G. Navarro K. Fredriksson and E. Ukkonen. An index for two dimensional string matching allowing rotations. In Proc. IFIP TCS'00, LNCS 1872, pages 59--75, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

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G. Navarro K. Fredriksson and E. Ukkonen. An index for two dimensional string matching allowing rotations. In Proc. IFIP TCS'00, LNCS 1872, pages 59--75, 2000.

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K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. In IFIP TCS2000.

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K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. In IFIP TCS2000.

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K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. In Proc. 1st IFIP International Conference on Theoretical Computer Science (IFIP TCS 2000.

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G. Navarro K. Fredriksson and E. Ukkonen. An index for two dimensional string matching allowing rotations. In J. van Leeuwen, O. Watanabe, M. Hagiya, P.D. Mosses, and T. Ito, editors, IFIP TCS2000, LNCS 1872, pages 59-75, 2000.

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G. Navarro K. Fredriksson and E. Ukkonen. An index for two dimensional string matching allowing rotations. In J. van Leeuwen, O. Watanabe, M. Hagiya, P.D. Mosses, and T. Ito, editors, IFIP TCS2000.

....because it allows errors along one of the dimensions only. Amir and Landau [5] also study this case, obtaining a O(n (k(k d) worst case algorithm. We do not consider the KS model for d 2. 2. 4 Related Problems Other problems related to comparing images is searching allowing rotations [20, 19, 18] and scaling [3, 2] i.e. the pattern appears in the image at a different size) Another related problem is geometric matching, where we have to match a geometric figure or a set of points. In this case, the problem is in a continuous space rather than a discrete space and usually the Hausdorff ....

K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. Technical Report TR/DCC-99-8, Dept. of Computer Science, Univ. of Chile, November 1999.

....between the pattern and its occurrence. Under this mismatches model a O(k average time (2D version) of the algorithm can be obtained to find the occurrences. This works for any 0 k m . For small k, an O(k 1=2 ) average time algorithm was given in [6] Finally, a more refined model [10, 6, 9] suitable for gray level images adds up the absolute values of the differences in the gray levels of the pattern and text cells supposed to match, and puts an upper limit k on this sum. Under this gray levels model they achieve O( k=oe) average time algorithm, assuming that the cell values ....

....cells supposed to match, and puts an upper limit k on this sum. Under this gray levels model they achieve O( k=oe) average time algorithm, assuming that the cell values are uniformly distributed among oe gray levels. Similar algorithms for 3D can be found in [9] and indexing algorithms in [10]. In this paper we present fast filters for searching allowing rotations under these three models. Our main results follow. ffl We give an O(n =m) average time search algorithm for the exact model. ffl We present a filter for searching under the mismatches model which is O(n k=m) average ....

G. Navarro K. Fredriksson and E. Ukkonen. An index for two dimensional string matching allowing rotations. In J. van Leeuwen, O. Watanabe, M. Hagiya, P.D Mosses, and T. Ito, editors, Proceedings of the 1st IFIP International Conference on Theoretical Computer Science (IFIP TCS2000.

....well as an O(k ) average time algorithm for computing the lower bound of the distance; here we will develop a 2D version whose running time is O(k ) This works for any 0 k m . For a small k, an O(k 1=2 ) average time algorithm was given in [9] Finally, a more re ned model [13, 9, 12] suitable for gray level images adds up the absolute values of the di erences in the gray levels of the pattern and text cells supposed to match, and puts an upper limit k on this sum. Under this gray levels model average time O( k= is achieved, assuming that the cell values are uniformly ....

....gray levels of the pattern and text cells supposed to match, and puts an upper limit k on this sum. Under this gray levels model average time O( k= is achieved, assuming that the cell values are uniformly distributed among gray levels. Similar algorithms for indexing are presented in [13]. In this paper we present fast lters for searching allowing rotations under these three models. Table 1 shows our main achievements (all are on the average) The time we obtain for exact searching is average case optimal. For the k mismatches model we present two di erent algorithms, based on ....

G. Navarro K. Fredriksson and E. Ukkonen. An index for two dimensional string matching allowing rotations. In J. van Leeuwen, O. Watanabe, M. Hagiya, P.D. Mosses, and T. Ito, editors, IFIP TCS2000, LNCS 1872, pages 59-75, 2000.

....2. The threshold problem is solved in sublinear O(n 2 ) expected time, for 1. The above expected time results hold only for low enough values of . All the results have their counterparts in three (and more) dimensions. Similar results hold for some other distance functions as well [14, 16, 17, 11, 12]. The article is organized as follows. Sec. 2 gives the basic de nitions and formulation of the problem and gives some analyses of the complexity of the problem. In Sec. 3 a simple (but optimal) algorithm for evaluating the distance between the pattern and the image in each position and ....

....this is not necessarily true when searching for pieces. Therefore, one might use the algorithm of Theorem 7 to compute the lower bound distance for the pieces. This is not a problem, because veri cation is required in any case. The net result in eciency is that the alphabet size becomes . In [12] it is shown that the probability that a piece matches for some rotation, is ( m=j) where = jP j, and 1 for 1 e= This worsens as j grows. This has to be multiplied by ) O(jP j =j) to account for all the rotations of all the pieces, resulting in jP j matching ....

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K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. In J. van Leeuwen, O. Watanabe, M. Hagiya, P.D Mosses, and T. Ito, editors, Proceedings of the 1st IFIP International Conference on Theoretical Computer Science (IFIP TCS2000.

....approximate and hence introduce another layer of inaccuracy on top of the noise in the data that can be very high in typical applications. Therefore we believe that our exact combinatorial analysis and methods can be useful. We are not aware of earlier similar results (expect for our own [5, 6, 4] that deals with image processing) For example, our analysis of the number and the structure of the relevant rotations gives a basis for comparing different heuristics that use a sparse set of rotations. Our filtration algorithms are very fast and as such of practical value. Also our slow ....

K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. In IFIP TCS2000, 2000. To appear.

....n when the pattern can appear in the text in rotated form. This was addressed from a combinatorial point of view first in [6] in which an online algorithm for exact search allowing pattern rotations 1 A work supported by ComBi. was presented. Off line searching (indexing) was considered in [5]. In [16] method called color indexing was introduced for application in image database indexing. These techniques use color histograms as indices of images stored in database. We also use the color histograms to produce fast filters for online algorithms. Many traditional methods concentrate on ....

K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. In IFIP TCS2000, 2000. To appear.

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K. Fredriksson, G. Navarro, and E. Ukkonen. An index for two dimensional string matching allowing rotations. In Prof. IFIP International Conference on Theoretical Computer Science (IFIP TCS), volume 1872 of LNCS, pages 59--75. Springer, 2000.

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