A Fast Frequency-Space Transform-Invariant Template Matching using a "Pseudo-Normalizable" Fourier Transform (PNFT)

Given a template image T, the task in template matching is to search for T in a larger image region S. While simple in concept, much effort in recent years has been channeled on improving its robustness to complex transformation, with attention being largely on the similarity measures. Much lesser attention has been on the efficiency of the search computation itself. This paper attempts to fill the gap by proposing Pseudo-Normalizable Fourier Transform (PNFT), a novel complex transform that enables efficient transform-invariant, vectorized template matching. The concept of normalization is overloaded to denote the transformation of a function over an arbitrarily located patch to that about the origin, enabling the efficient use of image integral to perform template matching. The paper discusses on the ’normalizability’ – whether the function can be normalized – and further introduces pseudo-normalization as an approximation. The approach proposed requires no learning and runs fast on lower-end CPU-only platform. Further, it is conceptually simple and can be implemented in approximately 200 lines of Python/Numpy code. The efficacy of the approach is empirically analyzed using a complex example image.