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Shape
Transformations
Using
Union of
Spheres
Vishwa
Ranjan and
Alain
Fournier
TR-95-30
ABSTRACT
Shape interpolation is the process of transforming continuously one object
into another. This is useful in applications such as object recognition,
object registration and computer animation. Unfortunately, "good" shape
interpolation is as ill-defined as "shape" itself. To be able to control the
process in a useful way, we need a representation for the objects using
primitives which capture at least some aspects of their shape, with methods to
convert other representations to this one. We present here a method to
interpolate between two objects represented as a union of spheres. We
briefly describe the representation and its properties, and show how to use it
to interpolate. Once a distance metric between the spheres is defined (we show
different metric producing controlled effects), the algorithm optimally
matches the spheres in the two models using a bipartite graph. The
transformation then consists in interpolating between the matched spheres. If
the union of spheres has been simplified, the other spheres are matched as a
function of their positions within their representative cluster. Examples are
shown and discussed with two- and three-dimensional objects. The results show
that the union of spheres helps capture some notion of shape, and helps to
automatically match and interpolate shapes.