GPT Correlation for 2D Projection Transformation Invariant Template Matching

This paper describes a new technique of 2D projection transformation invariant template matching, GPT (Global Projection Transformation) correlation, as a natural extension of our earlier work on the affine-invariant GAT (Global Affine Transformation) correlation method. The key ideas are threefold. First, we show that arbitrary 2D projection transformation (PT) can be decomposed into a product of affine transformation (AT) and partial projection transformation (PPT). Second, we propose an efficient computational model for determining sub-optimal components of AT and PPT separately that maximize a normalized cross-correlation value between an either AT- or PPT-superimposed input image and a template by solving linearized simultaneous equations. Third, we obtain optimal components of combined AT and PPT, i.e. PT, that maximize a normalized cross-correlation value between a PT-superimposed input image and a template via the successive iteration method. The proposed technique has the time complexity of O(n2), where n equals the number of pixels. Experiments using templates and their artificially distorted images as input images show that the proposed method is far superior to the GAT correlation method in 2D projection transformation tolerance, and, also, has a high tolerance for noise.