ewoksndreg.transformation.homography

Homography abstraction.

A homography transformation can be represented be the following change-of-frame matrix

$$ F=begin{bmatrix} C_{ntimes n}&T_{ntimes 1}\ P_{1times n}&1 end{bmatrix} $$

Different transformation types can be distinguished based on the properties of the translation vector $T$, change-of-basis matrix $C$ and projection vector $P$

• translation:

  • $C$ is the identity matrix and $P$ are all zeros

• proper rigid (euclidian) transformation:

  • $P$ are all zeros

  • $C$ is any orthogonal matrix ($C^T=C^{-1}$) with determinant $det{C}=+1$

  • preserves angles, distances and handedness

  • translation + rotation

• rigid (euclidian) transformation:

  • $P$ are all zeros

  • $C$ is any orthogonal matrix ($C^T=C^{-1}$)

  • preserves angles and distances

  • proper rigid transformation + reflection

• similarity transformation:

  • $P$ are all zeros

  • $C=rA$ where A any orthogonal matrix ($A^T=A^{-1}$) and $r>0$

  • preserves angles and ratios between distances

  • rigid transformation + isotropic scaling

• affine transformation:

  • $P$ are all zeros

  • $C$ is any invertible matrix (i.e. linear transformation)

  • preserves parallelism

  • similarity transformation + non-isotropic scaling and shear

• projective transformation (homography):

  • $C$ is any invertible matrix (i.e. linear transformation)

  • preserves collinearity

  • affine transformation + projection

Functions

matrix_from_params(params, transformation_type)	param params:
params_from_trans(transformation)	param transformation:
reverse_indices(matrix)	param matrix:
type_from_matrix(matrix)	param active: shape (N+1, N+1) or (K, N+1, N+1)

Classes

Homography(passive[, transfo_type])

param passive: