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

TL;DR

This paper extends Aspl{"u}nd's metric within the Logarithmic Image Processing framework to color and multivariate images, enhancing pattern matching robustness against lighting variations and noise.

Contribution

It introduces a novel extension of Aspl{"u}nd's metric for color and multivariate images using the LIP framework, with improved noise robustness.

Findings

Metric is insensitive to lighting variations

Proposed color variant is robust to noise

Extension applicable to multivariate images

Abstract

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.