Pseudo-Divergence and Bidimensional Histogram of Spectral Differences for Hyperspectral Image Processing

Abstract

Spectral Information Divergence (SID) was identified as the most efficient spectral similarity measure. However, we show that divergence are not adapted to direct use on spectra. Following an idea proposed by Nidamanuri, we construct a spectral pseudo-divergence based on the Kullback-Leibler divergence. This pseudo-divergence is composed of two parts: a shape and an intensity similarity measure. Consequently, bidimensional representation of spectral differences are constructed to display the histograms of similarity between a spectral reference and the spectra from a data-set or an hyperspectral image. We prove the efficiency of the spectral similarity measure and of the bidimensional histogram of spectral differences on artificial and Cultural Heritage spectral images.

Spectral-divergence based pigment discrimination and mapping: A case study on The Scream (1893) by Edvard Munch

“…Since then, there have been more fundamental studies focusing on how to accurately measure the difference between two contiguous spectra as in the case of the hyperspectral domain (Deborah, Richard, and Hardeberg 2015;Richard et al 2016). In those studies, theoretical and metrological 2 limitations of both SAM and SCM and other difference measures have been extensively studied.…”

“…In those studies, theoretical and metrological 2 limitations of both SAM and SCM and other difference measures have been extensively studied. A more suitable spectral difference function was then proposed based on information divergence, the Kullback-Leibler pseudo-divergence (KLPD) (Richard et al 2016), whose mathematical expression is as follows…”

“…Nevertheless, both SAM and SCM have been shown to have limitations in its accuracy (Deborah, Richard, and Hardeberg 2015). Since then, and a new spectral difference function has been proposed and validated theoretically and metrologically, i.e., Kullback Leibler pseudo-divergence (KLPD) (Richard et al 2016).…”

“…In this study, we present the use of a spectral-divergence based representation space for spectral variation, which is built based on KLPD, i.e., Bidimensional Histogram of Spectral Differences (BHSD) (Richard et al 2016) and its modified version (Deborah 2016). The aim of this article is to demonstrate its applicability and relevance for pigment analysis of cultural heritage paintings, using the hyperspectral dataset of the masterpiece The Scream (1893) by Edvard Munch (1863-1944).…”

Application of spectral statistics to surface defect detection

“…6 Furthermore, there is no valid addition and subtraction operations defined for reflectance spectra. 7 In order to develop metrological solutions, the proposed spectral statistics are based on the Kullback-Leibler pseudo-divergence function (KLPD), 8 which has been shown to respect all of the expected metrological constraints. 7 In addition to providing the building blocks of the spectral difference-based spectral statistics, this work will also demonstrate their use in visualising and analysing the surface variability of a set of pigment patches.…”