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Research Topic

The aim of the MAMEBIA project is the development of theoretical and concrete mathematical methods to model and analyse biological image data, with an emphasis on complex-valued methods and phase information.

At the moment, the mathematical models and transforms regarded in biological contexts, apart from the Fourier transform, are mostly real-valued. This restriction is often based on the assumption that all biological data is real valued, and that complex-valued methods only increase the needed storage space and computation time of algorithms, but don't contribute to better analysis quality.

But researchers in image analysis become more and more aware that even for real data complex-valued methods yield much better performance. These methods extract phase, which gives directional information for edge detection, and codes local features. Most information of an image is coded in the phase. But its extraction with mathematical transforms and its interpretation is not yet fully understood. This might be the reason why phase information is rarely used for biological image analysis.

The MAMEBIA project aims to bridge this gap. The team will model biological problems, and formulate them in a sound mathematical manner. On this basis, the team will develop new, and adapt existing complex-valued transforms to extract the modelled image features. Particularly, harmonic and nonharmonic Fourier transforms, as well as multiresolution approaches, as Gabor analysis and complex continuous and discrete wavelet methods will be emphasized, and their phase information will be evaluated. Algorithms and concrete programs will be developed and implemented. The team will closely cooperate with collaborators from biology to ensure the high quality of the models and to have a significant validation. This close cooperation allows the amalgamation of knowledge and know-how, and ensures that both mathematics and biology benefits strongly from this interdisciplinary research.