Spectral Shape Modeling for Medical Image Analysis

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Context This research program aims at exploring new directions for the analysis of shapes in medical images. The current challenge resides in the huge variability of complex biological shapes, such as the surface of the brain. Their complexity directly impacts the performance of learning algorithms in medical image analysis. This indicates a crucial need to better exploit the nature of shapes, particularly when data is analyzed on them. Shape analysis in medical imaging is today, often based on extrinsic geometric information, for instance, derived from Euclidean coordinates. As a result, traditional approaches inexorably require costly non-linear shape normalization, up to hours of computation for aligning shapes. On the other side, the intrinsic nature of shapes is often over simplified in medical image analysis, if not ignored. For instance, brain surfaces are typically treated as simple spheres in surface-based methods, increasing computational burden, or even ignored in volumetric methods, leading to misaligned surface data. This severely limits studies in medical imaging where data resides on complex surfaces.Research Directions and Methodology One promising avenue is to investigate shapes via spectral graph theory. This provides a foundation towards a truly intrinsic shape analysis, notably due to its invariance under isometry. The recent advances and the growing need to study surface data motivate the development of a new paradigm to perform statistics on complex biological shapes. To do so, I intend to develop three axes of research on spectral shape analysis: (i) shape representation, focused on harmonic shape modeling, (ii) shape statistics, focused on the learning of surface data, and (iii) shape dynamics, focused on motion of shapes. This program will first focus on the structural and functional variability of neuroimaging data, in order to discover the underlying mechanisms of neurodegenerative diseases. The long-term vision is to contribute towards a better use of medical data in learning algorithms by exploiting shape representations to detect biological abnormalities automatically.Impact Outcomes are expected to have a high direct impact in medical imaging, notably for studying functional data in the brain and cardiac imaging. The spectral framework provides a new paradigm to perform statistics on complex biological shapes. The computational advantage is expected to bring faster and more precise tools for studying functional data, notably in neuroimaging, which crucially needs a geometry-aware statistical framework. This brings, therefore, a strong advantage to lead future studies in functional neuroimaging with high potentials to significantly scale up future studies. The spectral framework is also relevant in various other fields where data fundamentally lives on surfaces, including in computer vision and machine learning.