Logarithm of Odds for Medical Images Analysis

• Activity Number: 59
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Kilian Pohl*+
• Companies: SRI International/Stanford University
• Keywords: Logarithm of Odds ; Medical Image Analysis ; Bayes' Rule ; Variational Mean Field ; Riemannian manifold

Abstract

Statistical interpretations of shapes are popular in medical image analysis to differentiate objects within a single subject or across populations. We revisit the Logarithm of Odds to embed statistical shape models into a vector space structure. We show that the addition operation on the space of Logarithm of Odds relates to Bayes' rule and infers Riemannian manifolds on the simplex of multinomial probabilities that define the family of prior invariant metrics.

To highlight the benefits of this representation, we will focus on two applications. First, we develop a new curve evolution formulation for estimating the posterior distribution of objects in medical images. We combine the variational mean field approach with a continuous space formulation to derive a Maximum a-Posteriori solution that is reminiscent of popular level-set implementations. Second, we present a compact encoding of the shape and brain connectivity of white matter fibers. This representation results in a statistical model that naturally infers grouping of individual fibers into clusters and comparing those clusters within individual subjects and across populations.