A structure feature for some image processing applications based on spiral functions

A new low-level vision primitive based on logarithmic spirals is presented for various image processing tasks. The detection of such primitives is equivalent to detection of lines and edges in another coordinate system which has been used to model the mapping of the visual field to the striate cortex. Algorithms detecting the proposed primitives and pointing out a matched subclass are presented along with necessary theory. As a result, if the local structure is describable by the proposed primitives then a certainty parameter based on a well-defined mismatch (error) function will indicate this. Moreover, the best fit of a subclass of the proposed primitives in the least squares sense will be computed. The resulting images are unthresholded. They are computed by means of simple convolutions and pixelwise arithmetic operations which make the algorithms suitable for real time image processing applications. Since the resulting images contain information about the local structure, they can be used as feature images in applications like remote sensing, texture analysis, and object recognition. Experimental results on the latter including synthetic as well as natural images are presented along with noise sensitivity tests. The results exhibit good detection properties for the subclasses of the modelled primitives along with uniform and reliable behavior of the corresponding certainty measures.