Splitting-shooting methods for nonlinear transformations of digitized patterns

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Abstract
New splitting-shooting methods are presented for nonlinear transformations T: ( xi , eta ) to (x,y) where x=x( xi , eta ), y=y( xi , eta ). These transformations are important in computer vision, image processing, pattern recognition, and shape transformations in computer graphics. The methods can eliminate superfluous holes or blanks, leading to better images while requiring only modest computer storage and CPU time. The implementation of the proposed algorithms is simple and straightforward. Moreover, these methods can be extended to images with gray levels, to color images, and to three dimensions. They can also be implemented on parallel computers or VLSI circuits. A theoretical analysis proving the convergence of the algorithms and providing error bounds for the resulting images is presented. The complexity of the algorithms is linear. Graphical and numerical experiments are presented to verify the analytical results and to demonstrate the effectiveness of the methods.

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