Schwarz Representation for Matching and Similarity Analysis
Abstract
This paper presents a novel multiscale representation of one-dimensional signal based on complex analysis. We show that a signal and its derivative at different scales can be represented by one analytic function defined on the unit disc in the complex plane, which is called the Schwarz representation of a signal. This representation is applied to the matching problem. Using the theory of analytic functions, we are able to define the inverse of a signal. The matching function between two signals can be defined as the composition of one signal's Schwarz representation and another signal's inverse. The matching function determined by this method has a group structure and is close-formed.
Cite
Text
Yang and Ma. "Schwarz Representation for Matching and Similarity Analysis." IEEE/CVF International Conference on Computer Vision, 1998. doi:10.1109/ICCV.1998.710774Markdown
[Yang and Ma. "Schwarz Representation for Matching and Similarity Analysis." IEEE/CVF International Conference on Computer Vision, 1998.](https://mlanthology.org/iccv/1998/yang1998iccv-schwarz/) doi:10.1109/ICCV.1998.710774BibTeX
@inproceedings{yang1998iccv-schwarz,
title = {{Schwarz Representation for Matching and Similarity Analysis}},
author = {Yang, Qing and Ma, Songde},
booktitle = {IEEE/CVF International Conference on Computer Vision},
year = {1998},
pages = {570-575},
doi = {10.1109/ICCV.1998.710774},
url = {https://mlanthology.org/iccv/1998/yang1998iccv-schwarz/}
}