Measuring regularity of network patterns by grid approximations using the LLL algorithm

In a recent work, we have proposed a novel way to approximate point sets with grids using the LLL algorithm, which operates in polynomial time. Now, we show how this approach can be applied to pattern recognition purposes with interpreting the rate of approximation as a new feature for regularity measurement. Our practical problem is the characterization of pigment networks in skin lesions. For this task we also introduce a novel image processing method for the extraction of the pigment network. Then, we show how our grid approximation framework can be applied with specializing it for the recognition of hexagonal patterns. The classification performance of our approach for the pigment network characterization problem is measured on a database annotated by a clinical expert. Throughout the paper we address several practical issues that may help to apply our general framework to other practical tasks, as well.