Transformation of digital images by discrete affine applications

Quasi-Affine Transformation in Higher Dimension

“…In dimension 2, the QAT appeared in several articles [4,5,6,7,8]. To summarize the main results, the authors have proved several arithmetical results on QAT in 2-D leading to efficient transformation algorithms.…”

The Quasi-Shear rotation

“…These are a special class of Quasi-Affine Transformations, called the Quasi Shear Transformations (QST). Many theoretical and practical results about the Quasi Affine Transformations are described in [3,7].…”

Homotopic Affine Transformations in the 2D Cartesian Grid

“…In Cartesian grids, various subfamilies of affine transformations have been investigated, namely translations [7,33], scalings [1,3], reflections [5,12], rotations [2,4,5,8,18,25,44,45,49,54], rigid motions [38, 39, 41-43, 46, 50], combined scalings and rotations [22], and affine transformations [11,21,23,24,27,29,37]. The purposes were manifold: describing the combinatorial structure of these transformations with respect to R n versus Z n [1-3, 7, 8, 18, 21-23, 33, 38, 48, 56], guaranteeing their bijectivity [4,5,12,25,44,49,50,54] or their transitivity [45] in Z n , preserving geometrical properties [41,42] and, less frequently, ensuring their topological invariance [39,43] in Z n .…”