Second order kinematic surface fitting in anatomical structures

Symmetry detection and morphological classification of anatomical structures play pivotal roles in medical image analysis. The application of kinematic surface fitting, a method for characterizing shapes through parametric stationary velocity fields, has shown promising results in computer vision and computer-aided design. However, existing research has predominantly focused on first order rotational velocity fields, which may not adequately capture the intricate curved and twisted nature of anatomical structures. To address this limitation, we propose an innovative approach utilizing a second order velocity field for kinematic surface fitting. This advancement accommodates higher rotational shape complexity and improves the accuracy of symmetry detection in anatomical structures. We introduce a robust fitting technique and validate its performance through testing on synthetic shapes and real anatomical structures. Our method not only enables the detection of curved rotational symmetries (core lines) but also facilitates morphological classification by deriving intrinsic shape parameters related to curvature and torsion. We illustrate the usefulness of our technique by categorizing the shape of human cochleae in terms of the intrinsic velocity field parameters. The results showcase the potential of our method as a valuable tool for medical image analysis, contributing to the assessment of complex anatomical shapes.