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

Katina, Stanislav

Tatra Mountains Mathematical Publications, Tome 51 (2012), / Harvested from Mathematical Institute

Résumé

Cleft lip/palate (CLP) is a relatively common birth defect so disfiguringthat nowadays it is almost always corrected surgically as early as possible.The postnatal surgical correction does not, however, result in a normally growingupper jaw, but instead, owing to scar tissue, one that grows abnormally. It isimportant to decide if a clinical treatment group is homogeneous. The exampleinvolves data from digitally processed lateral X-ray films of 48 boys who have completeunilateral CLP but no other malformation. 22 landmarks were representedby their Procrustes shape coordinates, principal components of matched-pair differenceswere examined, and the distribution of the 48 shape changes was studiedfor outliers in the affine and non-affine subspaces of the full Procrustes shapeand form space. To separate outliers from inliers we use bagplots. There are nooutliers apparent in the affine subspace. In the non-affine subspaces, we foundno outliers in the subspace of bending patterns at large scale but four outliersin the subspace of local changes at small scale. Almost the same outliers werefound by form-space PCA. These latter are associated with possible creases ofthe corresponding thin-plate splines. In those cases we can use the same splineformalism to relax the outlying form to an inlier by optimal relaxation alongthe curve d´ecolletage that weighs bending energy against Procrustes distanceand stop relaxation on the fence. These maneuvers suggest a possibly novel andinteresting fusion of the Procrustes-spline toolkit with outlier detection. Theyalso have practical implications for craniofacial management of CLP follow-up aswell as suggestive implications for outlier detection in applied craniometrics andanthropometrics more generally.

Détail

Publié le : 2012-01-01
DOI : https://doi.org/10.2478/tatra.v51i1.153