18276516
Interference Detection for Subdivision Surfaces
Accurate and robust interference detection and ray-tracing of subdivis ion surfaces requires safe linear approximations. Approximation of the limit surface by the subdivided control polyhe dron can be both inaccurate and, due to the exponential growth of the number of facets, costly. This paper shows how a standard intersection hierarchy, such as an OB B tree, can be made safe and efficient for subdivision surface interference detection. The key is to construct, on th e fly, optimally placed facets, whose spherical offsets tightly enclose the limit surface. The spherically offset fac ets can be locally subdivided and they can be efficiently intersected based on standard triangle-triangle interfere nce detection.
16426940
An accurate error measure for adaptive subdivision surfaces
A tight estimate on the maximum distance between a subdivision surface and its linear approximation is introduced to guide adaptive subdivision with guaranteed accuracy.
11584790
SLEVEs for planar spline curves
Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances. This is the simplest instance of a subdividable linear efficient variety enclosure, short sleve.We develop general criteria, that certify correctness of a global, polygonal enclosure built from a sequence of individual bounding boxes by extending and intersecting their edges. These criteria prove correctness of the sleve construction.
123098354
Globally optimal segmentation of interacting surfaces with geometric constraints
Efficient detection of globally optimal surfaces representing object boundaries in volumetric datasets is important and remains challenging in many medical image analysis applications. We have developed an optimal surface detection method that is capable of simultaneously detecting multiple interacting surfaces, in which the optimality is controlled by the cost functions designed for individual surfaces and several geometric constraints defining the surface smoothness and interrelations. The method solves the surface detection problems by transforming them into computing minimum s-t cuts in the derived edge-weighted directed graphs. The proposed algorithm has low-order polynomial complexity and is computationally efficient. The method has been validated on over 100 computer generated volumetric images and 96 CT-scanned datasets of different-sized plexiglas tubes, yielding highly accurate results (mean signed error of the measured inner- and outer-diameters of the plexiglas tubes was 0.21 /spl plusmn/ 3.20%). Our approach can be readily extended to higher dimensional image segmentation.
2863452
Optimal Polygon Cover Problems and Applications
Polygon cover problems are important in several applied areas, such as material layout, layered manufacturing, radiation therapy and radiosurgery, etc. In this paper, we study three optimal polygon cover problems: monotone polygon cover among obstacles, star-shaped polygon cover among obstacles, and strip cover for trapezoidalized polygons. Based on some interesting geometric observations, we develop efficient algorithms for solving these problems. The complexity bounds of our monotone cover and star-shaped cover algorithms are comparable to those of the previously best known algorithms for simpler cases of the problems without considering obstacles. Our strip cover algorithm improves the quality of the previously best known solutions.
43142618
Efficient Algorithms for k-Terminal Cuts on Planar Graphs
The minimum k-terminal cut problem is of considerable theoretical interest and arises in several applied areas such as parallel and distributed computing, VLSI circuit design, and networking. In this paper, we present two new approximation and exact algorithms for this problem on an n-vertex undirected weighted planar graph G. For the case when the k terminals are covered by the boundaries of m > 1 faces of G, we give a min{O(n2 log n log m), O(m2n1.5 log2 n+kn)} time algorithm with a (2 - 2/k)-approximation ratio (clearly, m ≤ k). For the case when all k terminals are covered by the boundary of one face of G, we give an O(nk3 +(n log n)k2) time exact algorithm, or a linear time exact algorithm if k = 3, for computing an optimal k-terminal cut. Our algorithms are based on interesting observations and improve the previous algorithms when they are applied to planar graphs.
15599036
Simultaneous Segmentation of Multiple Closed Surfaces Using Optimal Graph Searching
This paper presents a general graph-theoretic technique for simultaneously segmenting multiple closed surfaces in volumetric images, which employs a novel graph-construction scheme based on triangulated surface meshes obtained from a topological presegmentation. The method utilizes an efficient graph-cut algorithm that guarantees global optimality of the solution under given cost functions and geometric constraints. The method's applicability to difficult biomedical image analysis problems was demonstrated in a case study of co-segmenting the bone and cartilage surfaces in 3-D magnetic resonance (MR) images of human ankles. The results of our automated segmentation were validated against manual tracings in 55 randomly selected image slices. Highly accurate segmentation results were obtained, with signed surface positioning errors for the bone and cartilage surfaces being 0.02 +/- 0.11mm and 0.17 +/- 0.12mm, respectively.
13903489
Whole genome phylogeny based on clustered signature string composition
Peptide compositions constructed out of whole sets of protein sequences can be used as species signatures for phylogenetic analysis. To account for point mutations, an amino acid substitution model is integrated into the complete composition vectors through a novel peptide clustering algorithm. Such a refined signature is expected to highlight deeper evolutionary relationships among the species and employed into the whole genome phylogenetic analysis to define a new evolutionary distance measure. Computational experiments have been set up to validate the effectiveness of this new measure and a vertebrate evolutionary tree using a dataset of 832 proteins for 64 vertebrates is reported.