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.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Junping Wang
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Purdue University
West Lafayette
United States
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