The wavelet transform hierarchically decomposes images with prescribed bases, while multilinear 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.

Visual data comprise 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 transforms, wavelet packet transforms, 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 texture synthesis.

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 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 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.

Tensor approximation is necessary to obtain compact multilinear models for multi-dimensional visual datasets. Traditionally, each multi-dimensional data item is represented as a vector. Such a scheme flattens the data and partially destroys the internal structures established throughout the multiple dimensions. In this paper, we retain the original dimensionality of the data items to more effectively exploit existing spatial redundancy and allow more efficient computation. Since the size of visual datasets can easily exceed the memory capacity of a single machine, we also present an out-of-core algorithm for higher-order tensor approximation. The basic idea is to partition a tensor into smaller blocks and perform tensor-related operations blockwise. We have successfully applied our techniques to three graphics-related data-driven models, including 6D bidirectional texture functions, 7D dynamic BTFs and 4D volume simulation sequences. Experimental results indicate that our techniques can not only process out-of-core data, but also achieve higher compression ratios and quality than previous methods.

Abstract 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. Copyright © 2004 John Wiley & Sons, Ltd.

One significant problem in patch-based texture synthesis is the presence of broken features at the boundary of adjacent patches. The reason is that optimization schemes for patch merging may fail when neighborhood search cannot find satisfactory candidates in the sample texture because of an inaccurate similarity measure. In this paper, we consider both curvilinear features and their deformation. We develop a novel algorithm to perform feature matching and alignment by measuring structural similarity. Our technique extracts a feature map from the sample texture, and produces both a new feature map and texture map. Texture synthesis guided by feature maps can significantly reduce the number of feature discontinuities and related artifacts, and gives rise to satisfactory results.