Nurbs Approximation of A-Splines and A-Patches
Given A-spline curves and A-patch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for A-spline curves and a parametric tensor-product NURBS form for A-patch surfaces. We concentrate on cubic A-patches, providing a C1-continuous surface that interpolates a given triangulation together with surface normals at the vertices. In many cases we can generate cubic trimming curves that are rationally parametrizable on the triangular faces of the tetrahedra; for the remaining faces we resort to using quadratic curves, which are always rationally parametrizable, to approximate the cubic trimming curves.

title: Regular algebraic curve segments (II) - Interpolation and approximation
abstract: In this paper (part two of the trilogy) we introduce three classes of reduced form D -regular algebraic curve splines and use them for interpolation and approximation of various algebraic curves. Explicit formulas for interpolation and approximation are also given in some low degree cases.

title: Discrete Laplace-Beltrami Operator on Sphere and Optimal Spherical Triangulations
abstract: In this paper we first modify a widely used discrete Laplace-Beltrami operator proposed by Meyer et al over triangular surfaces, and then we show that the modified discrete operator has some convergence properties over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace-Beltrami operator is constructed. Optimal hierarchical spherical triangulations are also given. Truncation error bounds of the discrete Laplace-Beltrami operator over the constructed triangulations are provided.

title: Automatic reconstruction of surfaces and scalar fields from 3D scans
abstract: We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. A possible application is the rapid computer model reconstruction of an existing part or prototype from a three dimensional (3D) points scan of its surface. Color, texture or some scalar material property of the physical part, define natural scalar fields over the surface of the CAD model. Our reconstruction algorithm does not impose any convexity or differentiability restrictions on the surface of the original physical part or the scalar field function, except that it assumes that there is a sufficient sampling of the input point data to unambiguously reconstruct the CAD model. Compared to earlier methods our algorithm has the advantages of simplicity, efficiency and uniformity (both CAD model and scalar field reconstruction). The simplicity and efficiency of our approach is based on several novel uses of appropriate sub-structures (alpha shapes) of a three-dimensional Delaunay Triangulation, its dual the three-dimensional Voronoi diagram, and dual uses of trivariate Bernstein-Bezier forms. The boundary of the CAD model is modeled using implicit cubic Bernstein-Bezier patches, while the scalar field is reconstructed with functional cubic Bernstein-Bezier patches.

title: Hierarchical multiresolution reconstruction of shell surfaces
abstract: We present an adaptive, hierarchical Hh-multiresolution reconstruction algorithm to model shell surface objects from a matched pair of triangulated surfaces. Shell surfaces are an interval of contours of trivariate functions with prismatic support. In the H-direction, a hierarchical representation of the scaffold is constructed. For any adaptively extracted scaffold from the hierarchy, a sequence of functions in the h-direction (regularly subdivided mesh) is constructed so that their contours approximate the input shell to within a given error e. The shell surfaces can be made to capture sharp curve creases on the shell while being C1 smooth everywhere else. Using an interval of iso-contours of smooth trivariate spline functions, rather than a pair of inner and outer surface splines, one avoids the need for interference checks between the inner and outer surface boundaries.

title: Fast evaluation of the improved Loop's subdivision surfaces
abstract: For obtaining better curvature distributions of subdivision surfaces, various improvements for Loop's subdivision scheme (C. Loop, 1987) on triangular surface meshes have been made. A careful analysis shows that the fast evaluation technique of the subdivision surface proposed by Stam is no longer usable to these improved schemes. This paper describes a fast evaluating algorithm for improved Loop's subdivision surfaces. The algorithm is applicable to a vast class of subdivision schemes for triangular surface meshes. Using the proposed algorithm, one can evaluate the subdivision surface at any domain point for any set of input subdivision masks and a control mesh.

title: Statistical modeling and conceptualization of natural images
abstract: Multi-level annotation of images is a promising solution to enable semantic image retrieval by using various keywords at different semantic levels. In this paper, we propose a multi-level approach to interpret and annotate the semantics of natural images by using both the dominant image components and the relevant semantic image concepts. In contrast to the well-known image-based and region-based approaches, we use the concept-sensitive salient objects as the dominant image components to achieve automatic image annotation at the content level. By using the concept-sensitive salient objects for image content representation and feature extraction, a novel image classification technique is developed to achieve automatic image annotation at the concept level. To detect the concept-sensitive salient objects automatically, a set of detection functions are learned from the labeled image regions by using support vector machine (SVM) classifiers with an automatic scheme for searching the optimal model parameters. To generate the semantic image concepts, the finite mixture models are used to approximate the class distributions of the relevant concept-sensitive salient objects. An adaptive EM algorithm has been proposed to determine the optimal model structure and model parameters simultaneously. In addition, a large number of unlabeled samples have been integrated with a limited number of labeled samples to achieve more effective classifier training and knowledge discovery. We have also demonstrated that our algorithms are very effective to enable multi-level interpretation and annotation of natural images.

title: Human action recognition with primitive-based coupled-HMM
abstract: This paper presents a new approach named primitive-based coupled-HMM for human natural complex action recognition. First, the system proposes a hybrid human model and employs 2-order B-spline function to detect the two shoulder joints in the silhouette image to obtain the basic motion features including the elbow angles, motion parameters of the face and two hands. Then, primitive-based coupled hidden Markov model (PCHMM) is presented for natural context-dependent action recognition. Lastly, comparison experiments show that PCHMM is better than the conventional HMM and coupled HMM.

title: Learning object intrinsic structure for robust visual tracking
abstract: In this paper, a novel method to learn the intrinsic object structure for robust visual tracking is proposed. The basic assumption is that the parameterized object state lies on a low dimensional manifold and can be learned from training data. Based on this assumption, firstly we derived the dimensionality reduction and density estimation algorithm for unsupervised learning of object intrinsic representation, the obtained non-rigid part of object state reduces even to 2 dimensions. Secondly the dynamical model is derived and trained based on this intrinsic representation. Thirdly the learned intrinsic object structure is integrated into a particle-filter style tracker. We will show that this intrinsic object representation has some interesting properties and based on which the newly derived dynamical model makes particle-filter style tracker more robust and reliable. Experiments show that the learned tracker performs much better than existing trackers on the tracking of complex non-rigid motions such as fish twisting with self-occlusion and large inter-frame lip motion. The proposed method also has the potential to solve other type of tracking problems.

title: Hidden Markov Model Based Events Detection in Soccer Video
abstract: This paper presents an algorithm developed based on hidden Markov model for cues fusion and event inference in soccer video. Four events, shoot, foul, offside and normal playing, are defined to be detected. The states of the events are employed to model the observations of the five cues, which are extracted from the shot sequences directly. The experimental results show the algorithm is effective and robust in inferring events from roughly extracted cues.

title: Multi-cue-based face and facial feature detection on video segments
abstract: An approach is presented to detect faces and facial features on a video segment based on multi-cues, including gray-level distribution, color, motion, templates, algebraic features and so on. Faces are first detected across the frames by using color segmentation, template matching and artificial neural network. A PCA-based (Principal Component Analysis) feature detector for still images is then used to detect facial features on each single frame until the resulting features of three adjacent frames, named as base frames, are consistent with each other. The features of frames neighboring the base frames are first detected by the still-image feature detector, then verified and corrected according to the smoothness constraint and the planar surface motion constraint. Experiments have been performed on video segments captured under different environments, and the presented method is proved to be robust and accurate over variable poses, ages and illumination conditions.