  Density-equalizing maps are a class of mapping methods in which the shape
deformation is driven by prescribed density information. In recent years, they
have been widely used for data visualization on planar domains and planar
parameterization of open surfaces. However, the theory and computation of
density-equalizing maps for closed surfaces are much less explored. In this
work, we develop a novel method for computing spherical density-equalizing maps
for genus-0 closed surfaces. Specifically, we first compute a conformal
parameterization of the given genus-0 closed surface onto the unit sphere.
Then, we perform density equalization on the spherical domain based on the
given density information to achieve a spherical density-equalizing map. The
bijectivity of the mapping is guaranteed using quasi-conformal theory. We
further propose a method for incorporating the harmonic energy and landmark
constraints into our formulation to achieve landmark-aligned spherical
density-equalizing maps balancing different distortion measures. Using the
proposed methods, a large variety of spherical parameterizations can be
achieved. Applications to surface registration, remeshing, and data
visualization are presented to demonstrate the effectiveness of our methods.
