Collaborative Research: Efficient mathematical and computational framework for biological 3D image data retrieval

成像技术的进步导致了许多成像方式的三维生物和医学图像数据的激增，其中包括医学成像中的磁共振成像和计算机断层扫描，神经科学中使用光场显微镜的神经成像，成像细胞和组织的断层扫描，以及用于生物分子结构的冷冻电子显微镜。三维、体积结构的图像提供了关于器官、组织和分子的不可缺少的空间信息，这些信息不能用二维来捕获。因此，迫切需要开发工具，以便对这种体积数据集进行高效和有效的分析。该项目将开发普遍适用的数学和计算框架，以有效和准确地表示、比较和检索三维生物和医学数据。将要开发的方法将为使用多种成像方式和多种数据类型（不仅来自生物领域）获得的体积图像的分析提供一般基础。例如，这些技术在人脸识别、地理和气候数据分析以及计算机辅助设计等领域具有更广泛的影响。因此，该项目有助于促进许多领域的科学和技术进步，其中成像分析是至关重要的，具有重大的社会影响。在这个项目中，将发展和整合两种互补和协同的方法。要开发的第一种方法是基于数学矩的方法，它提供了体积数据的紧凑表示，非常适合局部三维图像数据比较。将基于矩不变量的二维图像比较方法扩展到处理体积数据。第二种方法是一种机器学习方法，它在分类体积数据方面很强大。这两种方法将被整合，以利用这两种方法的优势，并使用三维蛋白质结构数据进行验证。分析蛋白质形状之间的全局和局部相似性对于理解蛋白质功能至关重要，但也具有挑战性，因为形状完全不同的蛋白质可能具有相同的功能。此外，蛋白质适合于这一验证步骤，不仅因为许多结构在完善的公共数据库中可用，而且因为它们缺乏内在定向，不像以前研究的人造物体（如汽车、杯子和桌子）的数据集。由于所提出的方法是为给定体积的一般体素表示而定义的，因此它们通常适用于产生体素表示的任何数据集，包括使用电子显微镜、磁共振成像和计算机断层扫描收集的生物医学数据。除了项目的科学影响外，它还利用了普渡大学和东肯塔基大学跨学科计算生命科学和工程系的努力，通过跨学科课程和直接参与项目招募和培训学生。

Advances in imaging technology have led to a proliferation of three dimensional biological and medical image data from many imaging modalities, which include magnetic resonance imaging and computed tomography scans in medical imaging, neuroimaging using light-field microscopy in neuroscience, tomography for imaging cells and tissues, and cryo-electron microscopy for biomolecular structures. Images of three dimensional, volumetric, structures provide indispensable spatial information about organs, tissues, and molecules that cannot be captured using two dimensions. The development of tools for efficient and effective analysis of such volumetric data sets is, therefore, urgently required. This project will develop generally applicable mathematical and computational frameworks to effectively and accurately represent, compare, and retrieve biological and medical data in three dimensions. The methods to be developed will provide a general foundation for the analysis of volumetric images obtained using multiple imaging modalities and for multiple data types, not only from the biological domain. For example, the techniques have broader impact in areas such as human face recognition, analysis of geographical and climate data, and computer-aided design. This project, therefore, contributes to general promotion of the progress of science and technology in many domains in which imaging analysis is crucial and is of significant societal impact. In this project, two complementary and synergistic methods will be developed and integrated. The first method to be developed is a mathematical moment-based approach that provides a compact representation of volumetric data and is very suitable for localized three dimensional image data comparison. A two dimensional image comparison method that is based on a moment-based invariant will be expanded to handle volumetric data. The second method is a machine learning approach that will be powerful in classifying volumetric data. These two approaches will be integrated to take advantage of both methods and validated using three dimensional protein structural data. Analyzing global and local similarities between protein shapes is critical for understanding protein function but challenging because proteins with substantially different shapes may perform the same function. Further, proteins are appropriate for this validation step not only because many structures are available in well-established public databases but also because they lack intrinsic orientation, unlike previously studied datasets of man-made objects such as cars, cups, and tables. As the proposed methods are defined for a general voxel representation of a given volume, they will be generally applicable for any data set yielding a voxel representation, including biomedical data collected using electron microscopy, magnetic resonance imaging and computed tomography. Along side the scientific impact of the project, it also leverages efforts in the interdisciplinary computational life sciences and engineering departments at Purdue University and Eastern Kentucky University by recruiting and training students through interdisciplinary coursework and direct involvement with the project.