Publication details

Detection of non-affine shape outliers for matched-pair shape data

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KATINA Stanislav

Year of publication 2012
Type Article in Periodical
Magazine / Source Tatra Mountains Mathematical Publications
MU Faculty or unit

Faculty of Science

Field Applied statistics, operation research
Keywords shape outliers; relative warp analysis; matched-pair shape differences; bagplots; thin-plate splines; cleft lip/palate
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Description Cleft lip/palate (CLP) is a relatively common birth defect so disfiguring that nowadays it is almost always corrected surgically as early as possible. The postnatal surgical correction does not, however, result in a normally growing upper jaw, but instead, owing to scar tissue, one that grows abnormally. It is important to decide if a clinical treatment group is homogeneous. The example involves data from digitally processed lateral X-ray films of 48 boys who have complete unilateral CLP but no other malformation. 22 landmarks were represented by their Procrustes shape coordinates, principal components of matched-pair differences were examined, and the distribution of the 48 shape changes was studied for outliers in the affine and non-affine subspaces of the full Procrustes shape and form space. To separate outliers from inliers we use bagplots. There are no outliers apparent in the affine subspace. In the non-affine subspaces, we found no outliers in the subspace of bending patterns at large scale but four outliers in the subspace of local changes at small scale. Almost the same outliers were found by form-space PCA. These latter are associated with possible creases of the corresponding thin-plate splines. In those cases we can use the same spline formalism to relax the outlying form to an inlier by optimal relaxation along the curve decolletage that weighs bending energy against Procrustes distance and stop relaxation on the fence. These maneuvers suggest a possibly novel and interesting fusion of the Procrustes-spline toolkit with outlier detection. They also have practical implications for craniofacial management of CLP follow-up as well as suggestive implications for outlier detection in applied craniometrics and anthropometrics more generally.
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