Geometric subdivision and multiscale transforms
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations like averages. This chapter discusses different kinds of geometric structures like metric spaces, Riemannian manifolds, and groups, and in what way we can make elementary operations geometrically meaningful. A nice example of this is the Riemannian metric naturally associated with the space of positive definite matrices and the intrinsic operations on positive definite matrices derived from it. We disucss averages first and then proceed to refinement operations (subdivision) and multiscale transforms. In particular, we report on the current knowledge as regards convergence and smoothness.
NurtureToken New!

Token crowdsale for this paper ends in

Buy Nurture Tokens

Author

Are you an author of this paper? Check the Twitter handle we have for you is correct.

Johannes Wallner (add twitter)
Ask The Authors

Ask the authors of this paper a question or leave a comment.

Read it. Rate it.
#1. Which part of the paper did you read?

#2. The paper contains new data or analyses that is openly accessible?
#3. The conclusion is supported by the data and analyses?
#4. The conclusion is of scientific interest?
#5. The result is likely to lead to future research?

Github
User:
None (add)
Repo:
None (add)
Stargazers:
0
Forks:
0
Open Issues:
0
Network:
0
Subscribers:
0
Language:
None
Youtube
Link:
None (add)
Views:
0
Likes:
0
Dislikes:
0
Favorites:
0
Comments:
0
Other
Sample Sizes (N=):
Inserted:
Words Total:
Words Unique:
Source:
Abstract:
None
07/17/19 06:02PM
13,133
3,129
Tweets
mathNAb: Johannes Wallner : Geometric subdivision and multiscale transforms https://t.co/7m3rD2iI5K https://t.co/tnfkPUkzfy
Images
Related