minimal information loss after the resolution reduction, ie, the one corresponding to an ideal low pass filter Physically realizable, optimal generating kernels are presented The amount of computation required for generation of the image pyramid can be reduced significantly by employing half-band filters as components of the optimal kernel Image pyramids generated by the optimal kernel show a better command of details than the ones generated by a simple 4 × 4 averaging, or a computationally equivalent kernel

Frequency Domain Analysis and Synthesis of Image Pyramid Generating Kernels

The general goal of image pattern recognition is to generate descriptions of images, and relate those descriptions to models characterizing classes of images. This paper reviews the subject from a technique-oriented standpoint. Topics covered include preprocessing; registration and matching; segmentation into parts; representation of the parts; and description in terms of properties of and relationships among the parts.

Image pattern recognition

Some experiments in image segmentation by clustering of local feature values

Two methods are introduced for reducing additive noise in approximately piecewise constant images. In the first method, the correct gray level of a point P is estimated by a weighted average of the gray levels of P's immediate neighbors. To assign these weights for a given P so that the local averaging operation does not blur the image, the presence of any edges or lines passing through P's neighborhood must be determined. For example, when an edge is present, only those points on P's side of the edge should be used. In general, the distribution of gray levels in P's neighborhood will suggest many possible line and edge configurations which can be used to compute the weight distribution for the averaging operation. The averaging is performed in parallel over the entire image and is iterated for additional smoothing. The second method is a relaxation labeling formulation which can be psed in cases of more severe noise. Each point is now assigned a vector of probabilities over its allowable gray level set. These probabilities are updated as weighted averages of the gray level probabilities at neighboring points. Once again the presence of lines and edges determines how the contribution from each neighboring point is weighted. Examples demonstrating both methods are given.

Azriel Rosenfeld

Papers

Parallel Image Processing by Memory-Augmented Cellular Automata

Frequency Domain Analysis and Synthesis of Image Pyramid Generating Kernels

Image pattern recognition

Some experiments in image segmentation by clustering of local feature values

Iterative Enhancemnent of Noisy Images