LOGARITHMIC SPIRAL GRIDS FOR IMAGE-PROCESSING AND DISPLAY

A picture digitization grid based on logarithmic spirals rather than Cartesian coordinates is presented. Expressing this curvilinear grid as a conformal mapping yields many geometric observations useful for computer graphics and picture processing. The exponential mapping induces a computational simplification that suggests parallel architectures in which most geometric transformations are effected by data shifting in memory rather than arithmetic on coordinates. These include noise-free rotation, scaling, and some projective transformations. Conformality of the mapping also preserves many important local picture-processing operattions such as edge detection. Real-time animation or processing of arbitrarily shaded pictures is suggested. © 1979.