Metrics Based on Logarithmic Laws

Abstract After a short recall on metrics concept, we propose a logarithmic version of existing metrics. Furthermore, we extend the Asplund's metric to functions previously defined on binary shapes. Two extensions are proposed: a “natural” one based on the logarithmic scalar multiplication and another completely novel one called additive Asplund's metric. Such a metric possesses very powerful properties in combination with its insensitivity to source intensity variations or exposure time changing. We propose then to extend these metrics to color images and the end of the chapter is centered on notions related to metrics: stronger or weaker notions like norms or gauges.