Pattern matching

Abstract: This paper describes a simple, efficient algorithm to locate all occurrences of any of a finite number of keywords in a string of text. The algorithm consists of constructing a finite state pattern matching machine from the keywords and then using the pattern matching machine to process the text string in a single pass. Construction of the pattern matching machine takes time proportional to the sum of the lengths of the keywords. The number of state transitions made by the pattern matching machine in processing the text string is independent of the number of keywords. The algorithm has been used to improve the speed of a library bibliographic search program by a factor of 5 to 10.

Abstract: An algorithm is presented that searches for the location, “il” of the first occurrence of a character string, “pat,” in another string, “string.” During the search operation, the characters of pat are matched starting with the last character of pat. The information gained by starting the match at the end of the pattern often allows the algorithm to proceed in large jumps through the text being searched. Thus the algorithm has the unusual property that, in most cases, not all of the first i characters of string are inspected. The number of characters actually inspected (on the average) decreases as a function of the length of pat. For a random English pattern of length 5, the algorithm will typically inspect i/4 characters of string before finding a match at i. Furthermore, the algorithm has been implemented so that (on the average) fewer than i + patlen machine instructions are executed. These conclusions are supported with empirical evidence and a theoretical analysis of the average behavior of the algorithm. The worst case behavior of the algorithm is linear in i + patlen, assuming the availability of array space for tables linear in patlen plus the size of the alphabet.

Abstract: We present an image alignment algorithm based on the matching of relative gradient maps between images. This algorithm consists of two stages; namely, a learning-based approximate pattern search and an iterative energy-minimization procedure for matching relative image gradient. The first stage finds some candidate poses of the pattern in the image through a fast search of the best match of the relative gradient features from the database of training feature vectors. The training database is obtained from the synthesis of the template image under a number of uniform samplings in a range of the geometric transformation space. Subsequently, the approximate candidate poses are further verified and refined by matching the relative gradient images through an iterative energy-minimization procedure. This approach based on the matching of relative gradients has the advantage of robustness against inhomogeneous illumination variations. Some experimental results are shown to demonstrate the efficiency and robustness of the proposed algorithm.