Signal modeling for two-dimensional image structures

This paper presents a novel approach towards two-dimensional (2D) image structures modeling. To obtain more degrees of freedom, a 2D image signal is embedded into a certain geometric algebra. Coupling methods of differential geometry, tensor algebra, monogenic signal and quadrature filter, a general model for 2D image structures can be obtained as the monogenic extension of a curvature tensor. Based on this model, local representations for the intrinsically one-dimensional (i1D) and intrinsically two-dimensional (i2D) image structures are derived as the monogenic signal and the generalized monogenic curvature signal. From the local representation, independent features of local amplitude, phase and orientation are simultaneously extracted. Compared with the other related work, the remarkable advantage of our approach lies in the rotationally invariant phase evaluation of 2D structures, which delivers access to phase-based processing in many computer vision tasks.