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From: reiner@isy.liu.se (Reiner Lenz)
Newsgroups: comp.ai.neural-nets
Subject: Re: Which learning algorithm is best for scale/rotation invariant input?
Message-ID: <reiner.654779094@lennox>
Date: 1 Oct 90 11:04:54 GMT
References: <kilmer.653677625@sysp1>
Sender: news@isy.liu.se (Lord of the News)
Organization: Dept of EE, University of Linkoping
Lines: 88

We studied the problem of invariance in pattern recognition problems in 
top-down and bottom-fashion. 

A)

In the top-down approach you know that you want to recognize patterns
independent of some group of transformations. Using some theory you can
show that the transformation group gives you the desired feature extraction
process. For example: 2-D rotation invariance leads to Fourier transform
in polar coordinates, 3-D rotation invariance leads to surface harmonics,
scale invariance leads to the Mellin transform etc.

Ref.:

@article{Len_jos:89,
	author ="Reiner Lenz",
	title ="A Group Theoretical Model of Feature Extraction", 
	journal=josaa,
	volume="6",
	number="6",
	pages="827-834",
	year = "1989"
}

@book{Len:90ln,
	author= "Reiner Lenz",
	title =  "Group Theoretical Methods in Image Processing",
	publisher = "Springer Verlag",
	series = "Lecture Notes in Computer Science (Vol. 413)",
	address = "Heidelberg, Berlin, New York",
	year = "1990"
}

@article{Len:90,
	author= "Reiner Lenz",
	title =  "Group-Invariant Pattern Recognition",
	journal = "Pattern Recognition",
	volume="23",
	number="1/2",
	pages = "199-218",
	year = "1990"
}

A generalization is the following: 

Not all patterns in a group are equally important. This is the case in
scale invariance; since scaled patterns with very small or very large
scaling factors are not very similar to the original pattern. How the
theory must be modified in this case is described in one of our internal 
reports.

Ref.:

@techreport{Len_prob:91,
	author ="Reiner Lenz",
	title="On probabilistic Invariance",
        institution={Link\"oping University, ISY, S-58183 Link\"oping},
	note="Internal Report",
	year="1991"
}

We also investigated the problem in a bottom-up fashion. We design a 
learning filter system that consists of a fixed number of filter
functions. Then we train this system with examples of the pattern class
that we want to recognize. The learning rule is designed in such a way
that the resulting system produces filter functions with a minimum loss
of information and a maximum amount of concentration of the feature
components. Examples show that this system learns Fourier transformation
from examples of rotated patterns. 

Ref:

@inproceedings{Len:90ijcnn,
	author= {Reiner Lenz and Mats \"Osterberg},
	title =  "Learning Filter Systems",
	booktitle = "Proc. Int. Joint Conference on Neural Networks, San Diego",
	year = "1990"
}
-- 
"Kleinphi macht auch Mist"
Reiner Lenz | Dept. EE.                 |
            | Linkoeping University	| email:	reiner@isy.liu.se
            | S-58183 Linkoeping/Sweden |
--
"Kleinphi macht auch Mist"
Reiner Lenz | Dept. EE.                 |
            | Linkoeping University	| email:	reiner@isy.liu.se
            | S-58183 Linkoeping/Sweden |