CVGIP: Graphical Models and Image Processing最新文献

Three methods are introduced for generating complete scans of multidimensional spaces. The traditional method is to use a raster (typically generated by nested iteration) which generates points at the maximum resolution and fills the space slowly. New methods are desirable, because in many applications it is desirable for the scanned points to be distributed throughout the space and for the resolution to increase with the number of points scanned. Three simple methods are introduced in this paper. Two of the methods are members of a class of methods in which the reverse-bit-order operator maps points from "R(esolution)-space" to the desired space. In "R-space" the distance from the origin determines the resolution level of the scanned point. The two scans occupy points in such a way that a distance measure such as the L¹ norm or the L^∞ norm increases with the progress of the scan. The third method uses iteration of primitive polynomials modulo 2 to generate a nonrepeating sequence of binary numbers which eventually fills the space. This method is most computationally efficient, but the L^∞ norm method generates partial scans which completely sample the space at intermediate levels of resolution. Applications are expected in scientific visualization, graphics rendering, multicriterion optimization, and progressive image transmission.

We define a digital space to be a pair consisting of an arbitrary nonempty set V and a symmetric binary relation π on V with respect to which V is connected. Our intent is to investigate the notion of an oriented surface in this general environment. Our terminology reflects this: we refer to elements of V as spels (short for "spatial elements"), to artibrary nonempty subsets of π as surfaces, and we define the notions of the interior and the exterior of a surface. We introduce the notion of a near-Jordan surface, its interior and exterior partition V. We call a symmetric binary relation on V that contains π a spel-adjacency. For spel-adjacencies κ and λ, we call a surface κλ-Jordan if it is near-Jordan, its interior is κ-connected, and its exterior is λ-connected. We prove a number of results which characterize κλ-Jordan surfaces in general digital spaces and in binary pictures (in which there is an assignment of a 1 or a 0 to elements of V).

In this paper, we address the problem of testing homogeneity for unlabeled pixels observed in a subimage. Homogeneity testing is an essential component in split-and-merge segmentation algorithm. Two types of homogeneity tests are involved: tests for labeled data when deciding on merges between regions and tests for unlabeled data when deciding whether to split a region. In our study, we focus on images that are modeled as a mosaic of uniform regions corrupted by additive Gaussian noise. Using this model, we present a statistical analysis on the performance of two commonly used approaches for testing homogeneity of unlabeled data based on the region/subregion similarity and the data dispersion, respectively. We also propose and evaluate a new hierarchical homogeneity testing scheme for unlabeled data. The most important finding of this study is that the tests based on region/subregion similarity have a low power on average of detecting inhomogeneity in unlabeled data.

The diversity of lighting arrangements and fixtures in everyday life allows us great creative and functional control over the appearance of our environments. In computer graphics, the lack of realistic models of light sources does not permit the same level of control. To model a light source, one must (at least) be able to specify its geometry and its spatial intensity distribution. We describe a system that permits the interactive specification of point, linear, and area light sources having arbitrary and variable spatial intensity distributions across their domains. A continuous distribution of an extended light source is created by interpolating a set of sample distributions that are interactively placed on the light source. Rendering is accomplished by resampling the light source at a variable resolution. To speed up rendering, a pyramidal representation of the light source is created, allowing the dynamic selection of the resampling rate. We describe the theory, design, and implementation of our light-source modeling system. Pyramidal light-source models can be used in rendering environments such as conventional scanline or ray-tracing renderers, or renderers with programmable shaders.

In this paper, we define the straight segment approximation problem (SSAP) for a given digital arc as that of locating a minimum subset of vertices on the arc such that they form a connected sequence of digital straight segments. Sharaiha (Ph.D. thesis, Imperial College, London, 1991) introduced the compact chord property, and proved its equivalence to Rosenfeld′s chord property (IEEE Trans. Comput. C-23, 1974, 1264-1269). The SSAP is now constrained by the compact chord property, which offers a more convenient geometric representation than the chord property. We develop an O(n²) optimal algorithm for the solution of the SSAP using integer arithmetic. A relaxation of the problem is also presented such that the optimal number of vectors can be reduced according to a user definition. The original algorithm is adapted for the optimal solution of the relaxed problem. An extension to the relaxed problem is also addressed which finds a minimum level of relaxation such that the optimal number of vectors cannot be reduced.

The behavior of the normalized gradient of the Gaussian edge operator is analyzed over many scales in one and two dimensions. A knowledge of the changes that occur over scale in the output of the operator and the physical conditions that cause these changes is essential for the proper interpretation and application of the results. The behavior of several edge models and combinations of edges is examined. As a result it is shown that the slope of an edge can be estimated very accurately using one small scale. By following the rate of change in the output of the operator as scale changes, an optimal scale can be determined for estimating the width and total contrast of the edge. Results on real images are shown and it is demonstrated that the information obtained by these methods can be used to characterize edge points.

The problem of detection and line location estimation of multiple, parallel, dim, moving targets, such as the ones typically encountered when a geostationary satellite is tracking targets, is studied under the framework of signal detection theory. Part I of the paper considers two-dimensional data (or one frame of an image) and Part II considers an additional third dimension representing time. Optimal processors are derived for varying degrees of uncertainty in the data for the detection of parallel targets. The uncertainties include uncertainty in the knowledge of orientation, location, number, and direction of arrival of the targets. Performance of the optimal processors is presented in the form of Receiver Operating Characteristic (ROC) curves and compared, in Part I, with the Hough transform. The optimal 2-D processors perform better than the Hough transform under all cases of uncertainties. Likelihood-ratio-based optimal estimation algorithms resolve the location of targets under severe noise conditions. In Part II, ROCs for the optimal 3-D processors are compared with both 2-D optimal processors and the Hough transform that use the projected data. Simulation results indicate that substantial gains in performance can be achieved by processing the 3-D data directly instead of first projecting and optimally processing in 2-D. It is observed that the computational burden in optimally processing the 3-D data sequentially is comparable to the conventional techniques involving projection and the Hough transform.

A model for the uncertainty of straight lines extracted from digital images is proposed, which accounts both for the image discretization and for the scattering of the line points from the true line. First, some results about uncertainty are derived for the discrete model, in which the point scattering is neglected. Then, the proposed model is compared with the continuous model, in which the image discretization is neglected: experiments show that the continuous model underestimates uncertainty.

A powerful representation of plane curves by curvature primitives called codons has been proposed by Hoffman and Richards (Proceedings, AAAI, 1982, pp. 5-8). Previously these were limited to representing only continuously varying, smooth, closed curves. Also, in practice their extraction from real data is complicated by the presence of noise and fine detail. In this paper we have extended the set of codons so that both open and closed curves containing straight lines and cusps can be completely represented. The problems of noise and obscuring fine detail have been solved by representing curves at all their natural scales. Codons at different scales are linked to form a hierarchical curve representation, called the codon-tree. To increase their power for model matching the qualitative codon descriptions are augmented by a set of shape features. These are used in combination with an extended set of rewrite rules from Leyton′s process grammar (Artificial Intelligence 34, 1988, pp. 213-247), enabling one curve to be deformed until it matches another.

We discuss the problem of color organization and modeling in general and in computer graphics in particular. After a brief review of the Red, Green, and Blue (RGB) and Lightness, Hue, and Saturation (LHS) color models in computer graphics, a generalization of the latter, the Generalized Lightness, Hue, and Saturation (GLHS) model, is introduced, derived, and discussed. It is shown that previously used LHS color models are special cases of GLHS and can be obtained from it by appropriate assignments to its free parameters. We derive some mathematical results concerning the relation between GLHS and RGB. Using these, we are able to give a single pair of simple algorithms for transforming from GLHS to RGB and vice versa. This single pair of algorithms transforms between RGB and any of the previously published HSL, HSV, and HLS models, as well as any other special case of the generalized model. Nevertheless, they are as simple as the separate algorithms published previously. Illustrations are given of color gamuts defined by various assignments to the free parameters of the GLHS system as they appear on the display monitor under the control of a Multiple Color Model Image Display System. Finally, we discuss briefly the potential for finding within the GLHS family a model that provides the closest approximation to a uniform color space. Such a model shares the perceptual properties of a proven uniform model and, at the same time, the algorithmic properties of the GLHS family.