Bayesian Regularization of Diffusion Tensor Images Using Hierarchical MCMC and Loopy Belief PropagationS. Wei, J. Hua, C. Chen, J. Bu, and Y. YuInternational Conference on Image Processing, 2010, PDF. Based on the theory of Markov Random Fields, a Bayesian regularization model for diffusion tensor images (DTI) is proposed in this paper. The low-degree parameterization of diffusion tensors in our model makes it less computationally intensive to obtain a maximum a posteriori (MAP) estimation. An approximate solution to the problem is achieved efficiently using hierarchical Markov Chain Monte Carlo (HMCMC), and a loopy belief propagation algorithm is applied to a coarse grid to obtain a good initial solution for hierarchical MCMC. Experiments on synthetic and real data demonstrate the effectiveness of our methods. |
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Wavelet-Based Hybrid Multilinear Models for Multidimensional Image ApproximationQing Wu, Chun Chen, and Yizhou YuInternational Conference on Image Processing, 2008, PDF. The wavelet transform hierarchically decomposes images with prescribed bases, while multilineal models search for optimal bases to adapt visual data. In this paper, we integrate these two approaches to compactly represent 2D images and 3D volume data. Once a wavelet (packet) decomposition has been performed, the coefficients are subdivided into small blocks most of which have small energy and are pruned. Surviving blocks usually exhibit strong redundancy among different channels and subbands. To exploit this property, we organize the surviving blocks into small tensors, group the tensors into clusters using an EM algorithm, and compactly approximate each cluster using tensor ensemble approximation. Experimental results on images and medical volume data indicate that our approach achieves better approximation quality than wavelet (packet) transforms. |
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Hierarchical Tensor Approximation of Multi-Dimensional ImagesQing Wu, Tian Xia, and Yizhou YuInternational Conference on Image Processing, 2007, PDF. Visual data comprises of multi-scale and inhomogeneous signals. In this paper, we exploit these characteristics and develop an adaptive data approximation technique based on a hierarchical tensor-based transformation. In this technique, an original multi-dimensional image is transformed into a hierarchy of signals to expose its multiscale 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 collective tensor approximation technique. Experimental results indicate that our technique can achieve higher compression ratios than existing functional approximation methods, including wavelet transforms, wavelet packet transforms and single-level tensor approximation. |
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Reconstruction of 3-D Symmetric Curves from Perspective Images without Discrete FeaturesWei Hong, Yi Ma and Yizhou YuEuropean Conference on Computer Vision, 2004, PDF. The shapes of many natural and man-made objects have curved contours. The images of such contours usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. This paper shows that both the shape of curves in 3-D space and the camera poses can be accurately reconstructed from their perspective images with unknown point correspondences given that the curves have certain invariant properties such as symmetry. We show that in such cases the minimum number of views needed for a solution is remarkably small: one for planar curves and two for nonplanar curves (of arbitrary shapes), which is significantly less than what is required by most existing algorithms for general curves. Our solutions rely on minimizing the L2-distance between the shapes of the curves reconstructed via the "epipolar geometry" of symmetric curves. Both simulations and experiments on real images are presented to demonstrate the effectiveness of our approach. |
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Shadow Graphs and Surface ReconstructionYizhou Yu and Johnny ChangEuropean Conference on Computer Vision, 2002, PDF. An extended version appears in International Journal of Computer Vision, Vol. 62, No. 1-2, 2005. We present a method to solve shape-from-shadow using shadow graphs which give a new graph-based representation for shadow constraints. It can be shown that the shadow graph alone is enough to solve the shape-from-shadow problem from a dense set of images. Shadow graphs provide a simpler and more systematic approach to represent and integrate shadow constraints from multiple images. To recover shape from a sparse set of images, we propose a method for integrated shadow and shading constraints. Previous shape-from-shadow algorithms do not consider shading constraints while shape-from-shading usually assumes there is no shadow. Our method is based on collecting a set of images from a fixed viewpoint as a known light source changes its position. It first builds a shadow graph from shadow constraints from which an upper bound for each pixel can be derived if the height values of a small number of pixels are initialized properly. Finally, a constrained optimization procedure is designed to make the results from shape-from-shading consistent with the upper bounds derived from the shadow constraints. Our technique is demonstrated on both synthetic and real imagery. |
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Video Metamorphosis Using Dense Flow FieldsYizhou Yu and Qing WuComputer Animation and Virtual Worlds, Vol. 15, No. 3-4, 2004, pp.387-397. PDF When we perform video metamorphosis, it would be desirable to make smooth morphing transitions simultaneously along with the original motion in the image sequences. In this paper, we present a novel semi-automatic video morphing technique that exhibits this behavior. Our technique effectively exploits temporal coherence and automatic image matching. One-to-one dense mappings between pairs of corresponding frames are obtained by applying a compositing procedure and a hierarchical image matching technique. These dense mappings can be initialized with sparse frame-to-frame feature correspondences obtained semi-automatically by integrating a friendly user interface with a robust feature tracking algorithm. Experimental results show that our approach to video metamorphosis can produce superior results. |
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Two-Level Image Segmentation Based on Region and Edge IntegrationQing Wu and Yizhou YuDICTA 2003, PDF. This paper introduces a two-level approach for image segmentation based on region and edge integration. Edges are first detected in the original image using a combination of operators for intensity gradient and texture discontinuities. To preserve the spatial coherence of the edges and their surrounding image regions, the detected edges are vectorized into connected line segments which serve as the basis for a constrained Delaunay triangulation. Segmentation is first performed on the triangulation using graph cuts. Our method favors segmentations that pass through more vectorized line segments. Finally, the obtained segmentation on the triangulation is projected onto the original image and region boundaries are refined to achieve pixel accuracy. Experimental results show that the two-level approach can achieve accurate edge localization, better spatial coherence and improved efficiency. |
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Statistical Estimation of Fluid Flow FieldsJohnny Chang, David Edwards and Yizhou YuECCV 2002 workshop on Statistical Methods in Video Processing, PDF. Many natural phenomena involve dynamic fluids whose motion differs radically from that of rigid bodies. This paper presents a novel approach for estimating fluid motion fields. It first estimates a local flow probability distribution function at each pixel using the STAR model and the data from a spatio-temporal neighborhood. It then feeds the set of distribution functions into a global optimization framework. As a result, the optimization returns a motion field with a unique velocity vector at each pixel. Experiments with real fluid sequences show that this method can successfully estimate their motion fields. |
Acknowledgment: the material on this webpage is based upon work partially supported by the National Science Foundation.