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The wavelet transform as an important multiresolution analysis tool has already been commonly applied to texture analysis and classification. Nevertheless, it ignores the structural information while capturing the spectral information of the texture image at different scales. In this paper, we propose a texture analysis and classification approach with the linear regression model based on the wavelet transform. This method is motivated by the observation that there exists a distinctive correlation between the sample images, belonging to the same kind of texture, at different frequency regions obtained by 2-D wavelet packet transform. Experimentally, it was observed that this correlation varies from texture to texture. The linear regression model is employed to analyze this correlation and extract texture features that characterize the samples. Therefore, our method considers not only the frequency regions but also the correlation between these regions. In contrast, the pyramid-structured wavelet transform (PSWT) and the tree-structured wavelet transform (TSWT) do not consider the correlation between different frequency regions. Experiments show that our method significantly improves the texture classification rate in comparison with the multiresolution methods, including PSWT, TSWT, the Gabor transform, and some recently proposed methods derived from these.

In most realtime applications such as 3D games, in order to reduce the complexity of the scene being rendered, objects are often made by simple and large primitives. Thus, the phenomenon of edge highlighting, which would require chamfering structures made by lots of small patches at the seaming, is absent and is often faked by 'highlights' drawn on the texture. We proposed a realistic realtime rendering procedure for highlighting chamfering structures, or rounded edges, by considering specified edges as thin cylinders and obtained the intensity via integration. We derived a brief approximated formula generalized from Blinn's shadow model, and used a precomputed integration table to accelerate the render speed and reduce resources needed. The algorithm is implemented with shader language, and can be considered as a post-process on original result. Evaluation shows that the effect on rendering speed is limited even for scenes with large scale of vertices. [ABSTRACT FROM AUTHOR]

Depth-of-field is one of the most crucial rendering effects for synthesizing photorealistic images. Unfortunately, this effect is also extremely costly. It can take hundreds to thousands of samples to achieve noise-free results using Monte Carlo integration. This paper introduces an efficient adaptive depth-of-field rendering algorithm that achieves noise-free results using significantly fewer samples. Our algorithm consists of two main phases: adaptive sampling and image reconstruction. In the adaptive sampling phase, the adaptive sample density is determined by a 'blur-size' map and 'pixel-variance' map computed in the initialization. In the image reconstruction phase, based on the blur-size map, we use a novel multiscale reconstruction filter to dramatically reduce the noise in the defocused areas where the sampled radiance has high variance. Because of the efficiency of this new filter, only a few samples are required. With the combination of the adaptive sampler and the multiscale filter, our algorithm renders near-reference quality depth-of-field images with significantly fewer samples than previous techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a method to construct a B-spline surface that interpolates the specified four groups of boundary derivative curves in the B-spline form. The discontinuity can be bounded by an arbitrary geometric invariant as the tolerance. The method first handles the six types of the compatibility problems by continuity-preserving reparameterization, knot-insertion and local control-point tuning. The transformed boundary conditions are then parametrically compatible, so the Coons strategy can be applied to construct the final interpolant. Not only can it be used in the reliable geometric modeling, but the approach also can be applied to many other algorithms that require compatibility guarantee. [Copyright &y& Elsevier]

Abstract: This paper presents a practical polyline approach for approximating the Hausdorff distance between planar free-form curves. After the input curves are approximated with polylines using the recursively splitting method, the precise Hausdorff distance between polylines is computed as the approximation of the Hausdorff distance between free-form curves, and the error of the approximation is controllable. The computation of the Hausdorff distance between polylines is based on an incremental algorithm that computes the directed Hausdorff distance from a line segment to a polyline. Furthermore, not every segment on polylines contributes to the final Hausdorff distance. Based on the bound properties of the Hausdorff distance and the continuity of polylines, two pruning strategies are applied in order to prune useless segments. The R-Tree structure is employed as well to accelerate the pruning process. We experimented on Bezier curves, B-Spline curves and NURBS curves respectively with our algorithm, and there are 95% segments pruned on approximating polylines in average. Two comparisons are also presented: One is with an algorithm computing the directed Hausdorff distance on polylines by building Voronoi diagram of segments. The other comparison is with equation solving and pruning methods for computing the Hausdorff distance between free-form curves. [Copyright &y& Elsevier]

Abstract: This paper proposes an algorithm for calculating the orthogonal projection of parametric curves onto -spline surfaces. It consists of a second order tracing method with which we construct a polyline to approximate the pre-image curve of the orthogonal projection curve in the parametric domain of the base surface. The final 3D approximate curve is obtained by mapping the approximate polyline onto the base surface. The Hausdorff distance between the exact orthogonal projection curve and the approximate curve is controlled under the user-specified distance tolerance. And the continuity of the approximate curve is , where is the user-specified angle tolerance. Experiments demonstrate that our algorithm is faster than the existing first order algorithms. [Copyright &y& Elsevier]

Abstract: An unstructured tetrahedral mesh generation algorithm for 3D model with constraints is presented. To automatically generate a tetrahedral mesh for model with constraints, an advancing front algorithm is presented based on conforming constrained Delaunay tetrahedralization (CCDT). To reduce the number of visibility tests between vertices with respect to model faces as well as the computation of constrained Delaunay tetrahedra, a sufficient condition for DT (constrained Delaunay tetrahedralization whose simplexes are all Delaunay) existence is presented and utilized coupled to uniform grid and advancing front techniques in our algorithm. The mesh generator is robust and exhibits a linear time complexity for mechanical models with uniform density distribution. [Copyright &y& Elsevier]

Abstract: A new algorithm for Boolean operations on general planar polygons is presented. It is available for general planar polygons (manifold or non-manifold, with or without holes). Edges of the two general polygons are subdivided at the intersection points and touching points. Thus, the boundary of the Boolean operation resultant polygon is made of some whole edges of the polygons after the subdivision process. We use the simplex theory to build the basic mathematical model of the new algorithm. The subordination problem between an edge and a polygon is reduced to a problem of determining whether a point is on some edges of some simplices or inside the simplices, and the associated simplicial chain of the resultant polygon is just an assembly of some simplices and their coefficients of the two polygons after the subdivision process. Examples show that the running time required by the new algorithm is less than one-third of that by the Rivero and Feito algorithm. [Copyright &y& Elsevier]

Abstract: Assembly searching technologies are important for the improvement of design reusability. However, existing methods require that assemblies possess high-level information, and thus cannot be applied in lightweight assemblies. In this paper, we propose a novel relaxed lightweight assembly retrieval approach based on a vector space model (VSM). By decomposing the assemblies represented in a watertight polygon mesh into bags of parts, and considering the queries as a vague specification of a set of parts, the resilient ranking strategy in VSM is successfully applied in the assembly retrieval. Furthermore, we take the scale-sensitive similarities between parts into the evaluation of matching values, and extend the original VSM to a relaxed matching framework. This framework allows users to input any fuzzy queries, is capable of measuring the results quantitatively, and performs well in retrieving assemblies with specified characteristics. To accelerate the online matching procedure, a typical parts based matching process, as well as a greedy strategy based matching algorithm is presented and integrated in the framework, which makes our system achieve interactive performance. We demonstrate the efficiency and effectiveness of our approach through various experiments on the prototype system. [Copyright &y& Elsevier]

Abstract: This paper proposes a second order geometric iteration algorithm for point projection and inversion on parametric surfaces. The iteration starts from an initial projection estimation. In each iteration, we construct a second order osculating torus patch to the parametric surface at the previous projection. Then we project the test point onto the torus patch to compute the next projection and its parameter. This iterative process is terminated when the parameter satisfies the required precision. Experiments demonstrate the convergence speed of our algorithm. [Copyright &y& Elsevier]

Abstract: Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a parabola approximation method based on the cubic reparameterization of rational Bézier surfaces, which generates G1 continuous approximate curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified tolerance. Examples are given to show the performance of our algorithm. [Copyright &y& Elsevier]

Abstract: This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh 1 [1] A mesh is quad-dominant if it contains quad facets as its majority. The quantity of quad facets is much more than the quantity of triangular and other multi-sided facets. -continuously using regular Coons B-spline surfaces, which are popular in industrial CAD/CAM systems. We first decompose all non-quadrangular facets into quadrilaterals. The tangential and second-order derivative vectors are then estimated on each vertex of the quads. A least-square adjustment algorithm based on the homogeneous form of continuity condition is applied to achieve curvature continuity. Afterwards, the boundary curves, the first- and the second-order cross-boundary derivative curves are constructed fulfilling continuity and compatibility conditions. Coons B-spline patches are finally generated using these curves as boundary conditions. In this paper, the upper bound of the rank of continuity condition matrices is also strictly proved to be , and the method of tangent-vector estimation is improved to avoid petal-shaped patches in interpolating solids of revolution. Several examples demonstrate its feasibility. [ABSTRACT FROM AUTHOR]

Abstract: A new algorithm for reducing control points in lofted surface interpolation to rows of data points is presented in this paper. The key step of surface lofting is to obtain a set of compatible B-spline curves interpolating each row. Given a set of points and their parameterization, a necessary and sufficient condition is proposed to determine the existence of interpolating B-spline curves defined on a given knot vector. Based on this condition, we first properly construct a common knot vector that guarantees the existence of interpolating B-spline curves to each row of points. Then we calculate a set of interpolating B-spline curves defined on the common knot vector by energy minimization. Using this method, fewer control points are employed while maintaining a visually pleasing shape of the lofted surface. Several experimental results demonstrate the usability and quality of the proposed method. [Copyright &y& Elsevier]