Polarimetric learning: a Siamese approach to learning distance metrics of algal Mueller matrix images

Polarimetric measurements are becoming increasingly accurate and fast to perform in modern applications. However, analysis on the polarimetric data usually suffers from its high-dimensional nature spatially, temporally, or spectrally. This paper associates polarimetric techniques with metric learning algorithms, namely, polarimetric learning, by introducing a distance metric learning method called Siamese network that aims to learn good distance metrics of algal Mueller matrix images in low-dimensional feature spaces. As an experimental example, 12,162 Mueller matrix images of eight algal species are measured via a forward Mueller matrix microscope. Eight classical metric learning algorithms, including principle component analysis, multidimensional scaling, isometric feature mapping, t-distributed stochastic neighbor embedding, Laplacian eigenmaps, locally linear embedding, linear discriminant analysis, and metric learning to rank, are considered, by which the algal Mueller matrix images are mapped to two-dimensional (2D) feature spaces with different distance metrics. Support-vector-machine-based holdout sample classification accuracies of the 2D feature vectors are provided in a supervised manner for quantitative comparisons of the low-dimensional distance metrics, including the results of the eight metric learning algorithms and 16 Siamese architectures with varying convolution, inception, and full connection modules. This study shows that the Siamese approach is an effective metric learning algorithm that can adaptively extract features exhibiting empirical correlations with the fast-axis-orientation-dependent and spatially variant algal retardance induced by the algal microstructures.