
NSF Org: |
DMS Division Of Mathematical Sciences |
Recipient: |
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Initial Amendment Date: | July 26, 2005 |
Latest Amendment Date: | July 26, 2005 |
Award Number: | 0505729 |
Award Instrument: | Standard Grant |
Program Manager: |
Henry Warchall
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
Start Date: | August 1, 2005 |
End Date: | July 31, 2010 (Estimated) |
Total Intended Award Amount: | $139,900.00 |
Total Awarded Amount to Date: | $139,900.00 |
Funds Obligated to Date: |
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History of Investigator: |
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Recipient Sponsored Research Office: |
600 FORBES AVENUE PITTSBURGH PA US 15282 (412)396-1537 |
Sponsor Congressional District: |
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Primary Place of Performance: |
600 FORBES AVENUE PITTSBURGH PA US 15282 |
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): | APPLIED MATHEMATICS |
Primary Program Source: |
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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 will develop, analyze, and apply new models for solving three fundamental problems in image processing: (1) edge-preserving noise removal; (2) image decomposition into objects plus textures; (3) recovery of lost information through image interpolation (or 'image inpainting'). The main feature of this new class of models is their ability to isolate and detect in natural scenes target objects that are obstructed by noise, textures, or other occluding objects, without generating erroneous or misleading features in the process. The identification and/or development of false object boundaries has long been a challenge for edge-preserving image processing models; this project seeks to find a universal approach for solving this problem. These new models are based on variational methods and partial differential equations. The investigator will establish their mathematical validity, determine properties of their solutions, develop efficient and accurate numerical schemes for their implementation, and directly apply these models to solve critical problems in the sciences and engineering.
Through existing collaborations with researchers in medical imaging, materials science, geology, pharmaceuticals, and optical character recognition, the investigator and undergraduate students will use these new models to solve key issues in science and technology. These problems include removing noise while isolating key medical features in highly degraded magnetic resonance images, identifying and analyzing the grain structure of nanoscale materials for optimizing high technology metals, and identifying land cover regions that are at high risk for hazards such as wildfires or flooding in remotely sensed images where the boundaries of these regions are obstructed by textures such as roads or topography. Currently, the only reliable methods for treating each of these problems depend on hand-drawn object boundaries. This is prohibitively time consuming on large data sets, so automating the boundary detection process will greatly enhance the state of the art. False object detection can be devastating in any one of these applications, so existing automated methods cannot be directly applied. This project seeks to find theoretically sound approaches that avoid this drawback while removing obstructions and accurately identifying target objects.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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