Statistical Shape Analysis for the Human Back

Abstract

In this research, Procrustes and Euclidean distance matrix analysis (EDMA) have been investigated for analysing the three-dimensional shape and form of the human back. Procrustes analysis is used to distinguish deformed backs from normal backs. EDMA is used to locate the changes occurring on the back surface due to spinal deformity (scoliosis, kyphosis and lordosis) for back deformity patients. A surface topography system, ISIS2 (Integrated Shape Imaging System 2), is available to measure the three-dimensional back surface. The system presents clinical parameters, which are based on distances and angles relative to certain anatomical landmarks on the back surface. Location, rotation and scale definitely influence these parameters. Although the anatomical landmarks are used in the present system to take some account of patient stance, it is still felt that variability in the clinical parameters is increased by the use of length and angle data. Patients also grow and so their back size, shape and form change between appointments with the doctor. Instead of distances and angles, geometric shape that is independent of location, rotation and scale effects could be measured. This research is mainly focusing on the geometric shape and form change in the back surface, thus removing the unwanted effects. Landmarks are used for describing back information and an analysis of the variability in positioning the landmarks has been carried out for repeated measurements. Generalized Procrustes analysis has been applied to all normal backs to calculate a mean Procrustes shape, which is named the standard normal shape (SNS). Each back (normal and deformed) is then translated, rotated and scaled to give a best fit with the SNS using ordinary Procrustes analysis. Riemannian distances are then estimated between the SNS and all individual backs. The highest Riemannian distance value between the normal backs and the SNS is lower than the lowest Riemannian distance value between the deformed backs and the SNS. The results shows that deformed backs can be differentiated from normal backs. EDMA has been used to estimate a mean form, variance-covariance matrix and mean form difference from all the normal backs. This mean form is named the standard normal form (SNF). The influence of individual landmarks for form difference between each deformed back and the SNF is estimated. A high value indicates high deformity on the location of that landmark and a low value close to 1 indicates less deformity. The result is displayed in a graph that provides information regarding the degree and location of the deformity. The novel aspects of this research lie in the development of an effective method for assessing the three-dimensional back shape; extracting automatic landmarks; visualizing back shape and back form differences.