Graphical Models and Image Processing最新文献

It can be shown that a wide family of digital textures corresponds to percolation models (Pikaz and Averbuch, 1996, Technical Report 315/96, Tel-Aviv University). Percolation models supply statistical results and theoretical background for connectivity analysis. This paper focuses on the relation between second-order statistics (which are very common in use for digital texture analysis) and connectivity analysis. The paper also presents additional evidences to the tight relation between digital textures and percolation models.

An image warping method is presented that deforms an image continuously without foldover, while observing a given set of trajectories of feature elements. Any intermediate image during the morph is homeomorphic to the initial image and the morphing process is a homotopy. The method permits points, line-segments, and polygons to be included as features in the image. Our method is based on time-varying triangulation, that is, triangulation changes as features move. Accordingly, the deformation mapping is updated locally for the part for which the triangulation changes. Experimental results are included to demonstrate the feasibility of our approach and the complexity of the algorithm is analyzed.

Given two planar curves, their convolution curve is defined as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objects is closely related to the convolution curve of the two object boundary curves. That is, the convolution curve is a superset of the Minkowski sum boundary. By eliminating all redundant parts in the convolution curve, one can generate the Minkowski sum boundary. The Minkowski sum can be used in various important geometric computations, especially for collision detection among planar curved objects. Unfortunately, the convolution curve of two rational curves is not rational, in general. Therefore, in practice, one needs to approximate the convolution curves with polynomial/rational curves. Conventional approximation methods of convolution curves typically use piecewise linear approximations, which is not acceptable in many CAD systems due to data proliferation. In this paper, we generalize conventional approximation techniques of offset curves and develop several new methods for approximating convolution curves. Moreover, we introduce efficient methods to estimate the error in convolution curve approximation. This paper also discusses various other important issues in the boundary construction of the Minkowski sum.

A local smoothing operator applied in the reverse direction is used to obtain planar shape enhancement and exaggeration. Inversion of a smoothing operator is an inherently unstable operation. Therefore, a stable numerical scheme simulating the inverse smoothing effect is introduced. Enhancement is obtained for short time spans of evolution. Carrying the evolution further yields shape exaggeration or caricaturization effect. Introducing attraction forces between the evolving shape and the initial one yields an enhancement process that converges to a steady state. These forces depend on the distance of the evolving curve from the original one and on local properties. Results of applying the unrestrained and restrained evolution on planar shapes, based on a stabilized inverse geometric heat equation, are presented showing enhancement and caricaturization effects.

We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve, with no extraneous edges. The required sampling density varies with thelocal feature sizeon the curve, so that areas of less detail can be sampled less densely. We give two different graphs that, in this sense, reconstruct smooth curves: a simple new construction which we call thecrust, and the β-skeleton, using a specific value of β.

We present an approach for analyzing digital elevation model (DEM) data using the conceptcontact surface areaand mathema-tical morphology. DEMs are digital representations of the Earth's surface. Generally speaking a DEM is generated as a uniform rectangular grid organized in profiles. In order to analyze DEM data by means of binary morphology, the models are represented as binary solids composed of regular polyhedrons (voxels). In the content of this work, we use morphological operators to erode DEMs, simplify binary solid data, preserve essential shape characteristics, understand shape in terms of a decomposition, and identify object features. This is shown by means of some simple examples. We define the contact surface area for DEMs composed of voxels. The contact surface area corresponds to the sum of the contact surface areas of the neighboring voxels of DEMs. A relation between the area of the surface enclosing the volume and the contact surface area is presented. The definition of contact surface area permits us to obtain a fast and efficient method for plotting models composed of a large number of voxels.

We point out that the derivation of the Cramer–Rao lower bound for estimating a circular arc center and its radius by Chan and Thomas (Graphical Models Image Process.57, 1995, 527–532) has some problems although the final result is correct. Examining the mathematical structure of the problem carefully, we first correct their mistakes and then present a suitable formulation for the problem. We show that the result can be extended to more general problems including line and conic fitting.

In a two-valued digital picture (in brief: “image”), it is well known that changing a “simple” pixel from 1 to 0 or vice versa preserves the topology of the image—specifically, it preserves the adjacency/surroundedness relations between the connected components of 0's and 1's. We prove here that the converse is also true: Any two topologically equivalent images can be transformed into one another by changes in the values of simple pixels. As a preliminary, we show how an image can be magnified by an arbitrary integer factor, or translated along an arbitrary path, or rendered “well-composed,” by repeatedly changing the values of simple pixels. The relationship between the simple pixel method and other types of “topology-preserving” deformations of images is also briefly discussed.

This paper presents an efficient and robust geometric algorithm that classifies and detects all possible types of torus/sphere intersections, including all degenerate conic sections (circles) and singular intersections. Given a torus and a sphere, we treat one surface as an obstacle and the other surface as the envelope surface of a moving ball. In this case, theConfiguration space(C-space) obstacle is the same as the constant radius offset of the original obstacle, where the radius of the moving ball is taken as the offset distance. Based on the intersection between theC-spaceobstacle and the trajectory of the center of the moving ball, we detect all the intersection loops and singular contact point/circle of the original torus and sphere. Moreover, we generate exactly one starting point (for numerical curve tracing) on each connected component of the intersection curve. All required computations involve vector/distance computations and circle/circle intersections, which can be implemented efficiently and robustly. All degenerate conic sections (circles) can also be detected using a few additional simple geometric tests. The intersection curve itself (a quartic space curve, in general) is then approximated with a sequence of cubic curve segments.

In many applications it is important that one view a scene at different levels of detail. A prime example is flight simulation. A high level of detail is needed when flying low, whereas a low level of detail suffices when flying high. More precisely, one would like to visualize the part of the scene that is close at a high level of detail and the part that is far away at a low level of detail. We propose a hierarchy of detail levels for a polyhedral terrain (or, triangulated irregular network) that given a viewpoint, makes it possible to select the appropriate level of detail for each part of the terrain in such a way that the parts still fit together. The main advantage of our structure is that it uses the Delaunay triangulation at each level, so that triangles with very small angles are avoided. This is the first method that uses the Delaunay triangulation and still allows one to combine different levels into a single representation.