Graphical Models and Image Processing最新文献

This paper presents an approach to finding an approximate implicit equation and an approximate inversion map of a planar rational parametric curve or a rational parametric surface. High accuracy of the approximation is achieved with a relatively small number of low-degree curve segments or surface patches. By using monoid curves and surfaces, the method eliminates the undesirable singularities and “phantom” branches normally associated with implicit representation. The monoids are expressed in exact implicit and parametric equations simultaneously, and upper bounds are derived for the approximate errors of implicitization and inversion equations.

A new approach for reconstruction of 3D surfaces from 2D cross-sectional contours is presented. By using the so-called “equal importance criterion,” we reconstruct the surface based on the assumption that every point in the region contributes equally to the surface reconstruction process. In this context, the problem is formulated in terms of a partial differential equation, and we show that the solution for dense contours (contours in close proximity) can be efficiently derived from the distance transform. In the case of sparse contours, we add a regularization term to ensure smoothness in surface recovery. The approach is also generalized to other types of cross-sectional contours, where the spine may not be a straight line. The proposed technique allows for surface recovery at any desired resolution. The main advantages of our method is that inherent problems due to correspondence, tiling, and branching are avoided. In contrast to existing implicit methods, we find an optimal field function and develop an interpolation method that does not generate any artificial surfaces. We will demonstrate that the computed high-resolution surface is well represented for subsequent geometric analysis. We present results on both synthetic and real data.

A method for shape reconstruction from contours using isotopic deformation is presented. The proposed method considers the case where one contour encloses the other contour when they are projected in a common plane, as is the case for terrain contour maps. Unlike many other methods which generate piecewise linear interpolation, the proposed method smoothly interpolates between two contours located in parallel planes. The algorithm runs in O(nk+n log n) time, where n is the total number of vertices in two contours and k is an integer variable less than n which indicates how convoluted the contours are (the larger, the more convoluted). The running time of the algorithm is shown to be worst-case optimal for the class of task defined. The reconstructed shape is free of self-intersections and it can incorporate given feature correspondences. The method is extended to handle bifurcations and is shown to cope easily with some cases which are problematic for some other algorithms. The method proposed is suitable for terrain modeling, since reconstructed shapes generated by the method do not have overhangs. Experimental results are included to illustrate the feasibility of the approach.

The availability of large 3D datasets has made volume thinning essential for compact representation of shapes. The density of the skeletal structure resulting from the thinning process depends on the application. Current thinning techniques do not allow control over the density and can therefore address only specific applications. In this paper, we describe an algorithm which uses a thinness parameter to control the thinning process and thus the density of the skeletal structure. We present applications from CFD and medical visualization and show how the skeletal structure can be used in these domains. We also illustrate a technique for constructing a centerline for surgical navigation.

We present a method of approximating a nonsingular curve C in the plane or in space with the use of alpha shapes. The procedure is based on sampling the curve C with a finite set S and then construct the alpha shape,$S$_α, of S. Then,$S$_α is shown to be a piecewise linear curve that is ambiently homeomorphic to, and within a prescribed tolerance from, C.

We present an unstructured triangular mesh generation algorithm that approximates a set of mutually nonintersecting simple trimmed polynomial parametric surface patches within a user specified geometric tolerance. The proposed method uses numerically robust interval geometric representations/computations and also addresses the problem of topological consistency (homeomorphism) between the exact geometry and its approximation. Those are among the most important outstanding issues in geometry approximation problems. We also extract important differential geometric features of input geometry for use in the approximation. Our surface tessellation algorithm is based on the unstructured Delaunay mesh approach which leads to an efficient adaptive triangulation. A robust decision criterion is introduced to prevent possible failures in the conventional Delaunay triangulation. To satisfy the prescribed geometric tolerance, an adaptive node insertion algorithm is employed and furthermore, an efficient method to compute a tight upper bound of the approximation error is proposed. Unstructured triangular meshes for free-form surfaces frequently involve triangles with high aspect ratio and, accordingly, result in ill-conditioned meshing. Our proposed algorithm constructs 2D triangulation domains which sufficiently preserve the shape of triangles when mapped into 3D space and, furthermore, the algorithm provides an efficient method that explicitly controls the aspect ratio of the triangular elements.

We introduce a method for approximating a given surface by a developable surface. It will be either aG¹surface consisting of pieces of cones or cylinders of revolution or aG^rNURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding.

This paper presents a mathematical description of texture mapping onto planar polygons from a photogrammetry viewpoint. In principle, this approach can accommodate textures acquired from a variety of camera systems including panoramic, strip, pushbroom, multispectral scanners and synthetic aperture radar, as well as the common frame (snap-shot) camera. The main focus of this paper, however, is the frame camera. When this type of camera photographs an object obliquely, the transformation between polygon and texture is characterized by a perspective projection rather than an affine transformation. In particular, we derive the rational linear texture mapping transformation equation and show how to compute its coefficients in two ways using known values for the relevant camera parameters. We also show that the denominator term in this transformation is not equivalent to perspective depth as it is when the textures are face-on to the polygon surface. Although the specific case of perspective texture projection onto planar polygons has been discussed before using techniques based upon homogeneous coordinates, we believe that this paper will be interesting and beneficial due to the intuitive basis of the photogrammetry concepts.

The aim of this work is to provide a means to approximate the real boundary underlying the discrete boundary of a digitized 2D region. We require that the sampling of the reconstructed boundary be exactly the discrete one. To this end, we propose a new representation of the boundary of a discrete region that we call Euclidean paths. This paper fully describes the method used to build a Euclidean path and gives several examples of applications both for image analysis and image synthesis.