Previously, we discussed the limitations of assuming a default pinhole model in camera modeling, offering an alternative formulation using the unit sphere instead of the normalized image plane. Continuous optimization algorithms in robotics often involve minimizing errors or risks. In Differential Geometry, traveling efficiently on the unit sphere involves following geodesics or great circles rather than Rhumb Lines. Working with manifolds involves intrinsic vs. extrinsic representations, with the Tangent Bundle being a key concept. Optimization on a manifold requires computing directions and moving parameters using the exponential map. Differential Geometry provides a new perspective on multi-variable optimization, highlighting the importance of understanding tangent spaces and continuous symmetry in Euclidean space.
https://www.tangramvision.com/blog/the-deceptively-asymmetric-unit-sphere