A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions

globally and compactly supported basis functions is an active
area of research.

Fitting 3D scattered data by local, compactly supported, basis functions
leads to a simpler and faster computation procedure, while a practical
usage of globally supported basis functions requires sophisticated
mathematical techniques. On the other hand, globally supported basis
functions are extremely useful in repairing incomplete data
while approaches based on compactly supported functions are
sensitive to the density of interpolated/approximated scattered data.

In this talk, I will present a multi-scale approach to 3D scattered
data interpolation with compactly supported basis functions.
The approach is an attempt to integrate the best aspects of shape
modeling with locally and globally supported basis functions.
Employing compactly supported functions leads to an efficient
computational procedure, while a coarse-to-fine hierarchy makes
the proposed method insensitive to the denstity of scattered
data and allows us to restore large parts of missed data.