| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | July 16, 2019 |
| Latest Amendment Date: | August 25, 2021 |
| Award Number: | 1854853 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Yong Zeng
yzeng@nsf.gov (703)292-7299 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | August 1, 2019 |
| End Date: | July 31, 2023 (Estimated) |
| Total Intended Award Amount: | $405,996.00 |
| Total Awarded Amount to Date: | $405,996.00 |
| Funds Obligated to Date: |
FY 2020 = $135,521.00 FY 2021 = $136,580.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
4300 MARTIN LUTHER KING BLVD HOUSTON TX US 77204-3067 (713)743-5773 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
TX US 77204-2015 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | CDS&E-MSS |
| Primary Program Source: |
01002021DB NSF RESEARCH & RELATED ACTIVIT 01002122DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
This project aims to reconstruct and quantify the dynamic deformations of soft organ shapes which are routinely observed by clinicians or researchers in medical imaging data. Our mathematical and computational approaches can potentially impact many domains, ranging from computer aided medical diagnosis, to automatic shape recognition in computer vision, as well as automated clustering, classification, and fast retrieval of biomedical image sequences. We will study movies recording dynamics of three dimensional biomedical shapes, for instance in live echo-cardiographic imaging of patients beating hearts. We will quantify shape distortions by computing "elastic distances" between deformable shapes and by large numbers of "strain values" evaluating local deformation of tissues. In turn these deformations characteristics enable the use of artificial neural networks for automatic classification and clustering of deformable shapes.
Our work is motivated by the increasing availability of large databases of movies recording in 3D the dynamic deformations of "soft" shapes, such as human organs. We aim to generate quantified comparison between any pairs of movies recording the dynamic deformations of similar biomedical shapes, such as the mitral valves of cardiology patients. We will use one large seed set of actual echo-cardiographies of mitral valves dynamics to generate a large set of N = 1000 random diffeomorphic 3D surfaces deformations. In the spirit of computational anatomy, for each such movie, we will compute a time dependent diffeomorphic registration of successive frames, and extract an associated detailed strain map. For each pair of movies M1 and M2, after time registration, we will implement diffeomorphic registrations between corresponding key time frames of M1 and M2. This involves the numerical solving of a high dimensional variational calculus problems by innovative fast non-linear optimal control. From all these diffeomorphic registrations, we will extract multiple characteristics of each movie as well as quantitative "similarities" between pairs of movies. At this stage, powerful data mining techniques such as support vector machines and artificial neural networks will become implementable to generate multi-scale clustering as well as classification of shapes deformations. To handle the heavy computing challenges, we will implement highly parallelized computational schemes on remote high power computing resources.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The study, analysis, recognition, and classification of shapes and shape deformations have numerous applications in computer vision. This includes retrieval and classification of objects in large digital databases or the study of organs in biomedical image sequences. In this project, we focussed on the latter. This area of research is commonly referred to as computational anatomy. Our approaches build upon a rich mathematical framework that allows us to quantify and compare shapes in a Riemannian setting. Numerous research groups worldwide have been working on designing innovative methods to help clinicians diagnose diseases in a consistent way. Our main focus in this project was the automated clustering, classification, and fast retrieval of biomedical image sequences. We have designed and analyzed efficient mathematical methods and numerical approaches, as well as fast hardware-accelerated computational kernels to achieve these goals. This includes the design and implementation of fast algorithms to solve the underlying variational optimization problems. Aside from working on purely mathematical aspects, we have also pushed our methodology to the application. We have tested the discriminatory capabilities of our approach on different medical imaging data, including echo-cardiography of mitral valve dynamics.
Upon completion of the project, we would like to report the following concrete outcomes:
- We have developed a mathematical framework to classify smooth deformable objects.
- We have developed a mathematical framework to augment datasets by applying smooth, random diffeomorphic deformations.- We have designed mathematical methods for matching and tracking shapes and deformable objects in (time series) of medical images.
- We have applied the developed methodology to medical imaging data. We demonstrated that the methodology allows us to discriminate data from healthy from diseased patients.
- We have designed an operator-splitting algorithm for matching deformable shapes and tested it on clinical data.
- We have designed fast computational kernels and parallel algorithms that scale on heterogeneous computing architectures.- We have organized several mini-symposia on mathematical and computational methods with application to diffeomorphic image registration, computational anatomy, and diffeomorphic shape matching.
- We have disseminated this work through presentations and invited talks.
- We have trained two graduate students and one postdoctoral researcher.
Last Modified: 02/29/2024
Modified by: Andreas Mang
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