Abstract. In computer vision and graphics, various types of symmetries
are extensively studied since symmetry present in objects is a fundamental cue for understanding the shape and the structure of objects. In
this work, we detect the intrinsic reflective symmetry in triangle meshes
where we have to find the intrinsically symmetric point for each point
of the shape. We establish correspondences between functions defined
on the shapes by extending the functional map framework and then recover the point-to-point correspondences. Previous approaches using the
functional map for this task find the functional correspondences matrix
by solving a non-linear optimization problem which makes them slow.
In this work, we propose a closed form solution for this matrix which
makes our approach faster. We find the closed-form solution based on
our following results. If the given shape is intrinsically symmetric, then
the shortest length geodesic between two intrinsically symmetric points is
also intrinsically symmetric. If an eigenfunction of the Laplace-Beltrami
operator for the given shape is an even (odd) function, then its restriction on the shortest length geodesic between two intrinsically symmetric
points is also an even (odd) function. The sign of a low-frequency eigenfunction is the same on the neighboring points. Our method is invariant
to the ordering of the eigenfunctions and has the least time complexity.
We achieve the best performance on the SCAPE dataset and comparable
performance with the state-of-the-art methods on the TOSCA dataset