Cone spline approximation via fat conic spline fitting

Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error between the ruled surface and the cone spline can be estimated explicitly via fat conic spline fitting. An efficient fitting algorithm is also proposed for fat conic spline fitting with controllable tolerances. Several examples about approximation of general developable surfaces or other types of ruled surfaces by cone spline surfaces are presented.     

A unified subdivision approach for multi-dimensional non-manifold modeling

This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k≤3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k+1)-directional box splines over k-simplicial domains. Thus, it guarantees a certain level of smoothness in the limit on a regular mesh. The subdivision rules are modified by spatial averaging to guarantee C¹ smoothness near extraordinary cases. Within a single framework, we combine the subdivision rules that can produce 1-, 2-, and 3-manifolds in arbitrary n-D space. Possible solutions for non-manifold regions between the manifolds with different dimensions are suggested as a form of selective subdivision rules according to user preference. We briefly describe the subdivision matrix analysis to ensure a reasonable smoothness across extraordinary topologies, and empirical results support our assumption. In addition, through modifications, we show that the scheme can easily represent objects with singularities, such as cusps, creases, or corners. We further develop local adaptive refinement rules that can achieve level-of-detail control for hierarchical modeling. Our implementation is based on the topological properties of a simplicial domain. Therefore, it is flexible and extendable. We also develop a solid modeling system founded on our subdivision schemes to show potential benefits of our work in industrial design, geometric processing, and other applications.     

Face detection using discriminating feature analysis and Support Vector Machine

This paper presents a novel face detection method by applying discriminating feature analysis (DFA) and support vector machine (SVM). The novelty of our DFA-SVM method comes from the integration of DFA, face class modeling, and SVM for face detection. First, DFA derives a discriminating feature vector by combining the input image, its 1-D Haar wavelet representation, and its amplitude projections. While the Haar wavelets produce an effective representation for object detection, the amplitude projections capture the vertical symmetric distributions and the horizontal characteristics of human face images. Second, face class modeling estimates the probability density function of the face class and defines a distribution-based measure for face and nonface classification. The distribution-based measure thus separates the input patterns into three classes: the face class (patterns close to the face class), the nonface class (patterns far away from the face class), and the undecided class (patterns neither close to nor far away from the face class). Finally, SVM together with the distribution-based measure classifies the patterns in the undecided class into either the face class or the nonface class. Experiments using images from the MIT-CMU test sets demonstrate the feasibility of our new face detection method. In particular, when using 92 images (containing 282 faces) from the MIT-CMU test sets, our DFA-SVM method achieves 98.2% correct face detection rate with two false detections.     

From lines to epipoles through planes in two views

This paper addresses the computation of the fundamental matrix between two views, when camera motion and 3D structure are unknown, but planar surfaces can be assumed. We use line features which are automatically matched in two steps. Firstly, with image based parameters, a set of matches are obtained to secondly compute homographies, which allows to reject wrong ones, and to grow good matches in a final stage. The inclusion of projective transformations gives much better results to match features with short computing overload. When two or more planes are observed, different homographies can be computed, segmenting simultaneously the corresponding planar surfaces. These can be used to obtain the fundamental matrix, which gives constraints for the whole scene. The results show that the global process is robust enough, turning out stable and useful to obtain matches and epipolar geometry from lines in man made environments.     

Class-specific feature polynomial classifier for pattern classification and its application to handwritten numeral recognition

The polynomial classifier (PC) that takes the binomial terms of reduced subspace features as inputs has shown superior performance to multilayer neural networks in pattern classification. In this paper, we propose a class-specific feature polynomial classifier (CFPC) that extracts class-specific features from class-specific subspaces, unlike the ordinary PC that uses a class-independent subspace. The CFPC can be viewed as a hybrid of ordinary PC and projection distance method. The class-specific features better separate one class from the others, and the incorporation of class-specific projection distance further improves the separability. The connecting weights of CFPC are efficiently learned class-by-class to minimize the mean square error on training samples. To justify the promise of CFPC, we have conducted experiments of handwritten digit recognition and numeral string recognition on the NIST Special Database 19 (SD19). The digit recognition task was also benchmarked on two standard databases USPS and MNIST. The results show that the performance of CFPC is superior to that of ordinary PC, and is competitive with support vector classifiers (SVCs).     

Palmprint identification using feature-level fusion

In this paper, we propose a feature-level fusion approach for improving the efficiency of palmprint identification. Multiple elliptical Gabor filters with different orientations are employed to extract the phase information on a palmprint image, which is then merged according to a fusion rule to produce a single feature called the Fusion Code. The similarity of two Fusion Codes is measured by their normalized hamming distance. A dynamic threshold is used for the final decisions. A database containing 9599 palmprint images from 488 different palms is used to validate the performance of the proposed method. Comparing our previous non-fusion approach and the proposed method, improvement in verification and identification are ensured.     

Protein classification by matching and clustering surface graphs

In this paper, we address the problem of comparing and classifying protein surfaces with graph-based methods. Comparison relies on matching surface graphs, extracted from the surfaces by considering concave and convex patches, through a kernelized version of the Softassign graph-matching algorithm. On the other hand, classification is performed by clustering the surface graphs with an EM-like algorithm, also relying on kernelized Softassign, and then calculating the distance of an input surface graph to the closest prototype. We present experiments showing the suitability of kernelized Softassign for both comparing and classifying surface graphs.     

Enhanced Snake algorithm by embedded domain transformation

There have been many attempts to improve the original Snake algorithm by Kass et al. to enhance its ability to locate object boundaries with sharp corners or concave parts. But most of these variants of the Snake model require introducing additional external forces or modifying internal energy terms, all of which necessitate cumbersome fine-tuning by users for optimal performance. In this paper, we present a mathematical formulation for a new algorithm that embeds a domain transformation mapping within the Snake algorithm. The domain transformation step serves to render the object contour more convex and hence is more amenable to be better represented by the Snake contour. Analysis of the new algorithm is carried out which facilitated further enhancements to our technique, rendering a final algorithm that is computationally efficient and is easy and flexible to use. Our approach has been tested with very encouraging experimental results.     

Skeletonization based on error reduction

The accuracy of a non-pixel-based skeletonization method is largely dependent on the contour information chosen as input. When using a Constrained Delaunay Triangulation to construct an object's skeleton, a number of contour pixels must be chosen as a basis for triangulation. This paper presents a new method of selecting these contour pixels. A new method for measuring skeletonization error is proposed, which quantifies the deviation of a skeleton segment from the true medial axis of a stroke in an image. The goal of the proposed algorithm is to reduce this error to an acceptable level, whilst retaining the superior efficiencies of previous non-pixel-based techniques. Experimental results show that the proposed method is adept at following the medial axis of an image, and is capable of producing a skeleton that is confirmed by a human's perception of the image. It is also computationally efficient and robust against noise.