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Scoliosis is a common 3D spinal deformity that leads to aesthetic deformity of the torso. The cancer risk associated with the current diagnosis method, X-rays, motivates modifications of this method. This is especially important because of the high occurrence of scoliosis among teenagers. The computer has begun to take more and more important roles in the medical field; it has been used to study almost every part of the human body.

Many spatial deformation techniques have been developed: Free-form deformation and its several extensions, smoothing spline models, space deformations, etc. They offer the user control over deformation by different means: marker points, control lattices and even direct manipulations.

This project approached the problem of visualization and prediction of scoliosis with a method of spatial deformation, specifically, thin-plate spline models. For the prediction of scoliosis, we work on both the R^d index set, which we use for spatial interpolation and approximation, and the time index set, which we use for time-interpolation and time-extrapolation. We test and validate our models with real patient data. The real testing results we got are reasonable, based on the accuracy level of the available data: the external deformation results are pretty good, while the internal deformation results show some errors. Later work could extend from these two points, increase the accuracy of the real data and take more internal physical information into account.

A special contribution of this project is: we show the link between the thin-plate spline models based on [0,1] index set and R^d index set. These are two different spline models, but after some mathematical work (permutation and comparison), we can see that they really share something in common, which is quite useful.

Online version

Available here in English in Adobe PDF format (4.2 MB).


  author =       "Di Jiang",
  title =        "Visualization and Prediction of Spatial Deformation using Thin-plate Splines in the Context of Scoliosis",
  month =        aug,
  year =         2003,
  type =         "M.Sc. Thesis",
  school =       "D{\'e}partement d'Informatique et Recherche 
                  Op{\'e}rationnelle, Universit{\'e} de Montr{\'e}al",