Multi-way methods in image analysis—relationships and applications

This paper gives an overview of multi-way methods in image analysis, termed N-way image analysis. Both weak and strong multi-way methods are applied in order to decompose and characterize image data, and obtain insight into their abilities to capture and model the interpretable data structure. Multivariate Image Analysis (MIA) is a typical example based on weak multi-way methods like unfold-PCA/PLS. Strong multi-way methods such as PARAFAC, Tucker3, N-PLS are also introduced and applied to image analysis in this work. Which method to use is problem-dependent. Through macroscopic satellite images, virtual fluorescence images and microscopic functional property image examples, the performance of each alternative method is presented, as well as comparisons between weak and strong multi-way models. It is demonstrated that efficient handling of multiple images requires a clear a priori overview of the relationship between problem formulation and data array configuration. Appropriate preprocessing techniques, such as 2-D FFT and Wavelet transform, may also be needed in order to transform and configure some special types of image data to forms specifically suited for multi-way modeling. Application I shows the possibility for application of strong multi-way methods on multispectral images, otherwise conventionally analyzed by MIA. By contrast, application II attempts to investigate the feasibility of applying MIA models on typical three-way data, normally handled by the strong multi-way methods and provides a new perspective of dealing with fluorescence spectra as images. In application III, attempts have been made to predict rheological parameters from microscopic cheese images by multi-way methods. The present didactic exposition allows to draw some tentative first conclusions as to the dominant relationships between strong and weak multi-way data decompositions, their pros and cons and their relative merits.