Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models

doi:10.1016/S1361-8415(01)80003-7

Medical Image Analysis

Volume 1, Issue 1, March 1996, Pages 19-34

https://doi.org/10.1016/S1361-8415(01)80003-7 Get rights and content

Abstract

This paper describes a new model-based segmentation technique combining desirable properties of physical models (snakes), shape representation by Fourier parametrization, and modelling of natural shape variability. Flexible parametric shape models are represented by a parameter vector describing the mean contour and by a set of eigenmodes of the parameters characterizing the shape variation. Usually the segmentation process is divided into an initial placement of the mean model and an elastic deformation restricted to the model variability. This, however, leads to a separation of biological variation due to a global similarity transform from small-scale shape changes originating from elastic deformations of the normalized model contours only. The performance can be considerably improved by building shape models normalized with respect to a small set of stable landmarks (AC-PC in our application) and by explaining the remaining variability among a series of images with the model flexibility. This way the image interpretation is solved by a new coarse-to-fine segmentation procedure based on the set of deformation eigenmodes, making a separate initialization step unnecessary. Although straightforward, the extension to 3-D is severely impeded by difficulties arising during the generation of a proper surface parametrization for arbitrary objects with spherical topology. We apply a newly developed surface parametrization which achieves a uniform mapping between object surface and parameter space. The 3-D procedure is demonstrated by segmenting deep structures of the human brain from MR volume data.

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This implies that the number of parameters (i.e., SPHARM coefficients) needed to describe a shape instance is lower than other shape modeling methods like PDM. In medical image, SPHARM has played an crucial role in 3D-shape representation and modeling of anatomic structures in several applications, including computer assisted diagnosis (Shen et al., 2004; Styner et al., 2004; 2006; Shen et al., 2009b; 2009a), rigid registration (Dillenseger et al., 2006; Shen et al., 2009b) and organ segmentation (Brechbühler et al., 1995; Székely et al., 1996; Kelemen et al., 1999; Gerig et al., 2001; Tateyama et al., 2012), among others. In most of these applications, statistical shape models were developed by applying PCA to a training population of organ surfaces parameterized with SPHARM coefficients, where eigenmodes of maximum variation around the mean shape were calculated.
In radiotherapy for prostate cancer irradiation of neighboring organs at risk may lead to undesirable side-effects. Given this setting, the bladder presents the largest inter-fraction shape variations hampering the computation of the actual delivered dose vs. planned dose. This paper proposes a population model, based on longitudinal data, able to estimate the probability of bladder presence during treatment, using only the planning computed tomography (CT) scan as input information. As in previously-proposed principal component analysis (PCA) population-based models, we have used the data to obtain the dominant eigenmodes that describe bladder geometric variations between fractions. However, we have used a longitudinal analysis along each mode in order to properly characterize patient’s variance from the total population variance. We have proposed is a mixed-effects (ME) model in order to separate intra- and inter-patient variability, in an effort to control confounding cohort effects. Other than using PCA, bladder shapes are represented by using spherical harmonics (SPHARM) that additionally enables data compression without information lost. Based on training data from repeated CT scans, the ME model was thus implemented following dimensionality reduction by means of SPHARM and PCA. We have evaluated the model in a leave-one-out cross validation framework on the training data but also using independent data. Probability maps (PMs) were thus generated with several draws from the learnt model as predicted regions where the bladder will likely move and deform. These PMs were compared with the actual regions using metrics based on mutual information distance and misestimated voxels. The prediction was also compared with two previous population PCA-based models. The proposed model was able to reduce the uncertainties in the estimation of the probable region of bladder motion and deformation. This model can thus be used for tailoring radiotherapy treatments.
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Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models

Abstract

Section snippets

Supplementary Files

CVGIP: Image Understanding

CVGIP: Image Understanding

Image Vision Comp.

CVGIP

Surface parametrization and shape description

Proc. VBC'92 Conf.

Active shape models - ‘smart snakes’

Proc. British Mach. Vision Conf. '92

The Use of Active Shape Models For Locating Structures in Medical Imaging

Proc. IPMI'93

Automatic Segmentation of Dual-Echo MR Head Data

Proc. IPMI'91 (Wye)

Theoretische Physik - Ein Lehr- und Übungsbuch für Anfangssemester

Three-dimensional display of human organs from computer tomograms

CGIP

A Generic System for Image Interpretation Using Flexible Templates

Proc. British Mach. Vision Conf.'92

Model-Based Interpretation of 3-D Medical Images

Snakes: active contour models

Int. J. Comp. Vision