title: Multilevel principal component analysis (mPCA) in shape analysis: A feasibility study in medical and dental imaging.
abstract: OBJECTIVE
  Methods used in image processing should reflect any multilevel structures inherent in the image dataset or they run the risk of functioning inadequately. We wish to test the feasibility of multilevel principal components analysis (PCA) to build active shape models (ASMs) for cases relevant to medical and dental imaging.
  
  
  METHODS
  Multilevel PCA was used to carry out model fitting to sets of landmark points and it was compared to the results of "standard" (single-level) PCA. Proof of principle was tested by applying mPCA to model basic peri-oral expressions (happy, neutral, sad) approximated to the junction between the mouth/lips. Monte Carlo simulations were used to create this data which allowed exploration of practical implementation issues such as the number of landmark points, number of images, and number of groups (i.e., "expressions" for this example). To further test the robustness of the method, mPCA was subsequently applied to a dental imaging dataset utilising landmark points (placed by different clinicians) along the boundary of mandibular cortical bone in panoramic radiographs of the face.
  
  
  RESULTS
  Changes of expression that varied between groups were modelled correctly at one level of the model and changes in lip width that varied within groups at another for the Monte Carlo dataset. Extreme cases in the test dataset were modelled adequately by mPCA but not by standard PCA. Similarly, variations in the shape of the cortical bone were modelled by one level of mPCA and variations between the experts at another for the panoramic radiographs dataset. Results for mPCA were found to be comparable to those of standard PCA for point-to-point errors via miss-one-out testing for this dataset. These errors reduce with increasing number of eigenvectors/values retained, as expected.
  
  
  CONCLUSIONS
  We have shown that mPCA can be used in shape models for dental and medical image processing. mPCA was found to provide more control and flexibility when compared to standard "single-level" PCA. Specifically, mPCA is preferable to "standard" PCA when multiple levels occur naturally in the dataset.
authors.affiliation: School of Dentistry, Cardiff University, Heath Park, Cardiff CF14 4XY, United Kingdom. Electronic address: farnelld@cardiff.ac.uk.
authors.forename: D J J
authors.initials: DJ
authors.lastname: Farnell
authors.affiliation: School of Dentistry, Cardiff University, Heath Park, Cardiff CF14 4XY, United Kingdom.
authors.forename: H
authors.initials: H
authors.lastname: Popat
authors.affiliation: School of Dentistry, Cardiff University, Heath Park, Cardiff CF14 4XY, United Kingdom.
authors.forename: S
authors.initials: S
authors.lastname: Richmond
mesh_terms: D003952:Diagnostic Imaging; D005240:Feasibility Studies; D006801:Humans; D009010:Monte Carlo Method; D025341:Principal Component Analysis; D011862:Radiography, Panoramic
keywords: Active shape models; Dentistry; Multilevel PCA