Computer Graphics and Image Processing最新文献

Determining the inclusion of a point in volume-enclosing polyhedra (shapes) in 3D space is, in principle, the extension of the well-known problem of determining the inclusion of a point in a polygon in 2D space. However, the extra degree of freedom makes 3D point-polyhedron containment analysis much more difficult to solve than the 2D point-polygon problem, mainly because of the nonsequential ordering of the shape elements, which requires global shape data to be applied for resolving special cases. Two general O(n) algorithms for solving the problem by reducing the 3D case into the solvable 2D case are presented. The first algorithm, denoted “the projection method,” is applicable to any planar-faced polyhedron, reducing the dimensionality by employing parallel projection to generate planar images of the shape faces, together with an image of the point being tested for inclusion. The containment relationship of these images is used to increment a global parity-counter when appropriate, representing an abstraction for counting the intersections between the surface of the shape and a halfline extending from the point to infinity. An “inside” relationship is established when the parity-count is odd. Special cases (coincidence of the halfline with edges or vertices of the shape) are resolved by eliminating the coincidental elements and re-projecting the merged faces. The second algorithm, denoted “the intersection method,” is applicable to any well-formed shape, including curved-surfaced ones. It reduces the dimensionality by intersecting the shape with a plane which includes the point tested for inclusion, thereby generating a 2D polygonal trace of the shape surface at the plane of intersection, which is tested for containing the trace of the point in the plane, directly establishing the overall 3D containment relationship. A particular O(n) implementation of the 2D point-in-polygon inclusion algorithm, which is used for solving the problem once reduced in dimensionality, is also presented. The presentation is complemented by discussions of the problems associated with point-polyhedron relationship determination in general, and comparative analysis of the two particular algorithms presented.

The space efficiency of the quadtree representation is investigated for the case in which a single 2^m by 2^m square region occurs in a 2ⁿ by 2ⁿ image. When the square is equally likely to occur at any position, it is shown that the average and worst case numbers of nodes in the quadtree are both on the order of the region's perimeter plus the logarithm of the image's diameter.

The key to producing data-compressed images of improved fidelity (at a given compression ratio) using the adaptive transform approach is to improve subimage classification. Three simple measures are introduced to minimize inner-class differences based on image energy, directionality, and fineness of local detail. A fast compression scheme incorporating these measures is illustrated by a range of examples.

Based on sequential tracking, a machine composed of three sequentially connected automata is proposed for recognizing a plane shape given by binary pattern. The first automaton detects 10 kinds of quasi-local features which constitute a complete set of features in two consecutive lines. The second automaton integrates these features and segments a contour into letter L shaped segments which are considered as primitives for description of a shape. These L-type segments are arranged to form the structure. The third automaton extracts global features such as connectivity, hole, and concavity, where attribution of a hole to a blob is somewhat generally treated and some degree of closure of a concavity is described. Thus the systematic feature extraction of a plane shape and the simple and essential description of that shape is given.