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Asplu&#x0308;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 Asplu&#x0308;nd's metric to colour and multivariate images using the LIP framework. Asplu&#x0308;nd's metric is insensitive to lighting variations and we propose a colour variant which is robust to noise.

Asplünd's metric defined in the logarithmic image processing (LIP) framework for colour and multivariate images