How Many Templates Does It Take for a Good Segmentation?: Error Analysis in Multiatlas Segmentation as a Function of Database Size

Abstract

This paper proposes a novel formulation to model and analyze the statistical characteristics of some types of segmentation problems that are based on combining label maps / templates / atlases. Such segmentation-by-example approaches are quite powerful on their own for several clinical applications and they provide prior information, through spatial context, when combined with intensity-based segmentation methods. The proposed formulation models a class of multiatlas segmentation problems as nonparametric regression problems in the high-dimensional space of images. The paper presents a systematic analysis of the nonparametric estimation's convergence behavior (i.e. characterizing segmentation error as a function of the size of the multiatlas database) and shows that it has a specific analytic form involving several parameters that are fundamental to the specific segmentation problem (i.e. chosen anatomical structure, imaging modality, registration method, label-fusion algorithm, etc.). We describe how to estimate these parameters and show that several brain anatomical structures exhibit the trends determined analytically. The proposed framework also provides per-voxel confidence measures for the segmentation. We show that the segmentation error for large database sizes can be predicted using small-sized databases. Thus, small databases can be exploited to predict the database sizes required ("how many templates") to achieve "good" segmentations having errors lower than a specified tolerance. Such cost-benefit analysis is crucial for designing and deploying multiatlas segmentation systems.

Comparison of image intensity, local, and multi‐atlas priors in brain tissue classification

“…This is the main weakness of adopting the atlas selection in MAS. In addition to optimizing the number of atlases fused in MAS by applying cross‐validation, an alternative approach was proposed, which models MAS as a nonparametric regression problem and predicts the number of atlases required to keep the segmentation error below a specified tolerance level.…”

“…29 After that, the selected atlases are combined using global or local label fusion methods for the final tissue classification. 26,[30][31][32][33][34] Different from modeling MAS as a label prior, a statistical nonparametric regression framework was proposed 35,36 to model MAS in the high-dimensional space of images. The expected segmentation error of the regression estimator was characterized as a function of the size of the atlas database and optimized by estimating a set of parameters fundamental to the specific segmentation task.…”

Multi-Template Mesiotemporal Lobe Segmentation: Effects of Surface and Volume Feature Modeling

“…Alternatively, the very slow increase in Dice index observed at the test with 90+ templates likely explains the increase of the templates would not gain a very significant improvement of the current method. There have been studies dealing with the size of the template library using statistical models (Awate et al, 2012 ; Awate and Whitaker, 2014 ).…”

A Segmentation Method of Foramen Ovale Based on Multiatlas

“…However, Aljabar et al [ 20 ] found that the segmentation accuracy does not completely increase with the increase of the number of atlases, and the more the number of atlases, the time for segmentation calculation will also increase linearly. Awate et al's research [ 21 ] shows that the most appropriate number of atlases is about 10. Therefore, this article will select 10 moving images from the atlas for registration with the fixed image.…”