13221842
Rank-R approximation of tensors using image-as-matrix representation
We present a novel multilinear algebra based approach for reduced dimensionality representation of image ensembles. We treat an image as a matrix, instead of a vector as in traditional dimensionality reduction techniques like PCA, and higher-dimensional data as a tensor. This helps exploit spatio-temporal redundancies with less information loss than image-as-vector methods. The challenges lie in the computational and memory requirements for large ensembles. Currently, there exists a rank-R approximation algorithm which, although applicable to any number of dimensions, is efficient for only low-rank approximations. For larger dimensionality reductions, the memory and time costs of this algorithm become prohibitive. We propose a novel algorithm, for rank-R approximations of third-order tensors, which is efficient for arbitrary R but for the important special case of 2D image ensembles, e.g. video. Both of these algorithms reduce redundancies present in all dimensions. Rank-R tensor approximation yields the most compact data representation among all known image-as-matrix methods. We evaluated the performance of our algorithm vs. other approaches on a number of datasets with the following two main results. First, for a fixed compression ratio, the proposed algorithm yields the best representation of image ensembles visually as well as in the least squares sense. Second, proposed representation gives the best performance for object classification.
5819516
Facial expression decomposition
In this paper, we propose a novel approach for facial expression decomposition - higher-order singular value decomposition (HOSVD), a natural generalization of matrix SVD. We learn the expression subspace and person subspace from a corpus of images showing seven basic facial expressions, rather than resort to expert-coded facial expression parameters. We propose a simultaneous face and facial expression recognition algorithm, which can classify the given image into one of the seven basic facial expression categories, and then other facial expressions of the new person can be synthesized using the learned expression subspace model. The contributions of this work lie mainly in two aspects. First, we propose a new HOSVD based approach to model the mapping between persons and expressions, used for facial expression synthesis for a new person. Second, we realize simultaneous face and facial expression recognition as a result of facial expression decomposition. Experimental results are presented that illustrate the capability of the person subspace and expression subspace in both synthesis and recognition tasks. As a quantitative measure of the quality of synthesis, we propose using gradient minimum square error (GMSE) which measures the gradient difference between the original and synthesized images.
62685176
Seamless video editing
This paper presents a new framework for seamless video editing in the gradient domain. The spatio-temporal gradient fields of target videos are modified or mixed to generate a new gradient field, which is usually not integrable. We propose a 3D video integration algorithm, which finds a potential function, whose gradient field is closest to the resulting gradient field in the sense of least squares. The video is reconstructed by solving a 3D Poisson equation. We use a fast and accurate 3D discrete Poisson solver using diagonal multigrids. A set of gradient operators is defined for user interaction. The resulting video has temporal coherency and no artifacts. We evaluate our algorithm using a variety of examples.
16403613
Gradient Adaptive Image Restoration and Enhancement
Various methods have been proposed for image enhancement and restoration. The main difficulty is how to enhance the structures uniformly while suppressing the noise without artifacts. In this paper, we tackle this problem in the gradient domain instead of the traditional intensity domain. By enhancing the gradient field, we can enhance the structure uniformly without overshooting at the boundary. Because the gradient field is very sensitive to noise, we apply an orientation-isotropy adaptive filter to the gradient field, suppressing the gradients in the noise regions while enhancing along the object boundaries. Thus we obtain a modulated gradient field, which is usually not integrable. We reconstruct the enhanced image from the modulated gradient field with least square errors by solving a Poisson equation. This method can enhance the object contrast uniformly, suppress the noise with no artifacts, and avoid setting stopping time as in PDE methods. Experiments on noisy images show the efficacy of our method.
1542177
Out-of-core tensor approximation of multi-dimensional matrices of visual data
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.
123058798
Compact representation of multidimensional data using tensor rank-one decomposition
This paper presents a new approach for representing multidimensional data by a compact number of bases. We consider the multidimensional data as tensors instead of matrices or vectors, and propose a tensor rank-one decomposition (TROD) algorithm by decomposing Nth-order data into a collection of rank-1 tensors based on multilinear algebra. By applying this algorithm to image sequence compression, we obtain much higher quality images with the same compression ratio as principal component analysis (PCA). Experiments with gray-level and color video sequences are used to illustrate the validity of this approach.
2846401
Subgraph Join: Efficient Processing Subgraph Queries on Graph-Structured XML Document
The information in many applications can be naturally represented as graph-structured XML document. Structural query on graph structured XML document matches the subgraph of graph structured XML document on some given schema. The query processing of graph-structured XML document brings new challenges. 
 
In this paper, for the processing of subgraph query, we design a subgraph join algorithm based on reachability coding. Using efficient data structure, subgraph join algorithm can process subgraph query with various structures efficiently.
12595576
Demand-driven frequent itemset mining using pattern structures
Frequent itemset mining aims at discovering patterns the supports of which are beyond a given threshold. In many applications, including network event management systems, which motivated this work, patterns are composed of items each described by a subset of attributes of a relational table. As it involves an exponential mining space, the efficient implementation of user preferences and mining constraints becomes the first priority for a mining algorithm. User preferences and mining constraints are often expressed using patterns’ attribute structures. Unlike traditional methods that mine all frequent patterns indiscriminately, we regard frequent itemset mining as a two-step process: the mining of the pattern structures and the mining of patterns within each pattern structure. In this paper, we present a novel architecture that uses pattern structures to organize the mining space. In comparison with the previous techniques, the advantage of our approach is two-fold: (i) by exploiting the interrelationships among pattern structures, execution times for mining can be reduced significantly; and (ii) more importantly, it enables us to incorporate high-level simple user preferences and mining constraints into the mining process efficiently. These advantages are demonstrated by our experiments using both synthetic and real-life datasets.
2288578
Efficient algorithms for obtaining algebraic invariants from higher degree implicit polynomials for recognition of curved objects
Implicit polynomials can be used for describing a large variety of curved shapes. In most of the earlier works, the emphasis had been on the use of second degree implicit polynomials. To describe more complex curves and surfaces, it is necessary that higher degree implicit polynomials be used. In this paper, we have proposed a tensor based approach for obtaining affine and Euclidean invariants from the coefficients of higher degree implicit polynomials. Our approach is more general and computationally efficient than the matrix based approaches for obtaining invariants. For the Euclidean case, the algorithm can be used for both recognition and pose estimation. In this paper, we have demonstrated our approach for obtaining invariants of 2-D shapes using third and fourth degree implicit polynomials.
2366018
Constrained texture synthesis by scalable sub-patch algorithm
In this paper, we propose a novel scalable sub-patch algorithm for texture synthesis. Texture synthesis is an important research topic in computer graphics and image processing. We present an efficient algorithm which can paste a patch each time without boundary processing technique. In particular, the proposed sub-patch algorithm can be used in constrained texture synthesis to fill the large lost region. On the other hand, the searching neighborhood pixels can be changed due to different patch size in image reconstruction. The comparison of previous algorithms is also provided in this paper. We present a first algorithm used in constrained texture synthesis by regular synthesizing order
7895439
An efficient rate-distortion optimal shape coding approach utilizing a skeleton-based decomposition
In this paper, we present a new shape-coding approach, which decouples the shape information into two independent signal data sets; the skeleton and the boundary distance from the skeleton. The major benefit of this approach is that it allows for a more flexible tradeoff between approximation error and bit budget. Curves of arbitrary order can be utilized for approximating both the skeleton and distance signals. For a given bit budget for a video frame, we solve the problem of choosing the number and location of the control points for all skeleton and distance signals of all boundaries within a frame, so that the overall distortion is minimized. An operational rate-distortion (ORD) optimal approach using Lagrangian relaxation and a four-dimensional direct acyclic graph (DAG) shortest path algorithm is developed for solving the problem. To reduce the computational complexity from O(N(5)) to O(N(3)), where N is the number of admissible control points for a skeleton, a suboptimal greedy-trellis search algorithm is proposed and compared with the optimal algorithm. In addition, an even more efficient algorithm with computational complexity O(N(2)) that finds an ORD optimal solution using a relaxed distortion criterion is also proposed and compared with the optimal solution. Experimental results demonstrate that our proposed approaches outperform existing ORD optimal approaches, which do not follow the same decomposition of the source data.