Where I ( . ) is the indicator function, H _ m is the homography transformation from I _ 0 to I _ m, and \ epsilon is the threshold.
22.
Historically, the concept of homography had been introduced to understand, explain and study visual perspective, and, specifically, the difference in appearance of two plane objects viewed from different points of view.
23.
Finsterwalder observed that Rudolf Sturm's analysis of the " homography problem " ( 1869 ) can be used to solve the problem of 3D-reconstruction using point matches in two images; which is the mathematical foundation of photogrammetry.
24.
For example, acts on the eight points in the projective line over the finite field GF ( 7 ), while, which is isomorphic to the alternating group A 5, is the homography group of the projective line with five points.
25.
A "'homography "'( or " projective transformation " ) of PG ( 2, " K " ) is a collineation of this type of projective plane which is a linear transformation of the underlying vector space.
26.
Very importantly too, subsequent 18th century editions of the dictionary added the letters " J " and " V " to the French alphabet in replacement of consonant " I " and " U, " fixing many cases of homography.
27.
PGL and PSL are some of the fundamental groups of study, part of the so-called classical groups, and an element of PGL is called "'projective linear transformation "', "'projective transformation "'or "'homography " '.
