Functional Asplund's metrics for pattern matching robust to variable lighting conditions

In this paper, we propose a complete framework to process images captured under uncontrolled lighting and especially under low lighting. By taking advantage of the Logarithmic Image Processing (LIP) context, we study two novel functional metrics: i) the LIP-multiplicative Asplund's metric which is robust to object absorption variations and ii) the LIP-additive Asplund's metric which is robust to variations of source intensity and exposure-time. We introduce robust to noise versions of these metrics. We demonstrate that the maps of their corresponding distances between an image and a reference template are linked to Mathematical Morphology. This facilitates their implementation. We assess them in various situations with different lightings and movements. Results show that those maps of distances are robust to lighting variations. Importantly, they are efficient to detect patterns in low-contrast images with a template acquired under a different lighting.