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
Two-Dimensional Pattern Matching with Combined Scaling and Rotation
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Real Two Dimensional Scaled Matching
Algorithmica
Theoretical Computer Science
Two-dimensional pattern matching with rotations
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
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
Incremental and transitive discrete rotations
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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The problem of image matching under rotation is to find for two given digital images A and B a rotation that converts image A as close as possible to B . The research in combinatorial pattern matching led to a series of improving algorithms which commonly attack this problem by searching the complete set of all rotations of A . We present the first optimal algorithm of this kind, i.e, one that solves image matching in time for images of size n ×n . Subsequently, for image matching under compositions of rotation and scaling we show a new lower bound *** (n 6 / logn ) on the cardinality of , the set of rotated and scaled transformations of A . This bound almost matches the upper bound O (n 6).