Spatio-Colour Aspl\"und 's Metric and Logarithmic Image Processing for Colour Images (LIPC)

Aspl\"und 's metric, which is useful for pattern matching, consists in a double-sided probing, i.e. the over-graph and the sub-graph of a function are probed jointly. This paper extends the Aspl\"und 's metric we previously defined for colour and multivariate images using a marginal approach (i.e. component by component) to the first spatio-colour Aspl\"und 's metric based on the vectorial colour LIP model (LIPC). LIPC is a non-linear model with operations between colour images which are consistent with the human visual system. The defined colour metric is insensitive to lighting variations and a variant which is robust to noise is used for colour pattern matching.