Shape Modeling

Bayesian Hierarchical Modeling of Simply Connected 2D Shapes

Kelvin Gu, Debdeep Pati & David B. Dunson

Duke University

December 2011

(WARNING: this is OUT OF DATE, but will be updated soon!)

Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical probability models for the shape and size of simply connected 2D closed curves, avoiding the need to specify landmarks through modeling the entire curve while borrowing information across curves for related objects. Prevalent approaches follow a fundamentally different strategy in providing an initial point estimate of the curve and/or locations of landmarks, which are then fed into subsequent statistical analyses. Such two-stage methods ignore uncertainty in the first stage, and do not allow borrowing of information across objects in estimating object shapes and sizes. Our fully Bayesian hierarchical model is based on multiscale deformations within a linear combination of cyclic basis characterization, which facilitates automatic alignment of the different curves accounting for uncertainty. The characterization is shown to be highly flexible in representing 2D closed curves, leading to a nonparametric Bayesian prior with large support. Efficient Markov chain Monte Carlo methods are developed for simultaneous analysis of many objects. The methods are evaluated through simulation examples and applied to yeast cell imaging data.

Keywords: Bayesian nonparametrics, cyclic basis, deformation, hierarchical modeling, image cytometry, multiscale, 2d shapes

Manuscript available as a PDF.


Cell Segmentation via Shape Modeling

Kelvin Gu, Michael B. Mayhew & Alex J. Hartemink

Duke University

November 2011

(WARNING: this is OUT OF DATE, but will be updated soon!)

We develop a novel generative model for arbitrary 2D shapes, based on multiscale deformation. We demonstrate how our model can be used to segment objects within an image by fitting a shape-sensitive contour to each object's boundary. We demonstrate our model by performing segmentation on differential interference contrast microscopy (DIC) images of yeast, where many cells possess aberrant shape and boundaries that contain major gaps or touch other cells. Our method can be seen as a 'shape-sensitive' and statistical active contour.

Keywords: active contours, generative modeling, Bayesian nonparametrics, shape modeling, morphometry, Bezier curves, cell segmentation

Manuscript available as a PDF.