Aspl{\"u}nd's metric defined in the Logarithmic Image Processing (LIP) framework for colour and multivariate images

Aspl{\"u}nd'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. It has previously been defined for grey-scale images using the Logarithmic Image Processing (LIP) framework. LIP is a non-linear model to perform operations between images while being consistent with the human visual system. Our contribution consists in extending the Aspl{\"u}nd's metric to colour and multivariate images using the LIP framework. Aspl{\"u}nd's metric is insensitive to lighting variations and we propose a colour variant which is robust to noise.