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

http://cs.technion.ac.il/~romang/publications/traffic.pdf

Estimating Relative Vehicle Motions in Traffic Scenes

A hierarchical iterative algorithm is proposed for extracting structure from two-frame optical flow The algorithm exploits two facts: one is that in many applications, such as face and gesture recognition, the depth variation of the visible surface of an object in a scene is small compared to the distance between the optical center and the object; the other is that the time aliasing problem is alleviated at the coarse level for any two-frame optical flow estimate so that the estimate tends to be more accurate A hierarchical representation for the relationship between the optical flow, depth, and the motion parameters is derived, and the resulting non-linear system is iteratively solved through two linear subsystems At the coarsest level, the surface of the object tends to be flat, so that the inverse depth tends to be a constant, which is used as the initial depth map Inverse depth and motion parameters are estimated by the two linear subsystems at each level and the results are propagated to finer levels Error analysis and experiments using both computer-rendered images and real images demonstrate the correctness and effectiveness of our algorithm

A hierarchical approach for obtaining structure from two-frame optical flow

This paper presents a bibliography of nearly 1100 references related to the computer processing of pictorial information, arranged by subject matter. Coverage is restricted, for the most part, to a selected set of U.S. journals and proceedings of specialized meetings. The topics covered include digitization, approximation, and compression; transforms, filtering, enhancement, restoration, and reconstruction; architectures, systems, software, and techniques; pictorial pattern recognition; feature detection, segmentation, and image analysis; matching and time-varying imagery; shape and pattern; geometry; texture; and three-dimensional scene analysis. No attempt is made to evaluate or summarize the items cited; the purpose is simply to provide a convenient compendium of references.

Picture processing: 1985

Detecting image primitives using feature pyramids

We present an approach to tracking human activities in a monocular video. We model the human body by decomposing it into torso and limbs and use simple 3D shapes to approximate them. The limb motions are parametrized by the relative joint angles. The problems of motion tracking and estimation are posed as nonlinear state estimation problems. The measurements are computed using the outputs of 3D shape-encoded filters which extract the boundary gradient information of the body image. The uncertainties of body pose are propagated by a branching particle system. We first sample a set of particles approximating the initial distribution of the state vector conditioned on observations, where each particle encodes the body pose. The posterior density is realized by the weight of the particle, where the weight represents geometric and temporal fit, and computed bottom-up from the raw image using a shape-encoded filter. The particles branch so that the mean number of offspring is proportional to the weight. Applications to both synthetic and real video sequences show the effectiveness of this approach.

Azriel Rosenfeld

Papers

Estimating Relative Vehicle Motions in Traffic Scenes

A hierarchical approach for obtaining structure from two-frame optical flow

Picture processing: 1985

Detecting image primitives using feature pyramids

Tracking of human activities using shape-encoded particle propagation