---
res:
bibo_abstract:
- We introduce a new approach to modelling gradient flows of contours and surfaces.
While standard variational methods (e.g. level sets) compute local interface motion
in a differential fashion by estimating local contour velocity via energy derivatives,
we propose to solve surface evolution PDEs by explicitly estimating integral motion
of the whole surface. We formulate an optimization problem directly based on an
integral characterization of gradient flow as an infinitesimal move of the (whole)
surface giving the largest energy decrease among all moves of equal size. We show
that this problem can be efficiently solved using recent advances in algorithms
for global hypersurface optimization [4, 2, 11]. In particular, we employ the
geo-cuts method [4] that uses ideas from integral geometry to represent continuous
surfaces as cuts on discrete graphs. The resulting interface evolution algorithm
is validated on some 2D and 3D examples similar to typical demonstrations of level-set
methods. Our method can compute gradient flows of hypersurfaces with respect to
a fairly general class of continuous functional and it is flexible with respect
to distance metrics on the space of contours/surfaces. Preliminary tests for standard
L2 distance metric demonstrate numerical stability, topological changes and an
absence of any oscillatory motion.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Yuri
foaf_name: Boykov, Yuri
foaf_surname: Boykov
- foaf_Person:
foaf_givenName: Vladimir
foaf_name: Vladimir Kolmogorov
foaf_surname: Kolmogorov
foaf_workInfoHomepage: http://www.librecat.org/personId=3D50B0BA-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Daniel
foaf_name: Cremers, Daniel
foaf_surname: Cremers
- foaf_Person:
foaf_givenName: Andrew
foaf_name: Delong, Andrew
foaf_surname: Delong
bibo_doi: 10.1007/11744078_32
bibo_volume: 3953
dct_date: 2006^xs_gYear
dct_publisher: Springer@
dct_title: An integral solution to surface evolution PDEs via geo cuts@
...