Profile Scale-Spaces for Multiscale Image Match

Abstract

Abstract. We present a novel statistical image-match model for use in Bayesian segmentation, a multiscale extension of image profile models akin to those in Active Shape Models. A spherical-harmonic based 3D shape representation provides a mapping of the object boundary to the sphere S 2 , and a scale-space for profiles on the sphere defines a scalespace on the object. A key feature is that profiles are not blurred across the object boundary, but only along the boundary. This profile scalespace is sampled in a coarse-to-fine fashion to produce features for the statistical image-match model. A framework for model-building and segmentation has been built, and testing and validation are in progress with a dataset of 70 segmented images of the caudate nucleus. Why Are Anatomical Objects So Hard to Segment?Model-based segmentation has come a long way since Kass and Witkin's original snakes [1], but segmentation of anatomical structures from real-world 3D medical images still presents some difficult challenges for automatic methods. Bayesian model-based segmentation balances a geometry prior, guided by a model of the expected object shape, against an image match likelihood, guided by a model of the expected image appearance around the object. Much has been done on the shape representation and prior; here we will focus on the image match model. In many objects, a simple gradient-magnitude based image-match model is insufficient. The profile of the image across the object boundary can vary significantly from one portion of the boundary to another. Some portions of the boundary might not even have a visible contrast, in which case the shape prior is needed to define the contour. In real-world medical images, the contrast-to-noise ratio is often low, and models need to be robust to image noise.In our study, one of the applications we focus on is the caudate nucleus in the human brain. From a partnership with our Psychiatry department, we have access to over 70 high-resolution MRIs (T1-weighted, 1x1x1mm) with highquality manual expert segmentations of both left and right caudates. The manual raters, having spent much effort on developing a reliable protocol for manual segmentation, indicate some of the challenges in caudate segmentation, which motivate a multiscale statistical image-match model for automatic methods.

Statistical shape models for 3D medical image segmentation: A review

“…While the presented approaches cluster boundary appearance with respect to the feature values, Ho and Gerig (2004) suggest a spatial clustering. Working with profile models, they define a profile scale-space and combine profiles hierarchically based on their neighborhood relation.…”

Continuous Medial Representation for Anatomical Structures

“…Instead of defining parametrically, let us define another scalar field using our basis (10) Let us now find the radius field as the solution of some PDE of the form (11) where is some function and is some differential operator on the manifold . Clearly, if for some choice of and such an equation is well-posed, the solution will satisfy the equality constraint (6).…”

“…The key realization in this work is that the equality constraint (6) can be satisfied by defining as the solution of a stationary PDE whose boundary condition incorporates the equality constraint.…”

“…Roughly speaking, this is the approach taken by ASM, where appearance features are obtained by sampling image intensities along fixed-length profiles projected orthogonally from the boundary [2]. When the boundary is represented by a parameterized surface (as in [4] and [5]), each profile is associated with two parameter values, and the distance along the profile can serve as a third 'depth' coordinate for parameterizing the space around the boundary [6]. However, since the profiles have fixed length, they are not guaranteed to span the entire interior of the object and they may intersect, causing ambiguity in the parametrization.…”

Statistical Multi-Object Shape Models

“…Here we assume a likelihood distribution p(I|A) is available. For details on estimating this probability refer to [31,32].…”