Addresses the problem of obtaining natural descriptions of 3D shapes. The authors present one of the first attempts to address the description of 3D compound objects, where the parts are connected smoothly. The input the authors consider is either complete 3D data or range data from a single view. The authors suggest a volumetric graph representation of the object, where the nodes represent individual parts and the edges represent connectivity information. The authors suggest the use of properties of the parabolic curves for performing the part decomposition. The authors consider parts with tubular structure with a straight or curved axis. They are also interested in the internal description of the parts. The authors study two classes of shapes, namely straight homogeneous GCs, and planar right constant GCs. The authors suggest the use of properties of the parabolic curves for recovering natural descriptions of these classes in terms of their cross sections and axes.

A method for producing a segmented axial description of a given shape together with a hierarchical decomposition of the shape into its parts is presented. The novelty of this approach lies in the combination of several competing approaches and tools into a unified scheme and an efficient implementation producing natural descriptions. Smooth local symmetries are used for the axial description of parts, which are suggested by curvature sign changes. Parallel symmetries are used to provide information on global relationships within the shape. This information is used for parsing shape into a hierarchy of parts. This approach uses both region and contour information, can handle shapes with corners, and addresses the issue of local versus global information, the issue of scale, and the notion of part. The method is computationally efficient, robust, and stable. Results that show that it provides an intuitive shape description are included.>

The detection of edges is only one of many steps in the understanding of images. Further processing necessarily involves grouping operations between contours. We present a representation of edge contours by approximating B-splines and show that such a representation facilitates the extraction of symmetries between contours. Our representation is rich, compact, stable, and does not critically depend on feature extraction. We turn our attention to the detection of three types of symmetries: skew symmetries and parallel symmetries, which have proven to be of great importance in inferring shape from contour, and smooth local symmetries, which have been used for planar shape description. We show that our representation facilitates the computation of these symmetries.>

The problem of obtaining intuitive descriptions of planar shapes is addressed. In particular, a method for producing a segmented axial description of a given shape together with a hierarchical decomposition of the shape into its parts is suggested. Smooth local symmetries are used for the axial description of parts. Parallel symmetries are used to provide information on global relationships within the shape. It is assumed that the shape is a closed planar curve. The approach uses both region and contour information, can handle shapes with corners, and addresses the issues of local versus global information, the issue of scale and the notion of part. The method is computationally efficient, robust, and stable. Results showing that it provides an intuitive shape description are presented.>

An iterative method is described for segmenting image sequences into independently moving regions while computing the motion parameters of each region. In each iteration, image points are classified into regions based on their consistency with the different motion estimates, and motion estimates are then updated using the obtained regions. The motion estimates and the segmentation improve with every iteration, and the iteration stops when a stable segmentation is obtained. Accurate motion parameters are recovered for each segment. The process is performed directly on gray-level images and does not require detection of special feature points and the computation of point correspondence. It is also faster and more robust than optical-flow-based segmentation methods.>

It is shown that by defining a suitable measure for the comparison of images, changes in resolution can be treated with the same tool as changes in color resolution. A gray-tone image, for example, can be compared to a half-tone image having only two colors (black and white), but of higher spatial resolution. A graph-theoretical definition of the basic measure used is introduced. This is followed by application to spatial resampling and gray-level requantization. This results in a hybrid treatment of resolution, and the possibility of trading spatial for gray-level resolution and vice versa.>

An image is represented by the Voronoi tessellation generated from selected sampling points. Using a multiresolution approach, the density of the sampling points can be adaptive to image properties: smoother regions will have fewer sampling points than more detailed regions. The adaptation property results in better image quality than nonadaptive Voronoi representations, while preserving the property that only the holder of the seed of the pseudorandom number generator can reconstruct the original image.>