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 is one of a series of reports on the digital geometry of three-dimensional images, such as those produced by computed tomography. In this report we define simple surface points and simple closed surfaces, and show that any connected collection of simple surface points form a simple closed surface, thus proving a three-dimensional analog of the two-dimensional Jordan curve theorem. We also show that the converse is not a theorem (in contrast to the two-dimensional case), and discuss more complex surface types. Finally, we show that the two-dimensional analog of our definition of simple closed surface characterizes simple closed curves, but that several other characterizations of 2 D curves, when extended to 3 D , are not adequate to characterize surfaces.

Surfaces in three-dimensional digital images*

We present an approach to the recovery and recognition of 3-D objects from a single 2-D image. The approach is motivated by the need for more powerful indexing primitives, and shifts the burden of recognition from the model-based verification of simple image features to the bottom-up recovery of complex volumetric primitives. Given a recognition domain consisting of a database of objects, we first select a set of object-centered 3-D volumetric modeling primitives that can be used to construct the objects. Next, using a CAD system, we generate the set of aspects of the primitives. Unlike typical aspect-based recognition systems that use aspects to model entire objects, we use aspects to model the parts from which the objects are constructed. Consequently, the number of aspects is fixed and independent of the size of the object database. To accommodate the matching of partial aspects due to primitive occlusion, we introduce a hierarchical aspect representation based on the projected surfaces of the primitives; a set of conditional probabilities captures the ambiguity of mappings between the levels of the hierarchy. From a region segmentation of the input image, we present a novel formulation of the primitive recovery problem based on grouping the regions into aspects. No domain dependent heuristics are used; we exploit only the probabilities inherent in the aspect hierarchy. Once the aspects are recovered, we use the aspect hierarchy to infer a set of volumetric primitives and their connectivity relations. Subgraphs of the resulting graph, in which nodes represent 3-D primitives and arcs represent primitive connections, are used as indices to the object database. The verification of object hypotheses consists of a topological verification of the recovered graph, rather than a geometrical verification of image features. A system has been built to demonstrate the approach, and it has been successfully applied to both synthetic and real imagery.

From volumes to views: an approach to 3-D object recognition

Performance analysis of a simple vehicle detection algorithm

A taxonomy of local, regional, and global temporal clues that, along with a detailed examination of the document, allow temporal properties to be recovered from the image is provided. It is shown that this system will benefit from obtaining a comprehensive understanding of the handwriting signal and that it requires a detailed analysis of stroke and sub-stroke properties. It is suggested that this task requires breaking away from traditional thresholding and thinning techniques, and a framework for such analysis is presented. It is shown how the temporal clues can reliably be extracted from this framework and how many of the seemingly ambiguous situations can be resolved by the derived clues and knowledge of the writing process. >

Recovery of temporal information from static images of handwriting

A blind noise variance algorithm that recovers the variance of noise in two steps is proposed. The sample variances are computed for square cells tessellating the noise image. Several tessellations are applied with the size of the cells increasing fourfold for consecutive tessellations. The four smallest sample variance values are retained for each tessellation and combined through an outlier analysis into one estimate. The different tessellations thus yield a variance estimate sequence. The value of the noise variance is determined from this variance estimate sequence. The blind noise variance algorithm is applied to 500 noisy 256*256 images. In 98% of the cases, the relative estimation error was less than 0.2 with an average error of 0.06. Application of the algorithm to differently sized images is also discussed. >

Azriel Rosenfeld

Papers

Surfaces in three-dimensional digital images*

From volumes to views: an approach to 3-D object recognition

Performance analysis of a simple vehicle detection algorithm

Recovery of temporal information from static images of handwriting

A fast parallel algorithm for blind estimation of noise variance