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Andrew Todd-Pokropek: Analysis of multidimensional (and temporal) series of data and of image fusion |
A major problem with many current techniques in imaging (and in particular medical imaging) is the sheer volume of data of the results; examples in medicine are spiral and MDCT CT, MRI especially functional imaging, dynamic SPECT and PET etc. The same is true for satellite imaging In general the data are n-D, often 3-D plus time, plus multiple channels. Such data are hard to visualise without compression, specifically some kind of multi-dimensional projection to reduce dimensionality, for example reducing the n-D to a 2-D or 3-D image. But in additional to visualisation analysis of the data is required. Both linear and non-linear operations can be considered, and two classes of method are important: data driven and hypothesis driven. Illustrative of data driven methods is principal component analysis (and factor analysis) where from the statistical aim of reducing correlation, axes in the multi-dimensional space can be defined for the projection operation. Unfortunately, in practice, a pure statistical method does not generally map well on to expected physiological functions (or models), and some kind of oblique rotation is required, based on the choice of appropriate constraints such as that of positivity. Hypothesis driven methods are all implicitly or explicitly based on models. Thus associating data driven and hypothesis driven approaches leads to constrained statistical data (image) processing. Examples are shown as used in particular in nuclear medicine and MRI. Another important problem considered is that of multi-modality image registration and fusion and labelling. Although many methods exist, all based on the minimisation of an appropriate energy functions between two image data sets or of more complex models. Additional constraints or boundary conditions are required. Finally, in the analysis of such data, tests against reference data sets (atlases) are often required, The validation of such methods is very difficult especially in defining ground truth and some suitable distance measure. Again, incorporation of addition knowledge to the method seems to be really important in producing robust and reproducible techniques. A further good example is of data driven algorithms supervised using clinical constraints and models.
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