  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.
