Method and system for processing a non-linear two dimensional spatial transformation

TLDR: In this paper, an image transformation method for translating a non-linear 2D geometrical transformation into two separable 1D geometric transformations is presented. But the method is not suitable for image classification, as it does not meet a predetermined level of performance.

Abstract: An image transformation method for translating a non-linear 2D geometrical transformation into two separable 1D geometrical transformations first determines the inverse of the 2D geometrical transformation to form an inverse 2D geometrical transformation. Then the method converts the inverse 2D geometrical transformation into an analytical inverted 2D geometrical transformation and separates the analytical inverse 2D geometrical transformation into first and second 1D geometrical transformations. The method then represents said inverse 2D geometrical transformation and first and second 1D geometrical transformations as tensor spline surfaces and then compares an evaluation of said first and second 1D geometrical transformations at each pixel with an evaluation of the analytical inverse 2D geometrical transformation at each pixel. If the error evaluation does not meet a predetermined level of performance then the separation and transformation steps are repeated. One-dimensional spatial transform processing it results in reduced calculation, efficient memory access, and ability to process data in a real-time environment. In-addition, since the method provides a compact representation of the spatial transforms, it can be scaled for a particular level of precision.