Spectral Shape Modeling for Medical Image Analysis

本研究计划旨在探索医学图像中形状分析的新方向。目前的挑战在于复杂生物形状的巨大可变性，比如大脑表面。它们的复杂度直接影响到医学图像分析中学习算法的性能。这表明，我们迫切需要更好地利用形状的本质，尤其是在对形状进行数据分析时。如今，医学成像中的形状分析通常基于外在的几何信息，例如，从欧几里德坐标中推导出来的几何信息。因此，传统的方法不可避免地需要昂贵的非线性形状归一化，以及长达数小时的计算来对齐形状。另一方面，在医学图像分析中，形状的内在性质往往被过度简化，甚至被忽视。例如，在基于表面的方法中，大脑表面通常被视为简单的球体，这增加了计算负担，甚至在体积方法中被忽略，导致表面数据不对齐。这严重限制了数据驻留在复杂表面的医学成像研究。

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.