A Geometric Approach to Blind Deconvolution with Application to Shape from Defocu
Abstract
We propose a solution to the generic "bilinear calibration-estimation problem" when using a quadratic cost function and restricting to (locally) translation-invariant imaging models. We apply the solution to the problem of reconstructing the three-dimensional shape and radiance of a scene from a number of defocused images. Since the imaging process maps the continuum of three-dimensional space onto the discrete pixel grid, rather than discretizing the continuum we exploit the structure of maps between (finite-and infinite-dimensional) Hilbert spaces and arrive at a principled algorithm that does not involve any choice of basis or discretization. Rather, these are uniquely determined by the data, and exploited in a functional singular value decomposition in order to obtain a regularized solution.
Cite
Text
Soatto and Favaro. "A Geometric Approach to Blind Deconvolution with Application to Shape from Defocu." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2000. doi:10.1109/CVPR.2000.854725Markdown
[Soatto and Favaro. "A Geometric Approach to Blind Deconvolution with Application to Shape from Defocu." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2000.](https://mlanthology.org/cvpr/2000/soatto2000cvpr-geometric/) doi:10.1109/CVPR.2000.854725BibTeX
@inproceedings{soatto2000cvpr-geometric,
title = {{A Geometric Approach to Blind Deconvolution with Application to Shape from Defocu}},
author = {Soatto, Stefano and Favaro, Paolo},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2000},
pages = {2010-2017},
doi = {10.1109/CVPR.2000.854725},
url = {https://mlanthology.org/cvpr/2000/soatto2000cvpr-geometric/}
}