|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
27 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
A projection algorithm on measures sets | | Nicolas Chauffert
; Philippe Ciuciu
; Jonas Kahn
; Pierre Weiss
; | | Date: |
1 Sep 2015 | | Abstract: | We consider the problem of projecting a probability measure $pi$ on a set
$mathcal{M}\_N$ of Radon measures. The projection is defined as a solution of
the following variational problem:egin{equation*}inf\_{muin
mathcal{M}\_N} |hstar (mu - pi)|\_2^2,end{equation*}where $hin
L^2(Omega)$ is a kernel, $Omegasubset R^d$ and $star$ denotes the
convolution operator.To motivate and illustrate our study, we show that this
problem arises naturally in various practical image rendering problems such as
stippling (representing an image with $N$ dots) or continuous line drawing
(representing an image with a continuous line).We provide a necessary and
sufficient condition on the sequence $(mathcal{M}\_N)\_{Nin N}$ that ensures
weak convergence of the projections $(mu^*\_N)\_{Nin N}$ to $pi$.We then
provide a numerical algorithm to solve a discretized version of the problem and
show several illustrations related to computer-assisted synthesis of artistic
paintings/drawings. | | Source: | arXiv, 1509.0229 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER