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Pattern Matching under Polynomial Transformation [article]

Ayelet Butman, Peter Clifford, Raphael Clifford, Markus Jalsenius, Noa Lewenstein, Benny Porat, Ely Porat, Benjamin Sach
2011 arXiv   pre-print
Given a pattern of length m and a longer text of length n where both are assumed to contain integer values only, we first show O(n log m) time algorithms for pattern matching under linear transformations  ...  We consider a class of pattern matching problems where a normalising transformation is applied at every alignment.  ...  As a general class of problems, pattern matching under polynomial transformation is to the best of our knowledge new.  ... 
arXiv:1109.1494v2 fatcat:uigdbj57i5c6vhcgidqj2ri23u

Pattern Matching under Polynomial Transformation

Ayelet Butman, Peter Clifford, Raphaël Clifford, Markus Jalsenius, Noa Lewenstein, Benny Porat, Ely Porat, Benjamin Sach
2013 SIAM journal on computing (Print)  
Given a pattern of length m and a longer text of length n where both are assumed to contain integer values only, we first show O(n log m) time algorithms for pattern matching under linear transformations  ...  We consider a class of pattern matching problems where a normalising transformation is applied at every alignment.  ...  As a general class of problems, pattern matching under polynomial transformation is to the best of our knowledge new.  ... 
doi:10.1137/110853327 fatcat:rgtn3qefpfedjbmaqsku2xo7pa

Constraint Optimisation for Robust Image Matching with Inhomogeneous Photometric Variations and Affine Noise [chapter]

Al Shorin, Georgy Gimel'farb, Patrice Delmas, Patricia Riddle
2010 Lecture Notes in Computer Science  
A recent quadratic programming (QP) based matching allows for almost arbitrary photometric deviations.  ...  While modelling spatially uniform or low-order polynomial contrast and offset changes is mostly a solved problem, there has been limited progress in models which could represent highly inhomogeneous photometric  ...  Clearly, the low-order polynomial is incapable of approximating complex natural p-noise patterns.  ... 
doi:10.1007/978-3-642-17688-3_44 fatcat:egdkj24wlrbfzi5kcux7lworge

Pattern matching by sequential subdivision of transformation space

Mingtian Ni, S.E. Reichenbach
2004 Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004.  
Pattern matching techniques fall roughly into two categories: transformation space search techniques and matching space search techniques.  ...  Pattern matching is a well-known pattern recognition technique.  ...  Preliminary results on randomly generated point patterns show that the algorithm is effective and its computational complexity is low order polynomial in the size of the point templates under reasonably  ... 
doi:10.1109/icpr.2004.1334082 dblp:conf/icpr/NiR04 fatcat:shjohcnumrhgfdczar2ea7vduy

Image Matching with Spatially Variant Contrast and Offset: A Quadratic Programming Approach [chapter]

Alexander Shorin, Georgy Gimel'farb, Patrice Delmas, Jonh Morris
2008 Lecture Notes in Computer Science  
Most of the popular least-squares scores presume only simple smooth deviations that can be approximated with a low-order polynomial.  ...  Template matching is widely used in machine vision, digital photogrammetry, and multimedia data mining to search for a target object by similarity between its prototype image (template) and a sensed image  ...  The choice is due to the fact that most of the known template matching methods have p ≤ 2 as Low-order polynomials as idealised contrast factors: three out of a host of possible 2D polynomial patterns  ... 
doi:10.1007/978-3-540-89689-0_17 fatcat:h3ybdfhndnhhnasrqxnqcrgxne

Partitioned EDF scheduling on a few types of unrelated multiprocessors

Andreas Wiese, Vincenzo Bonifaci, Sanjoy Baruah
2012 Real-time systems  
A polynomial-time approximation scheme (PTAS) is derived for the partitioned EDF scheduling of implicit-deadline sporadic task systems upon unrelated multiprocessor platforms that are comprised of a constant  ...  Recall that we had constructed our ILP under the assumption that the pattern of big tasks under consideration corresponds to a feasible partitioning of the task system upon a platform in which each processor  ...  In fact, [10] has shown that under the assumption that P = NP, no polynomial-time algorithm with an approximation ratio smaller than 3/2 can exist for this problem.  ... 
doi:10.1007/s11241-012-9164-y fatcat:uceevabmurf4xhov4qg33hkfuq

A Kernel View of Spectral Point Pattern Matching [chapter]

Hongfang Wang, Edwin R. Hancock
2004 Lecture Notes in Computer Science  
This paper investigates spectral approaches to the problem of point pattern matching.  ...  under the existing of outliers and random position jitter.  ...  We focus in detail the Gaussian and polynomial kernels which are invariant to similarity transformations and reflection, and compare their performance in point pattern matching with previous approaches  ... 
doi:10.1007/978-3-540-27868-9_38 fatcat:xq45x6ktjnc2hejfhrthjwrhsu

Frequent Subgraph Retrieval in Geometric Graph Databases

Sebastian Nowozin, Koji Tsuda
2008 2008 Eighth IEEE International Conference on Data Mining  
matching.  ...  It enumerates all subgraphs of a single given query graph which are frequent geometric -subgraphs under the entire class of rigid geometric transformations in a database.  ...  One domain of graph mining is geometric graph mining, where each node of a graph has 2D or 3D coordinates and subgraph patterns have to match geometrically under a given transformation class [6, 7, 8]  ... 
doi:10.1109/icdm.2008.38 dblp:conf/icdm/NowozinT08 fatcat:j5we26e7obhmppczpc26ax3c54

Polynomials: a new tool for length reduction in binary discrete convolutions [article]

Amihood Amir, Oren Kapah, Ely Porat, Amir Rothschild
2014 arXiv   pre-print
Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved.  ...  In this paper we present such a new method - polynomials. This method enables the development of an efficient algorithm for computing the binary sparse Walsh transform.  ...  transform iff pattern index i ⊕ mask matches text index k ⊕ mask. transform is: 02000020 (since at locations 001 = 1 and 110 = 6 the 1's in the text and pattern match). 00 and 10 have value 0.  ... 
arXiv:1410.5607v1 fatcat:bfnk2apo3zd6jns36pyxfqcv2u

Evaluation of Control Points' Distribution on Distortions and Geometric Transformations for Aerial Images Rectification

Lee Hung Liew, Yin Chai Wang, Wai Shiang Cheah
2012 Procedia Engineering  
A simulation test is conducted using grid images to examine the effect of different distribution patterns of control points on distortions and geometric transformations.  ...  It shows that lower order global transformation has limitation in rectifying images with complex distortions.  ...  However, the total RMSE in each distribution pattern is reduced when second and third polynomial transformations are used.  ... 
doi:10.1016/j.proeng.2012.07.275 fatcat:5q7o4jrah5cppb2imyninb4hny

Shape recognition method using morphological hit-or-miss transform

Prabir Bhattacharya
1995 Optical Engineering: The Journal of SPIE  
Air Force Office of Scientific Research under grant No. AFOSR F49620-94-1-0029 and also by matching support by the Center for Communication and Information Sciences, University of Nebraska-Lincoln.  ...  we match the corners of the object instead of the block structure pattern.  ...  In the proposed method, we match the corners of the object instead of the block structure pattern.  ... 
doi:10.1117/12.203101 fatcat:dyoeiqzt5vedha2zfukb33fiju

From coding theory to efficient pattern matching [chapter]

Raphaël Clifford, Klim Efremenko, Ely Porat, Amir Rothschild
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
We consider the classic problem of pattern matching with few mismatches in the presence of promiscuously matching wildcard symbols.  ...  Given a text t of length n and a pattern p of length m with optional wildcard symbols and a bound k, our algorithm finds all the alignments for which the pattern matches the text with Hamming distance  ...  Two solutions for pattern matching without wildcards under the Hamming distance were given independently by both Abrahamson and Kosaraju in 1987 [1, 16] which both run in O(n √ m log m) time.  ... 
doi:10.1137/1.9781611973068.85 fatcat:kp475ghe6jafxeyyp76lep7k44

Matching in description logics: Preliminary results [chapter]

Franz Baader, Alex Borgida, Deborah L. McGuinness
1998 Lecture Notes in Computer Science  
As a result, matching can be performed (in polynomial time) using arbitrary concept patterns of the description language FL : , thus removing restrictions from previous work.  ...  Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of concept description languages (description logics), originally to help discard  ...  D under these conditions is decidable in polynomial time.  ... 
doi:10.1007/bfb0054902 fatcat:fly3lrdmwjd4zdrkwvgibaal5e

Antenna pattern synthesis utilizing spherical Bessel functions

Hsien-Peng Chang, T.K. Sarkar, O.M.C. Pereira-Filho
2000 IEEE Transactions on Antennas and Propagation  
Pattern synthesis of linear antennas utilizing the spherical bessel functions is presented.  ...  This leads to antenna current distribution by the Legendre polynomials of the first kind, which are of finite support. Some examples are given to illustrate this procedure.  ...  A third approach is to expand the current distri- Publisher Item Identifier S 0018-926x(00)04387-8. bution into a set of orthogonal polynomials and then their transform would match the pattern.  ... 
doi:10.1109/8.865216 fatcat:wxbeh6whlraq7dvq6cqeplx7xa

Robust Image Matching under Partial Occlusion and Spatially Varying Illumination Change

Shang-Hong Lai
2000 Computer Vision and Image Understanding  
Most existing methods cannot achieve precise pattern matching under spatially varying illumination variations and partial occlusions.  ...  We have successfully applied the proposed algorithm to estimate affine transformations under partial occlusion and spatially varying illumination change for various industrial inspection tasks.  ...  Examples of misalignment of the pattern specified in Fig. 4a under large areas of occlusion.  ... 
doi:10.1006/cviu.1999.0829 fatcat:rerqasylsfgpnpj5aa2gghfl2m
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