Award Abstract # 0505729
RUI: Variational and PDE based methods for image processing

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: DUQUESNE UNIVERSITY OF THE HOLY SPIRIT
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: FY 2005 = $139,900.00
History of Investigator:
  • Stacey Levine (Principal Investigator)
    sel@mathcs.duq.edu
Recipient Sponsored Research Office: Duquesne University
600 FORBES AVENUE
PITTSBURGH
PA  US  15282
(412)396-1537
Sponsor Congressional District: 12
Primary Place of Performance: Duquesne University
600 FORBES AVENUE
PITTSBURGH
PA  US  15282
Primary Place of Performance
Congressional District:
12
Unique Entity Identifier (UEI): NGYSJ2L1LZX3
Parent UEI: R8GSG4QZV989
NSF Program(s): APPLIED MATHEMATICS
Primary Program Source: app-0105 
Program Reference Code(s): OTHR, 9229, 0000
Program Element Code(s): 126600
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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Stacey Levine "An Adaptive Variational Model for Image Decomposition" Energy Minimization Methods in Computer Vision and Pattern Recognition, Springer Verlag LCNS , v.3757 , 2005 , p.382
Yunmei Chen, Stacey Levine, Murali Rao "Variable Exponent, Linear Growth Functionals in Image Restoration" SIAM Journal of Applied Mathematics , v.66(4) , 2006 , p.1383

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