Novel integro-differential schemes for multiscale image representation

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dc.contributor.advisorTadmor, Eitanen_US
dc.contributor.authorAthavale, Prashant Vinayaken_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2009-10-21T05:30:51Z
dc.date.available2009-10-21T05:30:51Z
dc.date.issued2009en_US
dc.description.abstractMultiscale representation of a given image is the problem of constructing a family of images, where each image in this family represents a scaled version of the given image. This finds its motivation from biological vision studies. Using the hierarchical multiscale image representation proposed by Tadmor et. al. [32], an image is decomposed into sums of simpler `slices', which extract more refined information from the previous scales. This approach motivates us to propose a novel integro-differential equation (IDE), for a multiscale image representation. We examine various properties of this IDE. The advantage of formulating the IDE this way is that, although this IDE is motivated by variational approach, we no longer need to be associated with any minimization problem and can modify the IDE, suitable to our image processing needs. For example, we may need to find different scales in the image, while retaining or enhancing prominent edges, which may define boundaries of objects. We propose some edge preserving modifications to our IDE. One of the important problems in image processing is deblurring a blurred image. Images get blurred due to various reasons, such as unfocused camera lens, relative motion between the camera and the object pictured, etc. The blurring can be modeled with a continuous, linear operator. Recovering a clean image from a blurry image, is an ill-posed problem, which is solved using Tikhonov-like regularization. We propose a different IDE to solve the deblurring problem. We propose hierarchical multiscale scheme based on (BV; L1) decomposition, proposed by Chan, Esedoglu, Nikolova and Alliney [12, 25, 3]. We finally propose another hierarchical multiscale representation based on a novel weighted (BV;L1) decomposition.en_US
dc.format.extent3609381 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/9691
dc.language.isoen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledEngineering, Electronics and Electricalen_US
dc.subject.pquncontrolleddeblurringen_US
dc.subject.pquncontrolleddenoisingen_US
dc.subject.pquncontrolledintegro-differential equationen_US
dc.subject.pquncontrolledmultiscale representationen_US
dc.subject.pquncontrollednatural imagesen_US
dc.subject.pquncontrolledtotal variationen_US
dc.titleNovel integro-differential schemes for multiscale image representationen_US
dc.typeDissertationen_US

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