677 research outputs found
Characterizing Retinotopic Mapping Using Conformal Geometry and Beltrami Coefficient: a Preliminary Study
abstract: Functional magnetic resonance imaging (fMRI) has been widely used to measure the retinotopic organization of early visual cortex in the human brain. Previous studies have identified multiple visual field maps (VFMs) based on statistical analysis of fMRI signals, but the resulting geometry has not been fully characterized with mathematical models. This thesis explores using concepts from computational conformal geometry to create a custom software framework for examining and generating quantitative mathematical models for characterizing the geometry of early visual areas in the human brain. The software framework includes a graphical user interface built on top of a selected core conformal flattening algorithm and various software tools compiled specifically for processing and examining retinotopic data. Three conformal flattening algorithms were implemented and evaluated for speed and how well they preserve the conformal metric. All three algorithms performed well in preserving the conformal metric but the speed and stability of the algorithms varied. The software framework performed correctly on actual retinotopic data collected using the standard travelling-wave experiment. Preliminary analysis of the Beltrami coefficient for the early data set shows that selected regions of V1 that contain reasonably smooth eccentricity and polar angle gradients do show significant local conformality, warranting further investigation of this approach for analysis of early and higher visual cortex.Dissertation/ThesisM.S. Computer Science 201
Density-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps
of simply-connected open surfaces in . Using a natural principle
of density diffusion in physics, we propose an effective algorithm for
computing density-equalizing flattening maps with any prescribed density
distribution. By varying the initial density distribution, a large variety of
mappings with different properties can be achieved. For instance,
area-preserving parameterizations of simply-connected open surfaces can be
easily computed. Experimental results are presented to demonstrate the
effectiveness of our proposed method. Applications to data visualization and
surface remeshing are explored
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