Designing optimal- and fast-on-average pattern matching algorithms

Given a pattern $w$ and a text $t$, the speed of a pattern matching algorithm over $t$ with regard to $w$, is the ratio of the length of $t$ to the number of text accesses performed to search $w$ into $t$. We first propose a general method for computing the limit of the expected speed of pattern matching algorithms, with regard to $w$, over iid texts. Next, we show how to determine the greatest speed which can be achieved among a large class of algorithms, altogether with an algorithm running this speed. Since the complexity of this determination make it impossible to deal with patterns of length greater than 4, we propose a polynomial heuristic. Finally, our approaches are compared with 9 pre-existing pattern matching algorithms from both a theoretical and a practical point of view, i.e. both in terms of limit expected speed on iid texts, and in terms of observed average speed on real data. In all cases, the pre-existing algorithms are outperformed

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)

Point pattern matching by heuristic methods : a genetic algorithm and simulated annealing

The problem we consider is to find a subset of points in a pattern that best match to a subset of points in another pattern through a transformation in an optimal sense. Exhaustive search to find the best assignment mapping one set of points to another set is, if the number of points that are to be matched is large, computationally expensive. We propose two stochastic searching techniques - a genetic algorithm and simulated annealing to search for the best ( almost the best ) assignment efficiently. To make the comparison between GA and SA fair, we introduce a piece-wise linear cooling schedule for the SA. As compared to conventional searching techniques such as simple hill climbing and random search techniques, the proposed methods are able to attain better solutions much faster. The proposed methods can be applied to n-dimensional point patterns and any transformation, but we only present results for two-dimensional point patterns and similarity transformations

Variable Block Based Motion Estimation Using Hexagon Diamond Full Search Algorithm (HDFSA) Via Block Subtraction Technique

Motion estimation is a technique to reduce high information redundancy which exists between successive frames in a video sequences. There are many types of motion estimation method but the most used method is the block matching method which is the fixed block matching and the variable block matching. The fixed block matching uses the same block size throughout the motion estimation process while the variable block matching uses different block size. The variable block matching developed based on four stages which is the video and frame selection, threshold calculation, block size selection and search pattern. In the video and frame selection, pre-defined video which have different type of motion and size is used for the algorithm evaluation purpose. The threshold calculation is based on the video selected. Each video selected will have its own threshold which is used for the block size selection. There is three block size selection which is 16×16 pixels block size (uniform motion), 8×8 pixels block size (moderate motion) and 4×4 pixels block size (complex motion). In order to calculate the threshold and block size selection, the block subtraction technique is implemented. The concept of the block subtraction technique is based on the changes of pixels value between successive frames which represent the existence of motion. The next stage of algorithm development is the search pattern which is the hexagon diamond (16×16 and 8×8 pixels block size) and full search pattern (4×4 pixels block size). To evaluate the performance of the developed algorithm, the average PSNR value, average search point and average elapsed processing time is calculated. Overall, the developed algorithms have similar PSNR value and lower average search point compared to superior algorithms. The average elapsed processing time have increased due to the implementation of the block subtraction technique and the variable block matching

Improving ICP with Easy Implementation for Free Form Surface Matching

Automatic range image registration and matching is an attractive but unresolved problem in both the machine vision and pattern recognition literature. Since automatic range image registration and matching is inherently a very difficult problem, the algorithms developed are becoming more and more complicated. In this paper, we propose a novel practical algorithm for automatic free-form surface matching. This method directly manipulates the possible point matches established by the traditional ICP criterion based on both the collinearity and closeness constraints without any feature extraction, image pre-processing, or motion estimation from outliers corrupted data. A comparative study based on a large number of real range images has shown the accuracy and robustness of the novel algorithm