Multivariate statistics
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, multivariate statistical methods have been 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.
A substantial fraction of the applied research in the section addresses problems on designing diagnostic tools where the proof of concept will involve quantification of uncertainties and deviations from state of the art that necessarily will involve statistical modelling.
A list of application areas is nearly endlessly varied and include
- food science,
- materials science,
- medical applications,
- industrial applications, and
- remote sensing/earth observation (related to mapping, mineral exploration, geology, agriculture, forestry, environmental monitoring, marine biology, oceanography, geodesy, and security).
Computer vision is one the core research fields of the Image section at DTU Compute. We aim to develop fundamental methods that allow for fast, accurate, and precise detections and measurements of the real world. Our area of focus spans all of object geometry, optical properties, lighting environments, as well as sub-resolution micro-geometry. The porpose is to be able to record the full digital twin of a natural scene by taking into account the interactions between light and material.
Highlights with links to original papers and other material illustrated below include
- change detection in remote sensing images with fast computation of eigenvalues,
- sea ice mapping in Greenlandic waters based on Sentinel-1 and AMSR-2 data by means of deep learning,
- in-vivo dosimetry, and
- fibre directionality.