Graph-based Construction and Search of a Similarity Manifold

Sevilmis, Berk

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Year:: 2020
Contributor:: Sevilmis, Berk (creator); Kimia, Benjamin (Advisor); Felzenszwalb, Pedro (Reader); Shakhnarovich, Greg (Reader); Brown University. Engineering: Electrical Sciences and Computer Engineering (sponsor)
Genre:: theses
Subject:: Computer Vision; proximity graphs; graph based indexing and search; dense semantic correspondence
Extent:: , None p.

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Abstract:: Many types of data observed in high dimensional spaces typically lie on or near low-dimensional manifolds and have much lower intrinsic dimension. Visual data captured in the form of an image, for example, is observed as a point in a vector space of very high dimension that is equal to its number of pixels, yet the types of visual variations that give rise to different images have fewer intrinsic degrees of freedom, namely the reduced dimension of the manifold the visual data lies on. A key issue is how to represent a data manifold and develop a methodology that allows working on the manifold rather than the ambient space it is embedded in. A graph is a natural representation for the discrete approximation of a data manifold. The set of vertices in a graph represent discrete samples of the manifold while the set of edges represent the local topology. In this thesis, a type of a proximity graph, namely the Relative Neighborhood Graph (RNG) is used to represent a data manifold which requires addressing the problems of efficient graph construction and finding neighbors of, i.e., locating, unobserved data items on the manifold which are collectively termed as graph-based “dataset/database indexing and search”. The first part of the thesis proposes a new family of proximity graphs to devise algorithms for efficient, hierarchical, and incremental construction and search of the RNG. The second part of the thesis proposes an application of image alignment, one of the core problems in computer vision, that makes use of image manifolds which are represented by graphs approximating the RNGs, which exemplifies and further supports the idea of performing operations directly on data manifolds.
Notes:: Thesis (Ph. D.)--Brown University, 2020

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Sevilmis, Berk, "Graph-based Construction and Search of a Similarity Manifold" (2020). Electrical Sciences and Computer Engineering Theses and Dissertations. Brown Digital Repository. Brown University Library. https://repository.library.brown.edu/studio/item/bdr:4trguakq/

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Electrical Sciences and Computer Engineering Theses and Dissertations

Theses and Dissertations for the Electrical Sciences and Computer Engineering department.
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