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18
Finding patterns in given intervals
 of Lecture Notes in Computer Science
, 2007
"... Abstract. In this paper, we study the pattern matching problem in given intervals. Depending on whether the intervals are given a priori for preprocessing, or during the query along with the pattern or, even in both cases, we develop solutions for different variants of this problem. In particular, ..."
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Abstract. In this paper, we study the pattern matching problem in given intervals. Depending on whether the intervals are given a priori for preprocessing, or during the query along with the pattern or, even in both cases, we develop solutions for different variants of this problem. In particular, we present efficient indexing schemes for each of the above variants of the problem. 1
Optimal exact and fast approximate two dimensional pattern matching allowing rotations
 In Proc. 13th Annual Symposium on Combinatorial Pattern Matching (CPM 2002), LNCS 2373
, 2002
"... Abstract. We give fast filtering algorithms to search for a 2 dimensional pattern in a 2dimensional text allowing any rotation of the pattern. We consider the cases of exact and approximate matching under several matching models, improving the previous results. For a text of size n \Theta n charac ..."
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Abstract. We give fast filtering algorithms to search for a 2 dimensional pattern in a 2dimensional text allowing any rotation of the pattern. We consider the cases of exact and approximate matching under several matching models, improving the previous results. For a text of size n \Theta n characters and a pattern of size m \Theta m characters, the exact matching takes average time O(n2 log m=m2), which is optimal. If we allow k mismatches of characters, then our best algorithm achieves O(n2k log m=m2) average time, for reasonable k values. For large k, we obtain an O(n2k3=2 p log m=m) average time algorithm. We generalize
Rotation and lighting invariant template matching
 In Proc. 6th Latin American Symposium on Theoretical Informatics (LATIN 2004), LNCS 2976
, 2003
"... We address the problem of searching for a twodimensional pattern in a twodimensional text (or image), such that the pattern can be found even if it appears rotated and it is brighter or darker than its occurrence. Furthermore, we consider approximate matching under several tolerance models. We obt ..."
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We address the problem of searching for a twodimensional pattern in a twodimensional text (or image), such that the pattern can be found even if it appears rotated and it is brighter or darker than its occurrence. Furthermore, we consider approximate matching under several tolerance models. We obtain algorithms that are almost optimal both in the worst and the average cases simultaneously. The complexities we obtain are very close to the best current results for the case where only rotations, but not lighting invariance, are supported. These are the first results for this problem under a combinatorial approach. 1
Incremental and Transitive Discrete Rotations
, 2005
"... A discrete rotation algorithm can be apprehended as a parametric application fα from Z[i] to Z[i], whose resulting permutation “looks like ” the map induced by an Euclidean rotation. For this kind of algorithm, to be incremental means to compute successively all the intermediate rotated copies of an ..."
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A discrete rotation algorithm can be apprehended as a parametric application fα from Z[i] to Z[i], whose resulting permutation “looks like ” the map induced by an Euclidean rotation. For this kind of algorithm, to be incremental means to compute successively all the intermediate rotated copies of an image for angles inbetween 0 and a destination angle. The discretized rotation consists in the composition of an Euclidean rotation with a discretization; the aim of this article is to describe an algorithm which computes incrementally a discretized rotation. The suggested method uses only integer arithmetic and does not compute any sine nor any cosine. More precisely, its design relies on the analysis of the discretized rotation as a step function: the precise description of the discontinuities turns to be the key ingredient that will make the resulting procedure optimally fast and exact. A complete description of the incremental rotation process is provided, also this result may be useful in the specification of a consistent set of definitions for discrete geometry.
Sequential and indexed twodimensional combinatorial template matching allowing rotations
 THEORETICAL COMPUTER SCIENCE A
, 2005
"... We present new and faster algorithms to search for a 2dimensional pattern in a 2dimensional text allowing any rotation of the pattern. This has applications such as image databases and computational biology. We consider the cases of exact and approximate matching under several matching models, usi ..."
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We present new and faster algorithms to search for a 2dimensional pattern in a 2dimensional text allowing any rotation of the pattern. This has applications such as image databases and computational biology. We consider the cases of exact and approximate matching under several matching models, using a combinatorial approach that generalizes string matching techniques. We focus on sequential algorithms, where only the pattern can be preprocessed, as well as on indexed algorithms, where the text is preprocessed and an index built on it. On sequential searching we derive averagecase lower bounds and then obtain optimal averagecase algorithms for all the matching models. At the same time, these algorithms are worstcase optimal. On indexed searching we obtain search time polylogarithmic on the text size, as well as sublinear time in general for approximate searching.
Efficient One Dimensional Real Scaled Matching
"... Real Scaled Matching is the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary realsized scale, appears. Real scaled matching is an important problem that was originally inspired by Computer Vision. In this paper, we present a new, more ..."
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Real Scaled Matching is the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary realsized scale, appears. Real scaled matching is an important problem that was originally inspired by Computer Vision. In this paper, we present a new, more precise and realistic, definition for one dimensional real scaled matching, and an efficient algorithm for solving this problem. For a text of length n and a pattern of length m, the algorithm runs in time O(n log m + √ nm 3/2 √ log m). 1
Optimal Prefix and Suffix Queries on Texts
, 2013
"... Abstract. In this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied Mäkinen and Navarro [PositionRestricted Substring Searching, LATIN 2006]. In the problem handled in this paper, we are interested in those occurrences of the pattern tha ..."
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Abstract. In this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied Mäkinen and Navarro [PositionRestricted Substring Searching, LATIN 2006]. In the problem handled in this paper, we are interested in those occurrences of the pattern that lies in a suffix or in a prefix of the given text. We achieve optimal query time for our problem against a data structure which is an extension of the classic suffix tree data structure. The time and space complexity of the data structure is dominated by that of the suffix tree. Notably, the (best) algorithm by Mäkinen and Navarro, if applied to our problem, gives suboptimal query time and the corresponding data structure also requires more time and space. 1
Theoretical issues of searching aerial photographs: a bird’s eye view
 Proceedings of the Prague Stringology Conference 2004, Czech Technical University in Prague, Czech Republic (2004) 1–23
"... Abstract. We review some pattern matching algorithms and techniques motivated by the discrete theory of image processing. The problem inspiring this research is that of searching an aerial photograph for all appearances of some object. The issues we discuss are digitization, local errors, rotation a ..."
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Abstract. We review some pattern matching algorithms and techniques motivated by the discrete theory of image processing. The problem inspiring this research is that of searching an aerial photograph for all appearances of some object. The issues we discuss are digitization, local errors, rotation and scaling. We review deterministic serial techniques that are used for multidimensional pattern matching and discuss their strengths and weaknesses.
Supervised by
, 2011
"... The discrete geometry is to classical geometry what the language is to thought, i.e. an imperfect means to represent the reality. It took centuries for the language to evolve in a way almost capable to faithfully describe our though. tel00596947, version 1 30 May 2011 Today the discrete geometry t ..."
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The discrete geometry is to classical geometry what the language is to thought, i.e. an imperfect means to represent the reality. It took centuries for the language to evolve in a way almost capable to faithfully describe our though. tel00596947, version 1 30 May 2011 Today the discrete geometry tries to do the same thing with the continuous geometry. The continuous geometry is a mathematical model that cannot be correctly or exactly reproduced in the real world and in computer science. A simple example is the famous number π. The theoretical mathematic model supposes an exact value of this number, however, the representation of a circle on the ground with a rope or on a sheet of paper by a compass can only give an approximated value of π, whatever the diameter of the circle, the size of the rope or the precision of the compass. In computer science, for any approximation of π used during computations, results will always be an approximation. Today, one of the biggest challenge in computer science is to nd new methods so that computers can represent reality as faithfully as possible. Regarding geometry, we strongly believe that these methods belong to the discrete geometry. tel00596947, version 1 30 May 2011