The structure tensor in projective spaces

摘要: The structure tensor has been used mainly for representation of local orientation in spaces arbitrary dimensions, where the eigenvectors represent and corresponding eigenvalues indicate type which is represented. Apart from being local, may be referred to as "object centered" since it describes relative a reference system. This paper proposes that basic properties can extended defined projective space rather than Euclidean space. result, "projective tensor", symmetric same way tensor, also uses eigensystem carry relevant information. However, instead orientation, represents geometrical primitives such points, lines, planes (depending on dimensionality underlying space). Furthermore, this useful property mapping operation forming affine hull points lines summation, e.g., sum two tensors amounts line passes through etc. "view each still scale, geometric primitive global image based implies combined, using meaningful over large regions.