Logarithmic spiral grids for image-processing and display

Abstract 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.

[1]  D. Casasent,et al.  Position, rotation, and scale invariant optical correlation. , 1976, Applied optics.

[2]  Herbert Freeman,et al.  On the Encoding of Arbitrary Geometric Configurations , 1961, IRE Trans. Electron. Comput..

[3]  David R. Smith,et al.  A Threshold Logic Network for Shape Invariance , 1967, IEEE Trans. Electron. Comput..

[4]  R. Jung.  Visual Perception and Neurophysiology , 1973 .

[5]  J. W. Brown,et al.  Complex Variables and Applications , 1985 .

[6]  W. Richards,et al.  The fortification illusions of migraines. , 1971, Scientific American.

[7]  Jerome Rothstein,et al.  Parallel and sequential specification of a context sensitive language for straight lines on grids , 1976 .

[8]  Max Johann Sigismund Schultze,et al.  Zur Anatomie und Physiologie der Retina , 1866 .

[9]  E. F. Codd,et al.  Cellular automata , 1968 .

[10]  J. Nicholls.  From neuron to brain , 1976 .

[11]  B. Julesz.  Foundations of Cyclopean Perception , 1971 .

[12]  H. Coxeter,et al.  Introduction to Geometry. , 1961 .

[13]  Irwin Sobel,et al.  On Calibrating Computer Controlled Cameras for Perceiving 3-D Scenes , 1973, IJCAI.

[14]  J. Kaas,et al.  Representation of the visual field on the medial wall of occipital-parietal cortex in the owl monkey. , 1976, Science.

[15]  M. H. Pirenne,et al.  VISION AND THE EYE , 1949 .

[16]  David Potter.  Computational physics , 1973 .

[17]  Berthold K. P. Horn,et al.  Determining lightness from an image , 1974, Comput. Graph. Image Process..

[18]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .

[19]  Donald K. Eddington,et al.  A Computer-Based Brain Stimulation System to Investigate Sensory Prostheses for the Blind and Deaf , 1976, IEEE Transactions on Biomedical Engineering.