Multivariate Statistics in Image Analysis
Multivariate statistics deals with development, computer implementation and application of methods related to the analysis of data where more than one attribute or variable is available for each observation taking into account the relations between these variables. Typically, the data are related to physical, chemical, biological, other natural, economical or societal phenomena.
Traditional multivariate statistical methods include test theory, regression analysis, discriminant analysis and classification, principal component analysis and other orthogonal transformations. We also work with iterative extensions of some of these methods and more computer intensive statistical learning based extensions such as kernel methods, binary decision tree based methods, ensemble methods, artificial neural networks, machine learning and deep learning.
In the context of image analysis and image processing more specifically, the analysis of colour and multispectral images almost inevitably leads to the use of multivariate methods. Multivariate statistics (MS) or statistics is the concept of describing what we observe taking into account the randomness of observations and all their inter-dependencies. In the Section for Visual Computing, multivariate statistical methods are developed and used in designing tools for enhancing relevant properties in such images. Examples are multivariate alteration detection using (iterated) canonical correlation or mutual information methods, mapping of changes in polSAR images using complex Wishart distributions, and monitoring food fermentation using color scales based on canonical discriminant functions and kernel versions of other orthogonal transformations, here principal components and maximum autocorrelation factors.