{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Computational Conformal Geometry and it's Applications","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/77312"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"Conformal geometry has deep roots in pure mathematics, combining complex analysis, Riemann surface theory, algebraic geometry, differential geometry and algebraic topology. Computational conformal geometry plays an important role in digital geometry processing. Recently, theory of discrete conformal geometry and algorithms of computational conformal geometry have been developed[50]. A series of practical algorithms are presented to compute conformal mapping, which has been broadly applied in a lot of practical fields, including computer graphics, medical imaging, wireless sensor networks, visualization, and so on. In this thesis proposal, we address three applications of computational conformal geometry in medical imaging, wireless sensor networks and computer graphics respectively. Firstly, automatic computation of surface correspondence via harmonicmap is an active research field in computer vision. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquer this problem by changing the Riemannian metric on the target surface to a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on the Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We apply our algorithm to study constrained surface registration problem which applied to both medical and computer vision applications. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic, and achieve relative high performance when evaluated with some popular surface registration evaluation standards. Secondly, in a wireless sensor network, random walk on a graph is a Markov chain and thus is memoryless as the next node to visit depends only on the current node and not on the sequence of events that preceded it. With these properties, random walk and its many variations have been used in network routing to randomize the traffic pattern and hide the location of the data sources. We show a myth in common understanding of the memoryless property of a random walk applied for protecting source location privacy in a wireless sensor network. In particular, if one monitors only the network boundary and records the first boundary node hit by a random walk, this distribution can be related to the location of the source node. For the scenario of a single data source, a very simple algorithm which integrates along the network boundary would reveal the location of the source. We also develop a generic algorithm to reconstruct the source locations for various sources that have simple descriptions (e.g., k source locations, sources on a line segment, sources in a disk). This represents a new type of traffic analysis attack for invading sensor data location privacy and essentially re-opens the problem for further examination. Finally, in medical imaging, we propose a new colon flattening algorithm that is efficient, shape-preserving, and robust to topological noise. Unlike previous approaches, which require a mandatory topological denoising to remove fake handles, our algorithm directly flattens the colon surface without any denoising. In our method, we replace the original Euclidean metric of the colon surface with a heat diffusion metric that is insensitive to topological noise. Using this heat diffusion metric, we then solve a Laplacian equation followed by an integration step to compute the final flattening. We demonstrate that our method is shape-preserving and the shape of the polyps are well preserved. The flattened colon also provides an efficient way to enhance the navigation and inspection in virtual colonoscopy. We further show how the existing colon registration pipeline is made more robust by using our colon flattening. We have tested our method on several colon wall surfaces and the experimental results demonstrate the robustness and the efficiency of our method."},{"label":"dcterms.available","value":"2017-09-20T16:52:29Z"},{"label":"dcterms.contributor","value":"Gu, Xianfeng"},{"label":"dcterms.creator","value":"Shi, Rui"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:52:29Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:52:29Z"},{"label":"dcterms.description","value":"Department of Computer Science."},{"label":"dcterms.extent","value":"136 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/77312"},{"label":"dcterms.issued","value":"2015-08-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:52:29Z (GMT). No. of bitstreams: 1\nShi_grad.sunysb_0771E_12115.pdf: 44593103 bytes, checksum: 9830672b0fc1550c96a14816e1d54ef2 (MD5)\n  Previous issue date: 2014"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Computer Vision, Conformal Geometry, Medical Imaging, Wireless Sensor Network"},{"label":"dcterms.title","value":"Computational Conformal Geometry and it's Applications"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/16%2F76%2F71%2F167671015183858565245197409373270602247/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/16%2F76%2F71%2F167671015183858565245197409373270602247","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}