The equivalence of two definitions of compatible homography matrices

• In many computer vision applications, one acquires images of planar surfaces from two different vantage points. One can use a projective transformation to map pixel coordinates associated with a particular planar surface from one image to another. The transformation, called a homography, can be represented by a unique, to within a scale factor, 3 × 3 matrix. One requires a different homography matrix, scale differences apart, for each planar surface whose two images one wants to relate. However, a collection of homography matrices forms a valid set only if the matrices satisfy consistency constraints implied by the rigidity of the motion and the scene. We explore what it means for a set of homography matrices to be compatible and show that two seemingly disparate definitions are in fact equivalent. Our insight lays the theoretical foundations upon which the derivation of various sets of homography consistency constraints can proceed. © 2020 Elsevier B.V.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datorseende och robotik (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Vision and Robotics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

Keyword

Fundamental matrix

Homography matrix

Latent variable

Multiple homographies

Pattern recognition

Software engineering

Computer vision applications

Consistency constraints

Homographies

Homography matrices

Planar surface

Projective transformation

Scale Factor

Theoretical foundations

Linear transformations

Publication and Content Type

ref (subject category)

art (subject category)