Theoretical Criterion For Image Matching Using Gpt Correlation

GAT (Global Affine Transformation) and GPT (Global Projection Transformation) correlation matchings were successively proposed by Wakahara and Yamashita which use affine transformation (AT) and 2D projection transformation (PT), respectively, to maximize the normalized cross-correlation value between a template and a GAT/GPT-superimposed input image. In theory, to maximize the degree of matching via normalized cross-correlation, the L2 norm of both images should be normalized. However, the criteria of conventional GAT/GPT correlation techniques did not take account of the conservation of the L2 norm. This research solves the above-mentioned problem which might impair the matching ability of GAT/GPT correlations. In particular, we focus on the enhanced GPT correlation recently proposed by Wakahara et al. to calculate optimal PT parameters simultaneously. Then, we propose an improved criterion satisfying the requirement of the L2 norm conservation together with the enhanced GPT correlation algorithm with norm normalization. Experimental results using artificially deformed images of chess board and handwritten digits from MNIST database by 2D projection transformation show that the proposed method clearly outperforms those conventional GPT correlation techniques with or without norm normalization in terms of both convergence speed and matching ability.