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

: Developments in the field of picture processing by computer during 1969-71 are surveyed. The topics covered include picture compression, image enhancement, pictorial pattern recognition, scene analysis, and picture grammars. (Author)

Progress in Picture Processing: 1969--71

Degree of adjacency or surroundedness

Signatures may be stylish or unconventional and have many personal characteristics that are challenging to reproduce by anyone other then the original author. For this reason, signatures are used and accepted as proof of authorship or consent on personal checks, credit purchases and legal documents. Currently signatures are verified only informally in many environments, but the rapid development of computer technology has stimulated great interest in research on automated signature verification and forgery detection. 
In this thesis, we focus on forgery detection of off-line signatures. Although a great deal of work has been done on off-line signature verification over the past two decades, the field is not as mature as on-line verification. Temporal information used in on-line verification is not available off-line and the subtle details necessary for off-line verification are embedded at the stroke level and are hard to recover robustly. We approach the off-line problem by establishing a local correspondence between a model and a questioned signature. The questioned signature is segmented into consecutive stroke segments that are matched to the stroke segments of the model. The cost of the match is determined by comparing a set of geometric properties of the corresponding sub-strokes and computing a weighted sum of the property value differences. The least invariant features of the least invariant sub-strokes are given the biggest weight, thus emphasizing features that are highly writer-dependent. 
Random forgeries are detected when a good correspondence cannot be found, i.e., the process of making the correspondence yields a high cost. Many simple forgeries can also be identified in this way. The threshold for making these decisions is determined by a Gaussian statistical model. 
Using the local correspondence between the model and a questioned signature, we perform skilled forgery detection by examining the writer-dependent information embedded at the sub-stroke level and trying to capture unballistic motion and tremor information in each stroke segment, rather than as global statistics. Experiments on random, simple and skilled forgery detection are presented.

Forgery detection by local correspondence

From the Publisher:
Computational geometry deals with the construction of algorithms and their complexity related to problems in geometry arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographic information systems. Digital geometry deals with geometric properties of subsets of digital images or, equivalently, with geometric properties of finite sets of lattice points. Digital geometry can anticipate progress in imaging technology allowing higher and higher spatial resolution. It seems that the input data in both fields will "converge" to data embedded in digital arrays of very high spatial resolution. This book covers the important developments in digital and computational geometry including methods of approximating geometric objects.

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Azriel Rosenfeld

Papers

Progress in Picture Processing: 1969--71

Degree of adjacency or surroundedness

Forgery detection by local correspondence

Advances in Digital and Computational Geometry

Reduction operations for constraint satisfaction