Two-Dimensional Pattern Matching with k Mismatches

We give an algorithm which finds all occurrences of an m1 x m2 pattern array embedded as subarrays in an n1 x n2 array of text, where at most k mismatches are allowed per occurrence. The algorithm runs in time O((k+a)(blogb+ n1n2)), where a = min(m1m2) and b=max(m1m2). This improves upon the previously best known algorithm, and is asymptotically optimal for k ≈ a

Analysis of two-dimensional approximate pattern matching algorithms

AbstractWe present a new and more rigorous analysis of the two algorithms for two-dimensional approximate pattern matching due to Kärkkäinen and Ukkonen. We also present modifications of these algorithms that use less space while keeping the same expected time

Duel and sweep algorithm for order-preserving pattern matching

Given a text $T$ and a pattern $P$ over alphabet $\Sigma$, the classic exact matching problem searches for all occurrences of pattern $P$ in text $T$. Unlike exact matching problem, order-preserving pattern matching (OPPM) considers the relative order of elements, rather than their real values. In this paper, we propose an efficient algorithm for OPPM problem using the "duel-and-sweep" paradigm. Our algorithm runs in $O(n + m\log m)$ time in general and $O(n + m)$ time under an assumption that the characters in a string can be sorted in linear time with respect to the string size. We also perform experiments and show that our algorithm is faster that KMP-based algorithm. Last, we introduce the two-dimensional order preserved pattern matching and give a duel and sweep algorithm that runs in $O(n^2)$ time for duel stage and $O(n^2 m)$ time for sweeping time with $O(m^3)$ preprocessing time.Comment: 13 pages, 5 figure

Towards a theory of patches

AbstractMany applications have a need for indexing unstructured data. It turns out that a similar ad-hoc method is being used in many of them – that of considering small particles of the data.In this paper we formalize this concept as a tiling problem and consider the efficiency of dealing with this model in the pattern matching setting.We present an efficient algorithm for the one-dimensional tiling problem, and the one-dimensional tiled pattern matching problem. We prove the two-dimensional problem is hard and then develop an approximation algorithm with an approximation ratio converging to 2. We show that other two-dimensional versions of the problem are also hard, regardless of the number of neighbors a tile has

A Fast and Accurate Nonlinear Spectral Method for Image Recognition and Registration

This article addresses the problem of two- and higher dimensional pattern matching, i.e. the identification of instances of a template within a larger signal space, which is a form of registration. Unlike traditional correlation, we aim at obtaining more selective matchings by considering more strict comparisons of gray-level intensity. In order to achieve fast matching, a nonlinear thresholded version of the fast Fourier transform is applied to a gray-level decomposition of the original 2D image. The potential of the method is substantiated with respect to real data involving the selective identification of neuronal cell bodies in gray-level images.Comment: 4 pages, 3 figure

The Bar Pattern Speed of NGC 1433 Estimated Via Sticky-Particle Simulations

We present detailed numerical simulations of NGC 1433, an intermediate-type barred spiral showing strong morphological features including a secondary bar, nuclear ring, inner ring, outer pseudoring, and two striking, detached spiral arcs known as ``plumes.'' This galaxy is an ideal candidate for recreating the observed morphology through dynamical models and determining the pattern speed. We derived a gravitational potential from an $H$-band image of the galaxy and simulated the behavior of a two-dimensional disk of 100,000 inelastically colliding gas particles. We find that the closest matching morphology between a $B$-band image and a simulation occurs with a pattern speed of 0.89 km s$^{-1}$ arcsec$^{-1}$ $\pm$ 5-10%. We also determine that the ratio of corotation radius to the average published bar radius is 1.7 $\pm$ 0.3, with the ambiguity in the bar radius being the largest contributor to the error.Comment: Accepted for publication by The Astronomical Journal. 34 pages, 13 figures, 2 table