Two-chart Beltrami Optimization for Distortion-Controlled Spherical Bijection with Application to Brain Surface Registration

Many genus-0 surface mapping tasks such as landmark alignment, feature matching, and image-driven registration, can be reduced (via an initial spherical conformal map) to optimizing a spherical self-homeomorphism with controlled distortion. However, existing works lack efficient mechanisms to control the geometric distortion of the resulting mapping. To resolve this issue, we formulate this as a Beltrami-space optimization problem, where the angle distortion is encoded explicitly by the Beltrami differential and bijectivity can be enforced through the constraint $\|μ\|_{\infty}