Jun-Hai Yong

Texture Analysis and Classification With Linear Regression Model Based on Wavelet Transform

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.

Geometric Hermite curves with minimum strain energy

The purpose of this paper is to provide yet another solution to a fundamental problem in computer aided geometric design, i.e., constructing a smooth curve satisfying given endpoint (position and tangent) conditions. A new class of curves, called optimized geometric Hermite (OGH) curves, is introduced. An OGH curve is defined by optimizing the magnitudes of the endpoint tangent vectors in the Hermite interpolation process so that the strain energy of the curve is a minimum. An OGH curve is not only mathematically smooth, i.e., with minimum strain energy, but also geometrically smooth, i.e., loop-, cusp- and fold-free if the geometric smoothness conditions and the tangent direction preserving conditions on the tangent angles are satisfied. If the given tangent vectors do not satisfy the tangent angle constraints, one can use a 2-segment or a 3-segment composite optimized geometric Hermite (COH) curve to meet the requirements. Two techniques for constructing 2-segment COH curves and five techniques for constructing 3-segment COH curves are presented. These techniques ensure automatic satisfaction of the tangent angle constraints for each OGH segment and, consequently, mathematical and geometric smoothness of each segment of the curve. The presented OGH and COH curves, combined with symmetry-based extension schemes, cover tangent angles of all possible cases. The new method has been compared with the high-accuracy Hermite interpolation method by de Boor et al. and the Pythagorean-hodograph (PH) curves by Farouki et al. While the other two methods both would generate unpleasant shapes in some cases, the new method generates satisfactory shapes in all the cases.

Computing the minimum distance between a point and a NURBS curve

A new method is presented for computing the minimum distance between a point and a NURBS curve. It utilizes a circular clipping technique to eliminate the curve parts outside a circle with the test point as its center point. The radius of the elimination circle becomes smaller and smaller during the subdivision process. A simple condition for terminating the subdivision process is provided, which leads to very few subdivision steps in the new method. Examples are shown to illustrate the efficiency and robustness of the new method.

Dynamic video summarization using two-level redundancy detection

The mushroom growth of video information, consequently, necessitates the progress of content-based video analysis techniques. Video summarization, aiming to provide a short video summary of the original video document, has drawn much attention these years. In this paper, we propose an algorithm for video summarization with a two-level redundancy detection procedure. By video segmentation and cast indexing, the algorithm first constructs story boards to let users know main scenes and cast (when this is a video with cast) in the video. Then it removes redundant video content using hierarchical agglomerative clustering in the key frame level. The impact factors of scenes and key frames are defined, and parts of key frames are selected to generate the initial video summary. Finally, a repetitive frame segment detection procedure is designed to remove redundant information in the initial video summary. Results of experimental applications on TV series, movies and cartoons are given to illustrate the proposed algorithm.

A rational extension of Piegl's method for filling n-sided holes

N-sided hole filling plays an important role in vertex blending. To deal with the case that the corner is surrounded by rational surfaces (i.e. NURBS surfaces), an algorithm to fill n-sided holes with @e- G^1 continuous NURBS patches that interpolate the given boundary curves and approximate the given cross-boundary derivatives is presented based on Piegls method. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance @e. The boundaries as well as cross-boundary derivatives can all be NURBS curves. No restrictions are imposed on the number of boundary curves, and the cross-boundary derivatives can be specified independently.

A torus patch approximation approach for point projection on surfaces

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.

Technical section: A new algorithm for Boolean operations on general polygons

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.

A numerically stable fragile watermarking scheme for authenticating 3D models

This paper analyzes the numerically instable problem in the current 3D fragile watermarking schemes. Some existing fragile watermarking schemes apply the floating-point arithmetic to embed the watermarks. However, these schemes fail to work properly due to the numerically instable problem, which is common in the floating-point arithmetic. This paper proposes a numerically stable fragile watermarking scheme. The scheme views the mantissa part of the floating-point number as an unsigned integer and operates on it by the bit XOR operator. Since there is no numerical problem in the bit operation, this scheme is numerically stable. The scheme can control the watermark strength through changing the embedding parameters. This paper further discusses selecting appropriate embedding parameters to achieve good performance in terms of the perceptual invisibility and the ability to detect unauthorized attacks on the 3D models. The experimental results show that the proposed public scheme could detect attacks such as adding noise, adding/deleting faces, inserting/removing vertices, etc. The comparisons with the existing fragile schemes show that this scheme is easier to implement and use.

Degree reduction of B-spline curves

This work deals with the problem of degree reducing a B-spline curve without intermediate conversion to Bezier form. Degree elevation for B-spline curves may easily be described in blossom form. We also use blossoms for the degree reduction problem, and set up least squares problems for finding the B-spline coefficients directly. We also give an application to curve fairing.

Bilateral blue noise sampling

Blue noise sampling is an important component in many graphics applications, but existing techniques consider mainly the spatial positions of samples, making them less effective when handling problems with non-spatial features. Examples include biological distribution in which plant spacing is influenced by non-positional factors such as tree type and size, photon mapping in which photon flux and direction are not a direct function of the attached surface, and point cloud sampling in which the underlying surface is unknown a priori. These scenarios can benefit from blue noise sample distributions, but cannot be adequately handled by prior art. Inspired by bilateral filtering, we propose a bilateral blue noise sampling strategy. Our key idea is a general formulation to modulate the traditional sample distance measures, which are determined by sample position in spatial domain, with a similarity measure that considers arbitrary per sample attributes. This modulation leads to the notion of bilateral blue noise whose properties are influenced by not only the uniformity of the sample positions but also the similarity of the sample attributes. We describe how to incorporate our modulation into various sample analysis and synthesis methods, and demonstrate applications in object distribution, photon density estimation, and point cloud sub-sampling.