The Monogenic Curvature Scale-Space

In this paper, we address the topic of monogenic curvature scale-space. Combining methods of tensor algebra, monogenic signal and quadrature filter, the monogenic curvature signal, as a novel model for intrinsically two-dimensional (i2D) structures, is derived in an algebraically extended framework. It is unified with a scale concept by employing damped spherical harmonics as basis functions. This results in a monogenic curvature scale-space. Local amplitude, phase and orientation, as independent local features, are extracted. In contrast to the Gaussian curvature scale-space, our approach has the advantage of simultaneous estimation of local phase and orientation. The main contribution is the rotationally invariant phase estimation in the scale-space, which delivers access to various phase-based applications in computer vision.