CODEWITHSUNDEEP
geometrycomputer-visionhomography
korp
korp

Reputation: 13

Are homography matrices commutative?

I have 3 sets of points A, B and C. The homography matrices H0 and H1 are such that H0(A) = B and H1(B) = C. So, H1(B) = H1(H0(A)) = C.

My question:

Is H0(H1(A)) = C? Or, what are the conditions under which H0(H1(A)) = H1(H0(A))?

Thanks very much for any help!!

Upvotes: 0

Views: 263

Answers (1)

voidpointer
voidpointer

Reputation: 36

A homography is by definition an invertible mapping from one plane P to another plane Q with the condition that points lying on a line in P are mapped to points on a line in Q. Since this property is transitive there is a homography from point set A to point set C. When H0, H1 are the matrix representations of the respective homographies, then H2 = H1 * H0 maps A to C. The only restriction on the matrices H0 and H1 is nonsingularity wherefore - as with matrix multiplication in general - it is in general not a commutative mapping.

Upvotes: 1

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