Scaled-Distance-Transforms and Monotonicity of Autocorrelations

In this letter, we investigate the use of distance transforms in a scale space domain for the image (and signal) misalignment problem. We show that it is possible to build an autocorrelation function that is monotonic with respect to the amount of translation. This creates a new paradigm for image comparison and gives yet a new generalization of distance transforms to grey-level images. Its behavior is analyzed on a natural scene image and its robustness against noise is verified numerically.