Email: christine.fernandez@univ-poitiers.fr ,noel.richard@univ-poitiers.fr

In this work, we are focusing on the non-uniformity assessment of a surface (so the textured aspect) kept by hyperspectral imaging and we are expressing how to satisfy the metrological constraints. To assess the non-uniformity of surfaces, we propose to characterize it as a joint distribution of the spectra and of the spatial distribution of these spectra.

By metrological solutions, we are expressing that the measures must be related to physical changes, preserve the human interpretability, the measurement genericity and the uncertainty management. In addition, spectra are not classical vectors due to the relationship to the reflectance functions.

In previous works, we demonstrated how the Kullback-Leibler Pseudo-divergence (KLPD) solved the metrological properties for the assessment of the similarity between two spectra [1, 2]. To assess the spectral diversity, the statistical analysis is translated into a spectral difference space, preserving so the metrological constraints. The spatial distribution is developed using a dedicated spectral texture feature, the Relocated Spectral Difference Occurrence Matrix (RSDOM) [3]. Also based on a spectral difference the RSDOM solves the limits of Grey-Level Cooccurrence Matrix (GLCM) for multivariate data (no prior quantization, no prior dimension reduction, straightforward interpretability and similarity processing…). Staying in the same neighbourhood spirit than the GLCM, the RSDOM allows multi-orientation and multi-scale analysis. Thanks to the mathematical decomposition of the KLPD into a spectral shape and intensity difference, the proposed texture feature allows a fine analysis of the spectral images and the relationship to the pigment recognition.

[1] N. Richard, D. Helbert, C. Olivier et M. Tamisier, «Pseudo-Divergence and Bidimensional Histogram of Spectral Differences for Hyperspectral Image Processing,» Journal of Imaging Science and Technology (JIST), Vols. %1 sur %260, n°5, pp. 050402.1 - 050402.13, Sept-Oct 2016.

[2] A.-C. Membre, F. Z. Fadanelli, A. Tournié, A. Michelin, N. Richard et C. Andraud, «Spectral variability of the optical properties of pictorial layers,» Applied Physics A, vol. 127(94), pp. 1-20, 2021.

[3] R.-J. Chu, N. Richard, H. Chatoux, C. Fernandez-Maloigne et J.-Y. Hardeberg, «Hyperspectral texture metrology based on joint probability of spectral and spatial distributions,» IEEE Transactions on Image Processing, vol. 30, pp. 4341-4356, 2021.