Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A survey of image registration techniques
ACM Computing Surveys (CSUR)
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Introductory Digital Image Processing: A Geographic Perspective
Introductory Digital Image Processing: A Geographic Perspective
Robot Vision
Elastic image matching is NP-complete
Pattern Recognition Letters
Optimal Exact and Fast Approximate Two Dimensional Pattern Matching Allowing Rotations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
A Rotation Invariant Filter for Two-Dimensional String Matching
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
Pattern Matching for Spatial Point Sets
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
An Image Similarity Measure Based on Graph Matching
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
A Monotonic and Continuous Two-Dimensional Warping Based on Dynamic Programming
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Two-dimensional pattern matching with rotations
Theoretical Computer Science
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The complexity of low-distortion embeddings between point sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Faster two dimensional scaled matching
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
On the intractability of inverting geometric distortions in watermarking schemes
IH'05 Proceedings of the 7th international conference on Information Hiding
Two-Dimensional Pattern Matching with Combined Scaling and Rotation
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Combinatorial Bounds and Algorithmic Aspects of Image Matching under Projective Transformations
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
New Complexity Bounds for Image Matching under Rotation and Scaling
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Theoretical Computer Science
Affine image matching is uniform TC0-complete
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
New complexity bounds for image matching under rotation and scaling
Journal of Discrete Algorithms
Combinatorial structure of rigid transformations in 2D digital images
Computer Vision and Image Understanding
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The problem of image matching is to find for two given digital images A and B an admissible transformation that converts image A as close as possible to B. This problem becomes hard if the space of admissible transformations is too complex. Consequently, in many real applications, like the ones allowing nonlinear elastic transformations, the known algorithms solving the problem either work in exponential worst-case time or can only guarantee to find a local optimum. Recently Keysers and Unger have proved that the image matching problem for this class of transformations is NP-complete, thus giving evidence that the known exponential time algorithms are justified. On the other hand, allowing only such transformations as translations, rotations, or scalings the problem becomes tractable. In this paper we analyse the computational complexity of image matching for a larger space of admissible transformations, namely for all affine transformations. In signal processing there are no efficient algorithms known for this class. Similarly, the research in combinatorial pattern matching does not cover this set of transformations neither providing efficient algorithms nor proving intractability of the problem, although it is a basic one and of high practical importance. The main result of this paper is that the image matching problem can be solved in polynomial time even allowing all affine transformations.