Asplünd׳s metric defined in the Logarithmic Image Processing (LIP) framework: A new way to perform double-sided image probing for non-linear grayscale pattern matching

The present paper focuses on non-linear pattern matching based on the Logarithmic Image Processing (LIP) Model. Our contribution consists first of using the scalar multiplication defined in the LIP context to extend the little-known Asplünd׳s metric to gray level images. Such a metric is explainable as a novel technique of double-sided image probing and presents the decisive advantage of being physically justified in the field of transmitted light acquisition. Moreover, thanks to the consistency of the LIP context with human vision, Asplünd׳s metric is also applicable to images acquired in reflected light: in fact, plenty of image processing algorithms aim at extracting information as a human eye would do. Finally, the proposed approach is particularly efficient in the presence of lighting variations or lighting drift. In the paper, we also suggest a solution to overcome the main drawback of probing techniques, which resides in a high sensitivity to noise. Various examples are presented to highlight the efficiency of the method.