Spectral Shape Modeling for Medical Image Analysis

本研究项目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，例如大脑的表面。它们的复杂性直接影响医学图像分析中学习算法的性能。这表明迫切需要更好地利用形状的性质，特别是在分析数据时。医学成像中的形状分析如今通常基于例如从欧几里德坐标导出的外部几何信息。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，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，形状的内在本质往往被过度简化，如果不是被忽视的话。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，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上的医学成像研究。研究方向和方法一个很有前途的途径是通过谱图理论研究形状。这为真正的内在形状分析提供了基础，特别是由于其在等距下的不变性。最近的进展和日益增长的需要，研究表面数据的动机发展的一个新的范例来执行复杂的生物形状的统计。为了做到这一点，我打算发展三个轴的研究频谱形状分析：（i）形状表示，侧重于谐波形状建模，（ii）形状统计，侧重于表面数据的学习，（iii）形状动力学，侧重于形状的运动。该计划将首先关注神经影像数据的结构和功能变异性，以发现神经退行性疾病的潜在机制。长期愿景是通过利用形状表示来自动检测生物异常，从而在学习算法中更好地使用医学数据。Impact Outcomes预计将对医学成像产生直接影响，特别是对大脑和心脏成像中的功能数据的研究。光谱框架提供了一个新的范例来执行复杂的生物形状的统计。预计计算优势将为研究功能数据带来更快，更精确的工具，特别是在神经成像领域，这迫切需要一个几何感知的统计框架。因此，这带来了一个强大的优势，导致未来的研究在功能性神经影像学具有高潜力，以显着扩大未来的研究。光谱框架也与数据基本上存在于表面上的各种其他领域有关，包括计算机视觉和机器学习。

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.