Abstract
We analyze the rate in which image details are suppressed as a function
of the regularization parameter, using first order Tikhonov regularization,
Linear Gaussian Scale Space and Total Variation image decomposition. The
squared L2-norm of the regularized solution and the residual are studied as a
function of the regularization parameter. For first order Tikhonov regularization
it is shown that the norm of the regularized solution is a convex function, while
the norm of the residual is not a concave function. The same result holds for
Gaussian Scale Space when the parameter is the variance of the Gaussian, but
may fail when the parameter is the standard deviation. Essentially this imply
that the norm of regularized solution can not be used for global scale selection
because it does not contain enough information. An empirical study based
on synthetic images as well as a database of natural images confirms that the
squared residual norms contain important scale information.
of the regularization parameter, using first order Tikhonov regularization,
Linear Gaussian Scale Space and Total Variation image decomposition. The
squared L2-norm of the regularized solution and the residual are studied as a
function of the regularization parameter. For first order Tikhonov regularization
it is shown that the norm of the regularized solution is a convex function, while
the norm of the residual is not a concave function. The same result holds for
Gaussian Scale Space when the parameter is the variance of the Gaussian, but
may fail when the parameter is the standard deviation. Essentially this imply
that the norm of regularized solution can not be used for global scale selection
because it does not contain enough information. An empirical study based
on synthetic images as well as a database of natural images confirms that the
squared residual norms contain important scale information.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of Scale Space and Variational Methods in Computer Vision (SSVM) 09 |
| Number of pages | 11 |
| Volume | 5567 |
| Publisher | Springer |
| Publication date | 2009 |
| Pages | 832-843 |
| ISBN (Print) | 978-3-642-02255-5 |
| DOIs | |
| Publication status | Published - 2009 |
| Event | Scale Space and Variational Methods in Computer Vision (SSVM) 09 - Voss, Norway Duration: 1 Jun 2009 → 5 Jun 2009 Conference number: 2 |
Conference
| Conference | Scale Space and Variational Methods in Computer Vision (SSVM) 09 |
|---|---|
| Number | 2 |
| Country/Territory | Norway |
| City | Voss |
| Period | 01/06/2009 → 05/06/2009 |
| Series | Lecture notes in computer science |
|---|---|
| Volume | 5567/209 |
| ISSN | 0302-9743 |