Optimizing Parametric Total Variation Models
Author
Summary, in English
One of the key factors for the success of recent energy
minimization methods is that they seek to compute global
solutions. Even for non-convex energy functionals, optimization
methods such as graph cuts have proven to produce
high-quality solutions by iterative minimization based on
large neighborhoods, making them less vulnerable to local
minima. Our approach takes this a step further by enlarging
the search neighborhood with one dimension.
In this paper we consider binary total variation problems
that depend on an additional set of parameters. Examples
include:
(i) the Chan-Vese model that we solve globally
(ii) ratio and constrained minimization which can be formulated
as parametric problems, and
(iii) variants of the Mumford-Shah functional.
Our approach is based on a recent theorem of Chambolle
which states that solving a one-parameter family of binary
problems amounts to solving a single convex variational
problem. We prove a generalization of this result and show
how it can be applied to parametric optimization.
minimization methods is that they seek to compute global
solutions. Even for non-convex energy functionals, optimization
methods such as graph cuts have proven to produce
high-quality solutions by iterative minimization based on
large neighborhoods, making them less vulnerable to local
minima. Our approach takes this a step further by enlarging
the search neighborhood with one dimension.
In this paper we consider binary total variation problems
that depend on an additional set of parameters. Examples
include:
(i) the Chan-Vese model that we solve globally
(ii) ratio and constrained minimization which can be formulated
as parametric problems, and
(iii) variants of the Mumford-Shah functional.
Our approach is based on a recent theorem of Chambolle
which states that solving a one-parameter family of binary
problems amounts to solving a single convex variational
problem. We prove a generalization of this result and show
how it can be applied to parametric optimization.
Department/s
- Mathematics (Faculty of Engineering)
- Mathematical Imaging Group
Publishing year
2009
Language
English
Pages
2240-2247
Publication/Series
[Host publication title missing]
Full text
Links
Document type
Conference paper
Topic
- Mathematics
- Computer Vision and Robotics (Autonomous Systems)
Keywords
- segmentation
- total variation
- image analysis
- optimization
Conference name
IEEE International Conference on Computer Vision (ICCV), 2009
Conference date
2009-09-27 - 2009-10-04
Conference place
Kyoto, Japan
Status
Published
Research group
- Mathematical Imaging Group