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Structure-function relations are central to the study of biological systems. This is true, for instance, in the central nervous system where neurons exhibit a remarkable morphological diversity attesting the importance of structural characteristics for brain function. During the last decade, remarkable advances in microscopy, MRI and other probing techniques, as well as the development of more sensitive staining techniques, have revolutionized the field of biomedical imaging by increasing the availability of high-quality images for applications ranging from basic science through drug discovery and medical diagnostics. Yet, such advances have not been matched with algorithmic and analytical tools capable of processing data with sufficient accuracy and computational efficiency to take full advantage of the information available. In response to this need, a significant effort is being made in applied mathematics to develop a new generation of image processing tools to analyze imaging data with high geometrical sensitivity and across multiple scales. The impact of these methods is expected to be very significant as they would enable to quantify a multiplicity of biological features, carry out more accurate statistical analyses and generate more realistic computational models. The scope of the minisymposium is to bring together experts from the area of anisotropic multiscale methods and their applications to biomedical imaging, and discuss emerging directions in this field.