Abstract—Shape discretization through union of weighted
points or balls appears as a common representation in different
fields of computer graphics and geometric modeling.
Among others, it has been very successful for implicit surface
reconstruction with radial basis functions, molecular atomic
models, fluid simulation from particle systems and deformation
tracking with particle filters. These representations are
commonly generated from real measurements or numerical
computations, which may require filtering and smoothing operations.
This work proposes a smoothing mechanism for union
of balls that tries to inherit from the scale-space properties
of bi-dimensional curvature motion: it avoids disconnecting
the shape, prevents self-intersection, regularly decreases the
area and convexifies the shape. The smoothing is computed
iteratively by moving each ball of the union according to a
combination of projected planar curvature motions. Experiments
exhibits nice properties of this scale-space.
Keywords-Union of Balls; Scale Spaces; Curvature Motion;