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)
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
Two-dimensional pattern matching with rotations
Theoretical Computer Science
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
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
Combinatorial structure of rigid transformations in 2D digital images
Computer Vision and Image Understanding
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Affine image matching is a computational problem to determine for two given images A and B how much an affine transformated A can resemble B. The research in combinatorial pattern matching led to a polynomial time algorithm which solves this problem by a sophisticated search in the set D(A) of all affine transformations of A. This paper shows that polynomial time is not the lowest complexity class containing this problem by providing its TC0-completeness. This result means not only that there are extremely efficient parallel solutions but also reveals further insight into the structural properties of image matching. The completeness in TC0 relates affine image matching to a number of most basic problems in computer science, like integer multiplication and division.