Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
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
Fast Multiple-Precision Evaluation of Elementary Functions
Journal of the ACM (JACM)
Digital image analysis: selected techniques and applications
Digital image analysis: selected techniques and applications
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
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
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
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
Real Two Dimensional Scaled Matching
Algorithmica
Theoretical Computer Science
On the complexity of affine image matching
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Faster two dimensional scaled matching
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
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Image matching under rotation is a computational problem to determine for two given images A and B a rotation of A that most accurately resembles B. The research in combinatorial pattern matching led to a series of improved algorithms which commonly solve this problem by a sophisticated search in the set of all rotations of A. This paper provides the lower bound @W(n^3) on the worst case cardinality of this set for images of size nxn and presents the first optimal algorithm of such kind, i.e., one that solves image matching under rotations in time O(n^3). Moreover, for image matching under compositions of rotation and scaling a new lower bound @W(n^6/logn) on the worst case cardinality of the set of rotated and scaled transformations of an nxn image is provided. This bound almost matches the upper bound O(n^6).