George Kukharev– Professor, Department of Software and Application of Computers, Faculty of Computer Technologies and Informatics, Saint Petersburg Electrotechnical University; Professor, West Pomeranian University of Technology, Szczecin, Poland.
Address: 5, Professora Popova str., St. Petersburg, 197376, Russian Federation.
E-mail: kuga41@gmail.ru, gkukharev@wi.zut.edu.pl

Ekaterina Kamenskaya– Software Engineer, Google Zürich, Switzerland.  
Addrress: 110, Brandschenkestrasse, Zürich, 8002, Switzerland.
E-mail: ekamenskaya@google.com

Nadezhda Shchegoleva – Associate Professor, Department of Software and Application of Computers, Faculty of Computer Technologies and Informatics, Saint Petersburg Electrotechnical University.  
Address: 5, Professora Popova str., St. Petersburg, 197376, Russian Federation.
E-mail: stil_hope@mail.ru

This paper discusses the methods of presentation and comparison for semantically unrelated images, visually similar (that is having similar color, shape, texture), and assessment of their similarity in the original feature space, and in Canonical Variables Space (CVS). The projection of the source images in CVS is implemented using two-dimensional canonical Canonical Correlation Analysis – 2D CCA/2D KLT presented in this paper, and the measure of their similarity in CVS is based on the phase correlation.
To compare images in the original feature space, we used color brightness histograms and mutual phase correlation between histograms, mutual phase correlation between images, Structural SIMilarity Index (SSIM). However, we could only partially prove similarity corresponding to subjective comparison of selected images - the presence of phase correlation between the color brightness histograms, that is based on the similarity of images colors. Mutual phase correlation between images, as well as structural similarity index showed no images similarity.
The projection in the space of canonical variables is implemented using 2D CCA/2D KLT, specifically designed to handle two sets of images and presented in detail in this paper. This allowed confirming the fact of the correlation between the images of the dog and its owner in the space of canonical variables, while other ways failed to confirm it. It is shown that what is «dissimilar» in the original feature space may be similar in the space of canonical variables. This allows indexing some images through other by using 2D CCA methods (search, recognition, model mapping of one image to another, reconstruction of images). The results prove that 2D CCA/2D KLT methods can be widely used in search, pattern recognition and image classification tasks, and to decrease redundancy of images representation regardless of their semantic relationships.