Caiming Zhang

Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation

One of the key problems in using B-splines successfully to approximate an object contour is to determine good knots. In this paper, the knots of a parametric B-spline curve were treated as variables, and the initial location of every knot was generated using the Monte Carlo method in its solution domain. The best km knot vectors among the initial candidates were searched according to the fitness. Based on the initial parameters estimated by an improved k-means algorithm, the Gaussian Mixture Model (GMM) for every knot was built according to the best km knot vectors. Then, the new generation of the population was generated according to the Gaussian mixture probabilistic models. An iterative procedure repeating these steps was carried out until a termination criterion was met. The GMM-based continuous optimization algorithm could determine the appropriate location of knots automatically. A set of experiments was then implemented to evaluate the performance of the new algorithm. The results show that the proposed method achieves better approximation accuracy than methods based on artificial immune system, genetic algorithm or squared distance minimization (SDM).

Robust modeling of constant mean curvature surfaces

We present a new method for modeling discrete constant mean curvature (CMC) surfaces, which arise frequently in nature and are highly demanded in architecture and other engineering applications. Our method is based on a novel use of the CVT (centroidal Voronoi tessellation) optimization framework. We devise a CVT-CMC energy function defined as a combination of an extended CVT energy and a volume functional. We show that minimizing the CVT-CMC energy is asymptotically equivalent to minimizing mesh surface area with a fixed volume, thus defining a discrete CMC surface. The CVT term in the energy function ensures high mesh quality throughout the evolution of a CMC surface in an interactive design process for form finding. Our method is capable of modeling CMC surfaces with fixed or free boundaries and is robust with respect to input mesh quality and topology changes. Experiments show that the new method generates discrete CMC surfaces of improved mesh quality over existing methods.

Q-MAT: Computing Medial Axis Transform By Quadratic Error Minimization

The medial axis transform (MAT) is an important shape representation for shape approximation, shape recognition, and shape retrieval. Despite years of research, there is still a lack of effective methods for efficient, robust and accurate computation of the MAT. We present an efficient method, called Q-MAT, that uses quadratic error minimization to compute a structurally simple, geometrically accurate, and compact representation of the MAT. We introduce a new error metric for approximation and a new quantitative characterization of unstable branches of the MAT, and integrate them in an extension of the well-known quadric error metric (QEM) framework for mesh decimation. Q-MAT is fast, removes insignificant unstable branches effectively, and produces a simple and accurate piecewise linear approximation of the MAT. The method is thoroughly validated and compared with existing methods for MAT computation.

Medical image segmentation using improved FCM

Image segmentation is one of the most important problems in medical image processing, and the existence of partial volume effect and other phenomena makes the problem much more complex. Fuzzy C-means, as an effective tool to deal with PVE, however, is faced with great challenges in efficiency. Aiming at this, this paper proposes one improved FCM algorithm based on the histogram of the given image, which will be denoted as HisFCM and divided into two phases. The first phase will retrieve several intervals on which to compute cluster centroids, and the second one will perform image segmentation based on improved FCM algorithm. Compared with FCM and other improved algorithms, HisFCM is of much higher efficiency with satisfying results. Experiments on medical images show that HisFCM can achieve good segmentation results in less than 0.1 second, and can satisfy real-time requirements of medical image processing.

Active contour method combining local fitting energy and global fitting energy dynamically

To get better segmentation results, local information and global information should be taken into consideration together. In this paper, we propose a new energy functional which combines a local intensity fitting term and an auxiliary global intensity fitting term, and we also give the method to adjust the weight of auxiliary global fitting term dynamically by using local contrast of the image. The combination of the two terms improves the accuracy of segmentation results obviously while reduces dependence on location of initial contour. The experiment results proved the effectiveness of our method.

Fringe pattern denoising via image decomposition

Filtering off noise from a fringe pattern is one of the key tasks in optical interferometry. In this Letter, using some suitable function spaces to model different components of a fringe pattern, we propose a new fringe pattern denoising method based on image decomposition. In our method, a fringe image is divided into three parts: low-frequency fringe, high-frequency fringe, and noise, which are processed in different spaces. An adaptive threshold in wavelet shrinkage involved in this algorithm improves its denoising performance. Simulation and experimental results show that our algorithm obtains smooth and clean fringes with different frequencies while preserving fringe features effectively.

IGA-based point cloud fitting using B-spline surfaces for reverse engineering

Reverse engineering is a viable method to create a 3D virtual model of real physical parts. Usually, reverse engineering consists of two main steps: (1) measure the object and (2) reconstruct it as a 3D model. The measured data are usually represented as a point cloud without topological information and must therefore often be converted into a tensor product B-spline surface format, which has become an industry standard in computer graphics and in CAD systems. In this paper, a new immune genetic algorithm (IGA) for point cloud fitting that fits a noisy 3D point cloud using a B-spline surface with approximate G1 continuity is presented. The point cloud is first segmented into a set of quadrilateral patches. For every patch, a B-spline surface is reconstructed using a least-squares approximation method, and then the surface is optimized to increase the approximation precision using an IGA-based knots adjustment algorithm. Finally, the B-spline patches are stitched together with approximate G1 continuity with a numerical method and the particle swarm optimization (PSO) algorithm. A set of experimental results shows that the proposed method achieves better approximation accuracy than the Bezier-based method and the GA-based method.

A robust high-capacity affine-transformation-invariant scheme for watermarking 3D geometric models

In this article we propose a novel, robust, and high-capacity watermarking method for 3D meshes with arbitrary connectivities in the spatial domain based on affine invariants. Given a 3D mesh model, a watermark is embedded as affine-invariant length ratios of one diagonal segment to the residing diagonal intersected by the other one in a coplanar convex quadrilateral. In the extraction process, a watermark is recovered by combining all the watermark pieces embedded in length ratios through majority voting. Extensive experimental results demonstrate the robustness, high computational efficiency, high capacity, and affine-transformation-invariant characteristics of the proposed approach.

Image denoising and deblurring: non-convex regularization, inverse diffusion and shock filter

A large number of applications in image processing and computer vision depend on image quality. In this paper, main concerns are image denoising and deblurring simultaneously in a restoration task by three types of methodologies: non-convex regularization, inverse diffusion and shock filter. We discuss their relations in the context of image deblurring: the inverse diffusion implied by the non-convex regularization, and the superior ability of deblurring edge of the shock filter to that of the inverse diffusion, both in 1D and 2D cases. Finally, we propose a region-based adaptive anisotropic diffusion with shock filter method, which shows advantages of deblurring edges, denoising and smoothing contours in experiments, compared with some related methods. Therein an idea of “divide and rule” is introduced.

Constructing geometric Hermite curve with minimum curvature variation

Based on the smoothness criterion of minimum curvature variation of the curve, tangent angle constraints guaranteeing an optimized geometric Hermite (OGH) curve both mathematically and geometrically smooths is given, and new methods for constructing composite optimized geometric Hermite (COH) curves are presented in this paper. The comparison of the new methods with Yong and Chengs methods based on strain energy minimization is included.