How to compute and represent the Gaussian approximations of planar curved objects is described. Also considered are various applications of the Gaussian approximation to various primitive geometric operations on monot...
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ISBN:
(纸本)0818690615
How to compute and represent the Gaussian approximations of planar curved objects is described. Also considered are various applications of the Gaussian approximation to various primitive geometric operations on monotone curve segments. The exact solutions for these problems can be computed by solving simultaneous polynomial equations, however, this required an intensive computation time. Efficient heuristic approximation algorithms using simple binary subdivisions on the original geometric components are suggested. It is shown that simple data structures such as arrays and circular lists can be used to represent the Gaussian approximations of planar curved objects.< >
This paperr describes a clustering algorithm for segmenting the color images of natural scenes. The proposed method operates in the 1976 CIE ( L ∗ , a ∗ , b ∗ )-uniform color coordinate system. It detects image cluste...
This paperr describes a clustering algorithm for segmenting the color images of natural scenes. The proposed method operates in the 1976 CIE ( L ∗ , a ∗ , b ∗ )-uniform color coordinate system. It detects image clusters in some circular-cylindrical decision elements of the color space. This estimates the clusters' color distributions without imposing any constraints on their forms. surfaces of the decision elements are formed with constant lightness and constant chromaticity loci. Each surface is obtained using only 1D histogramsof the L ∗ , H°, C ∗ cylindrical coordinates of the image data or the extracted feature vector. The Fisher linear discriminant method is then used to project simultaneously the detected color clusters onto a line for 1D thresholding. This permits utilization of all the color properties for segmentation and inherently recognizes their respective cross correlation. In this respect, the proposed algorithm also differs from the multiple histogram-based thresholding schemes.
A fast algorithm for 3D surface reconstruction from stereovision data, namely stratified triangulation, is presented. The algorithm assumes a dense set of world points obtained from passive stereovision, and reconstru...
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A fast algorithm for 3D surface reconstruction from stereovision data, namely stratified triangulation, is presented. The algorithm assumes a dense set of world points obtained from passive stereovision, and reconstructs a 3D scene. The stratification of random points follows a few heuristic rules. Triangles are formed only between strata, greatly limiting the search. The separation of surfaces is implemented by the standard region growing technique, from which road segments, obstacles, and other perceptual information can be derived. Some synthetic tests are shown to verify the algorithms. The envisaged application is autonomous navigation, e.g. of mobile robots.< >
The authors consider the 3-D shape representation problem for a class of range image where the natural model of the acquired range data is in the form of level set contours (equidistance contours), as exemplified by a...
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The authors consider the 3-D shape representation problem for a class of range image where the natural model of the acquired range data is in the form of level set contours (equidistance contours), as exemplified by a moire interferometry range system. They present a novel surface curvature computation scheme that directly computes the surface curvatures (the principal curvatures, Gaussian curvature, and mean curvature) from the equidistance contours without any explicit computations or implicit estimates of partial derivatives. They show how the special nature of the equidistance contours, specifically. the dense information of the surface curves in the 2-D contour plane, turns into an advantage for the computation of the surface curvatures. The approach is based on using simple geometric construction to obtain the surface normals, the normal sections, and the normal curvatures. This method is general and can be extended to any dense range image data. Computation results on both real and synthesized equidistance range contours are shown.< >
This paper describes an algorithm for generating piecewise parametric curved surfaces from arbitrary topological meshes. The algorithm is developed by extending and modifying Riesenfeld's constructive method for d...
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This paper describes an algorithm for generating piecewise parametric curved surfaces from arbitrary topological meshes. The algorithm is developed by extending and modifying Riesenfeld's constructive method for determining points on B -spline curves. The surfaces produced near extraordinary points are shown to be slope continuous and compatible with bi-quadratic B -spline surfaces generated from adjacent rectangular regions. In fact, applying this algorithm to rectangular meshes gives bi-quadratic B -spline surfaces. The implementation of this algorithm is simple and the evaluation of position vectors, tangent vectors and normal vectors of points on the surfaces is straightforward.
A theory describing the relations between the shapes of 3-D convex objects and the shapes of their silhouettes in orthographic projections is outlined. The theory is based on three representations of 3-D surfaces in t...
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ISBN:
(纸本)0818607793
A theory describing the relations between the shapes of 3-D convex objects and the shapes of their silhouettes in orthographic projections is outlined. The theory is based on three representations of 3-D surfaces in terms of scalar, vector, and tensor functions on the Gaussian sphere, and on the matching representations of 2-D curves by functions on the Gaussian circle. A slice through the spherical representation of a 3-D object is closely related to the circular representation of the silhouette of the object in a plane parallel to the slice. The theory provides interesting insight into problems of computergraphics and computervision.
This paper continues our work on visual representations of 2-dimensional surfaces. The theoretical component of our work is a study of classes of surface curves as a source of constraint on the surface on which they l...
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This paper continues our work on visual representations of 2-dimensional surfaces. The theoretical component of our work is a study of classes of surface curves as a source of constraint on the surface on which they lie, and as a basis for describing it. We analyze bounding contours, surface intersections, lines of curvature, and asymptotes. Our experimental work investigates whether the information suggested by our theoretical study can be computed reliably and efficiently. We demonstrate algorithms that compute lines of curvature of a (Gaussian smoothed) surface; determine planar patches and umbilic regions; extract axes of surfaces of revolution and tube surfaces. We report preliminary results on adapting the curvature primal sketch algorithms of Asada and Brady [1984] to detect and describe surface intersections.
This paper presents computational techniques using which subdivision algorithms may be devised for the processing (rendering, intersection detection, silhouette detection) of parametrically defined surfaces. These alg...
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This paper presents computational techniques using which subdivision algorithms may be devised for the processing (rendering, intersection detection, silhouette detection) of parametrically defined surfaces. These algorithms work by subdividing surface patches until they are simple enough for direct handling. For example, planar surface patches can be handled analytically. For interference it is necessary to box the surface as well. The computational techniques presented are essentially for efficient computation of surface properties needed by the processing tasks. The three properties considered are: (1) Euclidean bounds: this is done by working in extrema in x, y , and z over the patch; (2) planarity estimate: this test is defined in terms of the linearity of constituent curves; (3) Local visibility: which says whether a patch is totally visible, invisible, or partially visible from a given viewpoint. Rendering algorithms make use of this information. This too is done by working in extrema of the visibility function. All the techniques are based on the parametric form of the surface representation. The class of surfaces that can be handled by these techniques is very large, basically C 2 continuous surfaces. A class of surfaces known as product surfaces is specially introduced as the above methods are extremely efficient for this class. Application of these methods to bicubic surfaces is also discussed.
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