Raster image vectorization is increasingly  important since vector based graphical contents have been adopted in personal computers and on the Internet. In this paper, we introduce an effective vector-based representation and its associated vectorization algorithm for full-color raster images. There are two important characteristics of our representation. First, the image plane is decomposed into nonoverlapping parametric triangular patches with curved boundaries. The simplicial layout supports an adaptive patch distribution and a flexible topology. Second, a subset of the curved patch boundaries are dedicated to accurately representing curvilinear features. They are aligned with features automatically. Therefore, patches are expected to have moderate internal variations that can be well approximated using smooth functions. We have developed effective techniques for patch boundary optimization and patch color fitting.  A real-time GPU-based parallel algorithm has also been developed for rasterizing the resulting vector image. Experiments and comparisons indicate our image vectorization algorithm achieves a more accurate and compact vector-based representation than existing ones.

Publications:

Tian Xia, Binbin Liao, and Yizhou Yu, Patch-Based Image Vectorization with Automatic Curvilinear Feature Alignment, ACM Transactions on Graphics, SIGGRAPH Asia 2009, to appear.

Interactive selection of desired textures and textured objects from a video is a challenging problem in video editing. In this paper, we present a scalable framework that accurately selects textured objects with only moderate user interaction. Our method applies the active learning methodology, and the user only needs to label minimal initial training data and subsequent query data. An active learning algorithm uses these labeled data to obtain an initial classifier and iteratively improves it until its performance becomes satisfactory. A revised graph cut algorithm based on the trained classifier has also been developed to improve the spatial coherence of selected texture regions. We show that our system is responsive even with videos of a large number of frames, and it frees the user from extensive labeling work. A variety of operations, such as color editing, compositing and texture cloning, can be then applied to the selected textures to achieve interesting editing effects.

Publications:

Tian Xia, Qing Wu, and Yizhou Yu, Lazy Texture Selection Based on Active Learning, The Visual Computer Journal, to appear. [PDF]

Visual data comprises of multi-scale and inhomogeneous signals. In this paper, we exploit these characteristics and develop a compact data representation technique based on a hierarchical tensor-based transformation. In this technique, an original multi-dimensional dataset is transformed into a hierarchy of signals to expose its multi-scale structures. The signal at each level of the hierarchy is further divided into a number of smaller tensors to expose its spatially inhomogeneous structures. These smaller tensors are further transformed and pruned using a tensor approximation technique. Our hierarchical tensor approximation supports progressive transmission and partial decompression. Experimental results indicate that our technique can achieve higher compression ratios and quality than previous methods, including wavelet transform and single-level tensor approximation. We have successfully applied our technique to multiple tasks involving multi-dimensional visual data, including medical and scientific data visualization, data-driven rendering and dynamic texture synthesis.

Publications:

Qing Wu, Tian Xia, Hsueh-Yi Lin, Hongcheng Wang, and Yizhou Yu, Hierarchical Tensor Approximation of Multi-Dimensional Visual Data, IEEE Transactions on Visualization and Computer Graphics, Vol. 14, No. 1, 2008, pp.186-199.

Qing Wu, Tian Xia, and Yizhou Yu, Hierarchical Tensor Approximation of Multi-Dimensional Images, 14th IEEE International Conference on Image Processing, Vol. IV, pp.49-52, San Antonio, September 2007. [PDF]

Computational simulation of physical phenomena plays a central role in many important applications, including scientific visualization and the generation visual effects for entertainment. Typically, these simulations rely on high-quality meshes to model physical objects. Meshes with badly shaped elements degrade both the accuracy and efficiency of the simulation. Traditionally, mesh optimization has relied on global algorithms which are ill-suited to the massive meshes demanded by many modern applications. In this paper, we describe a streaming framework for tetrahedral mesh optimization. We provide empirical results demonstrating that streaming is faster and more memory efficient than global optimization while resulting in essentially identical mesh quality. We also describe a novel streaming method for optimizing the surface of a tetrahedral mesh that is efficient, preserves features, and significantly increases the tetrahedral mesh quality.

Publications:

Tian Xia and Eric Shaffer, Streaming Mesh Optimization for CAD, Proceedings of the 4th International Symposium on Visual Computing (ISVC 2008), pp. 1022-1033, Las Vegas, December 2008. [PDF]

Tian Xia and Eric Shaffer, Streaming Tetrahedral Mesh Optimization, Proceedings of ACM Symposium on Solid and Physical Modeling 2008 (SPM 2008), pp. 281-287, Stony Brook, June 2008. [PDF]

Little work has been presented on the real-time generation of a dynamic snowing scene, partially due to the fact that the process of simulating a dynamic snowing scene involves a complex modeling of the wind field and the interaction between the wind and the snow. In this paper, we construct a three-dimensional wind field based on the discrete form of the Boltzmann equation. By fully considering the physical characteristics of the wind and the snow, we simulate the falling, deposition, and erosion of the snow in 3D space. Experimental results show that realistic wind-driven snow scenes under different speed of the wind with different amounts of snowfall can be rendered in real-time.

Publications:

Changbo Wang, Zhangye Wang, Tian Xia, and Qunsheng Peng, Real-time Snowing Simulation, The Visual Computer Journal, 2006, Vol. 22, No. 5, pp.315-323. [PDF]

Changbo Wang, Tian Xia, Zhangye Wang, and Qunsheng Peng, Real-time Simulation of Wind-driven Snow Scene, The 17th annual conference on Computer Animation and Social Agents (CASA2004), Geneva, Switzerland, July 2004.