Title:
Label Space: A Coupled Multi-shape Representation
Label Space: A Coupled Multi-shape Representation
Author(s)
Malcolm, James G.
Rathi, Yogesh
Shenton, Martha E.
Tannenbaum, Allen R.
Rathi, Yogesh
Shenton, Martha E.
Tannenbaum, Allen R.
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Abstract
Richly labeled images representing several sub-structures of an organ occur quite frequently in medical images. For example, a typical brain image can be labeled into grey matter, white matter or cerebrospinal fluid, each of which may be subdivided further. Many manipulations such as interpolation, transformation, smoothing, or registration need to be performed on these images before
they can be used in further analysis. In this work, we present a novel multi-shape
representation and compare it with the existing representations to demonstrate
certain advantages of using the proposed scheme. Specifically, we propose label
space, a representation that is both flexible and well suited for coupled multishape analysis. Under this framework, object labels are mapped to vertices of a
regular simplex, e.g. the unit interval for two labels, a triangle for three labels, a
tetrahedron for four labels, etc. This forms the basis of a convex linear structure
with the property that all labels are equally spaced. We will demonstrate that this
representation has several desirable properties: algebraic operations may be performed directly, label uncertainty is expressed equivalently as a weighted mixture
of labels or in a probabilistic manner, and interpolation is unbiased toward any label
or the background. In order to demonstrate these properties, we compare label
space to signed distance maps as well as other implicit representations in tasks
such as smoothing, interpolation, registration, and principal component analysis.
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Date Issued
2008-09
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Text
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Post-print