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Anthony Yezzi
School of Electrical and Computer Engineering
Georgia Institute of Technology
Part I: A PDE approach for measuring tissue thickness
We outline an Eulerian framework for computing the thickness of
tissues between two simply connected boundaries. Thickness is defined
as the length of trajectories which follow a smooth vector field
constructed in the region between the boundaries. A pair of
partial differential equations (PDE's) are then solved and combined to
yield length without requiring the explicit construction of the
trajectories. An efficient, stable, and computationally fast solution
to these PDE's is found by careful selection of finite differences
according to an upwinding condition.
Part II: Shape Priors and Region Based Active Contours
We propose a model-based curve evolution technique for
segmentation of images containing known object types. In particular,
motivated by the work of Leventon, Grimson, and Faugeras,
we derive a parametric model for an
implied representation of the segmenting curve by applying principal
component analysis to a collection of signed distance representations
of the training data. The parameters of this representation are then
calculated to minimize an objective function for segmentation. We
found the resulting algorithm to be computationally efficient, able to
handle multidimensional data, robust to noise and initial contour
placements, while at the same time, avoiding the need for point
correspondences during the training phase of the algorithm.
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