shift invariance

[Edelman Shimon]

> Date: Mon, 26 Feb 1996 10:05:33 +1000 (EST)
> From: Shlomo Geva <geva at fit.qut.edu.au>
>
> Regarding shift invariance: 
> 
> [some stuff omitted]
>
> Now I'd like to make a conjecture.
> It appears to make sense to assume that this difficulty is inherent
> to the shift invariance requirement itself. If this is so 
> then unless you have an additional constraint imposed on objects -
> they cannot be allowed to be identical under the invariant feature
> extraction transformation you wish to employ -
> then you cannot solve the problem. In other words, one needs a guarantee that
> all permissible objects are uniquely transformed by the procedure.
> It seems to follow that
> no general procedure, that does not take into account the nature of the objects
> for which the procedure is intended, can exist.
> 
> I am wondering if anyone could clarify whether this is a valid argument.
> 
> Shlomo Geva

A number of people (see the refs below) have proved in the past that
no universal invariants with respect to viewpoint exist for objects
represented as point sets in 3D. The proofs hinged on the possibility
of two different objects having the same 2D projection. Offhand, it
seems that a similar argument could be used to prove Shlomo's
conjecture.

-Shimon

Dr. Shimon Edelman, Applied Math. & Computer Science
Weizmann Institute of Science, Rehovot 76100, Israel
The Web:  http://eris.wisdom.weizmann.ac.il/~edelman
fax: (+972) 8 344122   tel: 8 342856   sec: 8 343545


@inproceedings{MosesUllman92,
author="Y. Moses and S. Ullman",
title="Limitations of non model-based recognition schemes",
booktitle="Proc. 2nd European Conf. on Computer Vision, Lecture Notes
		  in Computer Science",  
volume="588",
pages="820-828", 
editor="G. Sandini",
publisher="Springer Verlag", 
addredd="Berlin",
year="1992"
}

@article{BurWeiRis93,
author="J.B. Burns and R. Weiss and E. Riseman",
title="View variation of point-set and line segment features",
journal=pami,
volume="15",
pages = "51-68",
year = 1993
}