Subspace procrustes analysis

Postprint (author's final draft

A New Computational Framework for Efficient Parallelization and Optimization of Large Scale Graph Matching

There are so many applications in data fusion, comparison, and recognition that require a robust and efficient algorithm to match features of multiple images. To improve accuracy and get a more stable result is important to take into consideration both local appearance and the pairwise relationship of features. Graphs are a powerful and flexible data structure, allowing for the description of complex relationships between data elements, whose nodes correspond to salient features and edges correspond to relational aspects between features. Therefore, the problem of graph matching is to find a mapping between the two sets of nodes that preserves the relationships between them as much as possible. This graph-matching problem is mathematically formulated as an IQP problem which solving it is NP-hard, and obtaining exact Optima only plausible for very small data. Therefore, handling large-scale scientific visual data is quite limited, necessitating both efficient serial algorithms, as well as scalable parallel formulations. In this thesis, we first focused on exploring techniques to reduce the computation cost as well as memory usage of Pairwise graph matching by adopting a heuristic pruning strategy together with a redundancy pattern suppression scheme. We also modified the structure of the affinity matrix for minimizing memory requirement and parallelizing our algorithm by employing CPU’s and GPU’s accelerated libraries. Any pair of features with similar distance from first image results in same sub-matrices, therefore instead of constructing the whole affinity matrix, we only built the sub-blocked affinity for those distinct feature distances. By employing this scheme not only saved large memory and reduced computation time tremendously but also, the matrix-vector multiplication of gradient computation performed in parallel, where each block-vector calculation computed independently without synchronization. The accelerated libraries such as MKL, cuSparse, cuBlas and thrust applied to solving the GM problem, following the scheme of the spectral matching algorithm. We also extended our work for Multi-graph imaging, since many tasks require finding correspondences across multiple images. Also, considering more graph improves the matching accuracy. Most algorithms obtain approximate solutions for solving the GM NP-hard problem, result in a weak optimal solution. Therefore, we proposed a new solver, which iteratively modified the affinity matrix and binarized the solution by optimizing the original problem with its integer constraints

Automatic Classification of Fish in Underwater Video; Pattern Matching - Affine Invariance and Beyond

Underwater video is used by marine biologists to observe, identify, and quantify living marine resources. Video sequences are typically analyzed manually, which is a time consuming and laborious process. Automating this process will significantly save time and cost. This work proposes a technique for automatic fish classification in underwater video. The steps involved are background subtracting, fish region tracking and classification using features. The background processing is used to separate moving objects from their surrounding environment. Tracking associates multiple views of the same fish in consecutive frames. This step is especially important since recognizing and classifying one or a few of the views as a species of interest may allow labeling the sequence as that particular species. Shape features are extracted using Fourier descriptors from each object and are presented to nearest neighbor classifier for classification. Finally, the nearest neighbor classifier results are combined using a probabilistic-like framework to classify an entire sequence. The majority of the existing pattern matching techniques focus on affine invariance, mainly because rotation, scale, translation and shear are common image transformations. However, in some situations, other transformations may be modeled as a small deformation on top of an affine transformation. The proposed algorithm complements the existing Fourier transform-based pattern matching methods in such a situation. First, the spatial domain pattern is decomposed into non-overlapping concentric circular rings with centers at the middle of the pattern. The Fourier transforms of the rings are computed, and are then mapped to polar domain. The algorithm assumes that the individual rings are rotated with respect to each other. The variable angles of rotation provide information about the directional features of the pattern. This angle of rotation is determined starting from the Fourier transform of the outermost ring and moving inwards to the innermost ring. Two different approaches, one using dynamic programming algorithm and second using a greedy algorithm, are used to determine the directional features of the pattern

DeepMatching: Hierarchical Deformable Dense Matching

We introduce a novel matching algorithm, called DeepMatching, to compute dense correspondences between images. DeepMatching relies on a hierarchical, multi-layer, correlational architecture designed for matching images and was inspired by deep convolutional approaches. The proposed matching algorithm can handle non-rigid deformations and repetitive textures and efficiently determines dense correspondences in the presence of significant changes between images. We evaluate the performance of DeepMatching, in comparison with state-of-the-art matching algorithms, on the Mikolajczyk (Mikolajczyk et al 2005), the MPI-Sintel (Butler et al 2012) and the Kitti (Geiger et al 2013) datasets. DeepMatching outperforms the state-of-the-art algorithms and shows excellent results in particular for repetitive textures.We also propose a method for estimating optical flow, called DeepFlow, by integrating DeepMatching in the large displacement optical flow (LDOF) approach of Brox and Malik (2011). Compared to existing matching algorithms, additional robustness to large displacements and complex motion is obtained thanks to our matching approach. DeepFlow obtains competitive performance on public benchmarks for optical flow estimation

On the Combinatorics of Locally Repairable Codes via Matroid Theory

This paper provides a link between matroid theory and locally repairable codes (LRCs) that are either linear or more generally almost affine. Using this link, new results on both LRCs and matroid theory are derived. The parameters $(n,k,d,r,\delta)$ of LRCs are generalized to matroids, and the matroid analogue of the generalized Singleton bound in [P. Gopalan et al., "On the locality of codeword symbols," IEEE Trans. Inf. Theory] for linear LRCs is given for matroids. It is shown that the given bound is not tight for certain classes of parameters, implying a nonexistence result for the corresponding locally repairable almost affine codes, that are coined perfect in this paper. Constructions of classes of matroids with a large span of the parameters $(n,k,d,r,\delta)$ and the corresponding local repair sets are given. Using these matroid constructions, new LRCs are constructed with prescribed parameters. The existence results on linear LRCs and the nonexistence results on almost affine LRCs given in this paper strengthen the nonexistence and existence results on perfect linear LRCs given in [W. Song et al., "Optimal locally repairable codes," IEEE J. Sel. Areas Comm.].Comment: 48 pages. Submitted for publication. In this version: The text has been edited to improve the readability. Parameter d for matroids is now defined by the use of the rank function instead of the dual matroid. Typos are corrected. Section III is divided into two parts, and some numberings of theorems etc. have been change