Methods of two-dimensional projection of digital images into eigen-subspaces: peculiarities of implementation and application

Abstract

The history of development of algorithms for projection of digital images into their eigensubspaces using linear methods based on PCA (principal component analysis), LDA (linear discriminant analysis), PLS (partial least squares), and CCA (canonical correlation analysis) is considered. We show that the emergence of new application areas has changed the requirements for the methods, with major changes involving (i) the use of PCA, LDA, PLS and CCA methods for both small and extremely large face image (FI) samples in the initial sets; (ii) a criterion for determining the eigen-basis, which also should provide the solution of a particular problem (the minimum error of face image approximation, etc.); (iii) the applicability of the methods under consideration to the processing of two or more image sets from different sensors or several sets of any number of matrices; and (iv) the possibility of realizing two-dimensional projections of face images (or other numerical matrices) directly into the layers of convolutional neural networks (NN) and/or integrating their functions into the NN as separate blocks. Estimates of the computational complexity and examples of solving image processing problems are also given.

Keywords

• face image (FI) sets and numeric matrices
• an eigen-basis and eigensubspaces
• principal components analysis (PCA)
• linear discriminant analysis (LDA)
• partial least squares (PLS)
• canonical correlation analysis (CCA)
• Karhunen-Loeve transformation (KLT)
• 2DPCA/2DKLT
• 2DPLS/2DKLT
• 2DCCA/2DKLT
• CNN
• Deep NNю
• Deep NN