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dc.contributor.authorWakin, Michael
Donoho, David
Choi, Hyeokho
Baraniuk, Richard G.
dc.creatorWakin, Michael
Donoho, David
Choi, Hyeokho
Baraniuk, Richard G.
dc.date.accessioned 2007-10-31T01:09:03Z
dc.date.available 2007-10-31T01:09:03Z
dc.date.issued 2005-08-01
dc.date.submitted 2005-08-01
dc.identifier.citation M. Wakin, D. Donoho, H. Choi and R. G. Baraniuk, "The Multiscale Structure of Non-Differentiable Image Manifolds," 2005.
dc.identifier.urihttps://hdl.handle.net/1911/20432
dc.description Conference Paper
dc.description.abstract In this paper, we study families of images generated by varying a parameter that controls the appearance of the object/scene in each image. Each image is viewed as a point in high-dimensional space; the family of images forms a low-dimensional submanifold that we call an image appearance manifold (IAM). We conduct a detailed study of some representative IAMs generated by translations/rotations of simple objects in the plane and by rotations of objects in 3-D space. Our central, somewhat surprising, finding is that IAMs generated by images with sharp edges are nowhere differentiable. Moreover, IAMs have an inherent multiscale structure in that approximate tangent planes fitted to ps-neighborhoods continually twist off into new dimensions as the scale parameter $\eps$ varies. We explore and explain this phenomenon. An additional, more exotic kind of local non-differentiability happens at some exceptional parameter points where occlusions cause image edges to disappear. These non-differentiabilities help to understand some key phenomena in image processing. They imply that Newton's method will not work in general for image registration, but that a multiscale Newton's method will work. Such a multiscale Newton's method is similar to existing coarse-to-fine differential estimation algorithms for image registration; the manifold perspective offers a well-founded theoretical motivation for the multiscale approach and allows quantitative study of convergence and approximation. The manifold viewpoint is also generalizable to other image understanding problems.
dc.description.sponsorship Texas Instruments
dc.description.sponsorship Office of Naval Research
dc.description.sponsorship National Science Foundation
dc.language.iso eng
dc.publisher SPIE
dc.subjectImage appearance manifolds
non-differentiable manifolds
angle between subspaces
sampling theorems
multiscale registration
pose estimation.
dc.subject.otherMultiscale geometry processing
dc.title The Multiscale Structure of Non-Differentiable Image Manifolds
dc.type Conference paper
dc.date.note 2005-07-07
dc.citation.bibtexName inproceedings
dc.date.modified 2006-06-05
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)
dc.subject.keywordImage appearance manifolds
non-differentiable manifolds
angle between subspaces
sampling theorems
multiscale registration
pose estimation.
dc.citation.location San Diego, CA
dc.citation.conferenceName Proc. SPIE
dc.type.dcmi Text
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1117/12.617822


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  • DSP Publications [508]
    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1317]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students

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