Non-Euclidean classification of medically imaged objects via s-reps

Abstract

Classifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging. We propose a novel classification scheme that uses a skeletal representation to provide rich non-Euclidean geometric object properties. Our statistical method combines distance weighted discrimination (DWD) with a carefully chosen Euclideanization which takes full advantage of the geometry of the manifold on which these non-Euclidean geometric object properties (GOPs) live. Our method is evaluated via the task of classifying 3D hippocampi between schizophrenics and healthy controls. We address three central questions. 1) Does adding shape features increase discriminative power over the more standard classification based only on global volume? 2) If so, does our skeletal representation provide greater discriminative power than a conventional boundary point distribution model (PDM)? 3) Especially, is Euclideanization of non-Euclidean shape properties important in achieving high discriminative power? Measuring the capability of a method in terms of area under the receiver operator characteristic (ROC) curve, we show that our proposed method achieves strongly better classification than both the classification method based on global volume alone and the s-rep-based classification method without proper Euclideanization of non-Euclidean GOPs. We show classification using Euclideanized s-reps is also superior to classification using PDMs, whether the PDMs are first Euclideanized or not. We also show improved performance with Euclideanized boundary PDMs over non-linear boundary PDMs. This demonstrates the benefit that proper Euclideanization of non-Euclidean GOPs brings not only to s-rep-based classification but also to PDM-based classification.

Skeletal Shape Correspondence Through Entropy

“…This observation is consistent with [4, 22, 61] that the use of point information alone ignores many of the higher order geometric features that s-reps provide, such as orientation and width.…”

A segmentation editing framework based on shape change statistics

“…10 It has been shown in various publications to be more powerful in capturing the interior of most non-branching anatomic objects and providing efficient shape statistical summaries when compared to boundary point distribution models (PDMs). 10, 13–15 An s-rep fitting procedure starts with an initial template model of the object and a distance map that was computed from the binary image of the target object. The fitting process is based on thin plate spline transformation of a spherical harmonic representation of the surfaces of the template (initial caudate model) as well as the target objects.…”

Diffeomorphic Medial Modeling

“…. , b n , and condition (5) ensures that this ball is inscribed in φ t O, and thus an MIB in φ t O. Note that conditions (3) and (4) only involve local geometry of φ t B O around the tuple, while condition (5) requires the knowledge of the entire φ t B O .…”

“…Medial models have also been used to impose geometrical constraints on automatic segmentation of sheet-like structures, e.g., imposing prior knowledge about heart wall thickness during myocardium segmentation [11]. Medial modeling methods include m-reps [10] and s-reps [5] (which approximate medial axis surfaces using discrete primitives), cm-reps [12] (which use splines and subdivision surfaces to model medial axis surfaces), and boundary-constrained m-reps [13] (which implicitly model medial geometry by imposing symmetry constraints on a boundary-based model).…”