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

This paper discusses some methods of image analysis that make use of a “pyramid” of reduced-scale representations of the information in the given image. Section 2 discusses “intensity pyramids” that consist of reduced-resolution versions of the image, and indicates how such pyramids provide an efficient means of performing “coarse” feature detection operations on the image. Section 3 describes “feature pyramids” based on the approximate representations of edges or curves, and shows that such pyramids can be used to efficiently detect simple shapes such as blobs and ribbons in an image. Section 4 suggests that pyramids provide a vehicle for “pixel-region cooperation” in which global properties of regions are able to influence the segmentation processes that give rise to these regions.

Pyramid Architectures for Image Analysis

Image analysis techniques applicable to remote sensing data and covering image models, feature detection, segmentation and classification, texture analysis, and matching are studied. Model types for characterizing images examined include random-field, mosaic, and facet models. Edge and corner detection as well as global extraction of linear features are discussed. Pixel clustering and classification are covered in addition to the regional approach to segmentation. Autocorrelation, second-order gray level probability density, and the use of primitive element statistics are discussed in relation to texture analysis. Finally, reducing the cost of (sub)imaging matching methods (e.g., pixelwise comparison of gray levels and normalized cross-correlation between two images) as well as improving match sharpness is considered.

Image processing in remote sensing data analysis - The state of the art

: This paper describes steps toward the recognition of cultural features such as buildings and roads on aerial photographs. The approach involves several successive stages of grouping of edge segments. Straight line segments are fitted to sets of edge pixels; compatibilities between pairs of these segments, based on gray level and geometric information, are computed; and the segments are then grouped into building-like and road-like groupings based on these compatibilities. Examples of the results obtained using this approach are given, and some variations on the initial stages of the process are also investigated.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA109558&Location=U2&doc=GetTRDoc.pdf

Toward the Recognition of Buildings and Roads on Aerial Photographs

Publisher Summary
This chapter reviews various topics in digital geometry—the theory of geometrical properties of subsets of digital pictures. This theory provides the foundations for a number of basic array automaton algorithms, for example, border following and region traversal. From a more practical standpoint, it serves as a basis for defining and proving the correctness of various fundamental image analysis operations such as object counting, that is, connected component counting, and chain encoding of region borders. Many other topics are included in the chapter; among these are digital homotopy, dimension , elongatedness, straightness, convexity, and a variety of algorithms for connected component tracking and counting, adjacency tree construction, and border finding. In the process of analyzing a digital picture, one usually begins by extracting subsets of various types from the picture, and this process is called segmentation.

Azriel Rosenfeld

Papers

Pyramid Architectures for Image Analysis

Image processing in remote sensing data analysis - The state of the art

Toward the Recognition of Buildings and Roads on Aerial Photographs

Chapter 2 – DIGITAL GEOMETRY

Computer Vision: Attitudes, Barriers, Counseling.