APPROXIMATION ALGORITHMS FOR POINT PATTERN MATCHING AND SEARCHI NG

Point pattern matching is a fundamental problem in computational geometry. For given a reference set and pattern set, the problem is to find a geometric transformation applied to the pattern set that minimizes some given distance measure with respect to the reference set. This problem has been heavily researched under various distance measures and error models. Point set similarity searching is variation of this problem in which a large database of point sets is given, and the task is to preprocess this database into a data structure so that, given a query point set, it is possible to rapidly find the nearest point set among elements of the database. Here, the term nearest is understood in above sense of pattern matching, where the elements of the database may be transformed to match the given query set. The approach presented here is to compute a low distortion embedding of the pattern matching problem into an (ideally) low dimensional metric space and then apply any standard algorithm for nearest neighbor searching over this metric space. This main focus of this dissertation is on two problems in the area of point pattern matching and searching algorithms: (i) improving the accuracy of alignment-based point pattern matching and (ii) computing low-distortion embeddings of point sets into vector spaces. For the first problem, new methods are presented for matching point sets based on alignments of small subsets of points. It is shown that these methods lead to better approximation bounds for alignment-based planar point pattern matching algorithms under the Hausdorff distance. Furthermore, it is shown that these approximation bounds are nearly the best achievable by alignment-based methods. For the second problem, results are presented for two different distance measures. First, point pattern similarity search under translation for point sets in multidimensional integer space is considered, where the distance function is the symmetric difference. A randomized embedding into real space under the L1 metric is given. The algorithm achieves an expected distortion of O(log2 n). Second, an algorithm is given for embedding Rd under the Earth Mover's Distance (EMD) into multidimensional integer space under the symmetric difference distance. This embedding achieves a distortion of O(log D), where D is the diameter of the point set. Combining this with the above result implies that point pattern similarity search with translation under the EMD can be embedded in to real space in the L1 metric with an expected distortion of O(log2 n log D)

A soft Lasso model for the motion of a ball falling in the non-Newtonian fluid

From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a discrete iterative algorithm combining the Newton-Stokes term and the soft Lasso's term is developed to simulate the motion of a ball falling in non-Newtonian fluids. The theory is validated by numerical examples and shows satisfactory results, which exhibit the chaotic phenomena, sudden accelerations and the continual random oscillations. The pattern of the motion is independent of initial values and is preserved for long time

On the AER Stereo-Vision Processing: A Spike Approach to Epipolar Matching

Image processing in digital computer systems usually considers visual information as a sequence of frames. These frames are from cameras that capture reality for a short period of time. They are renewed and transmitted at a rate of 25-30 fps (typical real-time scenario). Digital video processing has to process each frame in order to detect a feature on the input. In stereo vision, existing algorithms use frames from two digital cameras and process them pixel by pixel until it finds a pattern match in a section of both stereo frames. To process stereo vision information, an image matching process is essential, but it needs very high computational cost. Moreover, as more information is processed, the more time spent by the matching algorithm, the more inefficient it is. Spike-based processing is a relatively new approach that implements processing by manipulating spikes one by one at the time they are transmitted, like a human brain. The mammal nervous system is able to solve much more complex problems, such as visual recognition by manipulating neuron’s spikes. The spike-based philosophy for visual information processing based on the neuro-inspired Address-Event- Representation (AER) is achieving nowadays very high performances. The aim of this work is to study the viability of a matching mechanism in a stereo-vision system, using AER codification. This kind of mechanism has not been done before to an AER system. To do that, epipolar geometry basis applied to AER system are studied, and several tests are run, using recorded data and a computer. The results and an average error are shown (error less than 2 pixels per point); and the viability is proved

Algorithm engineering : string processing

The string matching problem has attracted a lot of interest throughout the history of computer science, and is crucial to the computing industry. The theoretical community in Computer Science has a developed a rich literature in the design and analysis of string matching algorithms. To date, most of this work has been based on the asymptotic analysis of the algorithms. This analysis rarely tell us how the algorithm will perform in practice and considerable experimentation and fine-tuning is typically required to get the most out of a theoretical idea. In this thesis, promising string matching algorithms discovered by the theoretical community are implemented, tested and refined to the point where they can be usefully applied in practice. In the course of this work we have presented the following new algorithms. We prove that the time complexity of the new algorithms, for the average case is linear. We also compared the new algorithms with the existing algorithms by experimentation. " We implemented the existing one dimensional string matching algorithms for English texts. From the findings of the experimental results we identified the best two algorithms. We combined these two algorithms and introduce a new algorithm. " We developed a new two dimensional string matching algorithm. This algorithm uses the structure of the pattern to reduce the number of comparisons required to search for the pattern. " We described a method for efficiently storing text. Although this reduces the size of the storage space, it is not a compression method as in the literature. Our aim is to improve both space and time taken by a string matching algorithm. Our new algorithm searches for patterns in the efficiently stored text without decompressing the text. " We illustrated that by pre-processing the text we can improve the speed of the string matching algorithm when we search for a large number of patterns in a given text. " We proposed a hardware solution for searching in an efficiently stored DNA text

Partial surface matching by using directed footprints

AbstractIn this paper we present a new technique for partial surface and volume matching of images in three dimensions. In this problem, we are given two objects in 3-space, each represented as a set of points, scattered uniformly along its boundary or inside its volume. The goal is to find a rigid motion of one object which makes a sufficiently large portion of its boundary lying sufficiently close to a corresponding portion of the boundary of the second object. This is an important problem in pattern recognition and in computer vision, with many industrial, medical, and chemical applications. Our algorithm is based on assigning a directed footprint to every point of the two sets, and locating all the pairs of points (one of each set) whose undirected components of the footprints are sufficiently similar. The algorithm then computes for each such pair of points all the rigid transformations that map the first point to the second, while making the respective direction components of their footprints coincide. A voting scheme is employed for computing transformations which map significantly large number of points of the first set to points of the second set. Experimental results on various examples are presented and show the accurate and robust performance of our algorithm

Structural graph matching using the EM algorithm and singular value decomposition

This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method