This paper describes a Graphics Processing Unit (GPU)-assisted real-time three-dimensional shape measurement system. Our experiments demonstrated that the absolute coordinates calculation and rendering speed of a GPU is more than four times faster than that of a dual CPU workstation with the same graphics card. By implementing the GPU into our system, we realized simultaneous absolute coordinate acquisition, reconstruction and display at 30 frames per second with a resolution of approximately 266K points per frame. Moreover, a 2+1 phase-shifting algorithm was employed to alleviate the measurement error caused by motion. Applications of the system include medical imaging, manufacturing, entertainment, and security.

Texture mapping and texture synthesis are two popular methods for the decoration of surfaces with visual detail. Here, an existing challenge is to preserve, or at least balance, two competing metrics: scale and angle. In this paper we present two methods for this, both based on global conformal parameterization. First, we describe a texture synthesis algorithm for surfaces with arbitrary topology. By using the conformal parameterization, the 3D surface texture synthesis problem can be converted to a 2D image synthesis problem, which is more intuitive, easier, and conceptually simpler. While the conformality of the parameterization naturally preserves the angles of the texture, in this paper we provide a multi-scale technique to also maintain a more uniform area scaling factor. A second novel contribution is to employ the global parameterization to simultaneously preserve orthogonality and size in texture

Superpixels are perceptually meaningful atomic regions that can effectively capture image features. Among various methods for computing uniform superpixels, simple linear iterative clustering (SLIC) is popular due to its simplicity and high performance. In this paper, we extend SLIC to compute content-sensitive superpixels, i.e., small superpixels in content-dense regions with high intensity or colour variation and large superpixels in content-sparse regions. Rather than using the conventional SLIC method that clusters pixels in R^5, we map the input image I to a 2-dimensional manifoldMR5, whose area elements are a good measure of the content density in I. We propose a simple method, called intrinsic manifold SLIC (IMSLIC), for computing a geodesic centroidal Voronoi tessellation (GCVT)—a uniform tessellation—onM, which induces the content-sensitive superpixels in I. In contrast to the existing algorithms, IMSLIC characterizes the content sensitivity by measuring areas of Voronoi cells onM. Using a simple and fast approximation to a closed-form solution, the method can compute the GCVT at a very low cost and guarantees that all Voronoi cells are simply connected. We thoroughly evaluate IMSLIC and compare it with eleven representative methods on the BSDS500 dataset and seven representative methods on the NYUV2 dataset. Computational results show that IMSLIC outperforms existing methods in terms of commonly used quality measures pertaining to superpixels such as compactness, adherence to boundaries, and achievable segmentation accuracy. We also evaluate IMSLIC and seven representative methods in an image contour closure application, and the results on two datasets, WHD and WSD, show that IMSLIC achieves the best foreground segmentation performance.

In this paper we show that stability for holomorphic vector bundles are equivalent to the existence of solutions to certain system of Monge Ampere equations parametrized by a parameter k. We solve this fully nonlinear elliptic system by singular perturbation technique and show that the vanishing of obstructions for the perturbation is given precisely by the stability condition. This can be interpreted as an infinite dimensional analog of the equivalencybetween Geometric Invariant Theory and Symplectic Reduction for moduli space of vector bundles.

Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the conformal parameterization of a simply-connected open surface onto the unit disk, which significantly speeds up the computation, enhances the conformality and stability, and guarantees the bijectivity. The conformality distortions at the inner region and on the boundary are corrected by two steps, with the aid of an iterative scheme using quasi-conformal theories. Experimental results demonstrate the effectiveness of our proposed method.