Motion estimation using invariance under group transformations

Vision with Direction

“…The six parameters represented by v 0 and A 0 steer the tangent curves of s. It can be shown that a small motion along these curves can be achieved by an affine infinitesimal operator 9 [58], Accordingly, the trajectory of a point in the image plane, s(t) = (x(t), y(t)) T , can be solved analytically.…”

Extracting Group Transformations from Image Moments

“…Unfortunately, the existing methods for computing group transformations suffer from the requirement for corresponding image features [13,22,26], limitation to the amount of image motions [8], and/or high sensitivity to noise [1,3]. If the interest areas (focus of attention) in images are identified, moment-based methods [4,7,9,12,25] are useful.…”

“…For this objective, we first review the Lie group theory [10,23], which has recently been imported to computer vision research [8,14,29], and investigate how the change in image moments under general group transformations can be described by the basis vector fields of the group. Especially, we will exploit a prolonged space [23], an extended space for derivatives, and analyze the change in values of functions with derivatives explicitly from a geometric point of view.…”