Newsgroups: comp.ai
Path: cantaloupe.srv.cs.cmu.edu!europa.chnt.gtegsc.com!news.mathworks.com!news.kei.com!bloom-beacon.mit.edu!news!minsky
From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: Corners as a model to visual recognition
Message-ID: <1995Jun29.050214.940@media.mit.edu>
Sender: news@media.mit.edu (USENET News System)
Cc: minsky
Organization: MIT Media Laboratory
References: <3slka9$msg@nuscc.nus.sg>
Date: Thu, 29 Jun 1995 05:02:14 GMT
Lines: 35

In article <3slka9$msg@nuscc.nus.sg> ngkaihoe@iscs.nus.sg (StarGazer @ LUP) writes:

>As I was saying, I am a student in NUS and under some research programme
>organised by the University, the topic is computer vision. The approach
>I used is to use corners to describe an object (eg : a three corners
>object describe a triangle, four corners object describe a rectangle,
>square, trapezium etc). The strange thing is, I dont seem to be able
>to find any book in my University library touching on using corners
>to recognise objects. Any1 know of any source on this ?? Any1 researching
>on visual recognition too ?? can email me so we can share some results ?
>
>Some of the interesting results I got is that even though the model
>seems to suggest that curve edges cannot be recognised by this model.
>When U visualise a circle to be a regular polygon with an infinite 
>number of corners, programming to recognise curve surface becomes a
>matter of implementation... This model seems to be able to recognise
>very complex shapes (but that would be an extension to my present
>project, if I continue on this project). Can some1 email me ??

Take a look at chapter 6 (Geometric Patterns of Small Order) of
"Perceptrons" by me and Papert. Yes, you can recognize some geometric
patterns by counting features on their borders, you cannot recognize
others, especially when they're non-convex and, in general, you cannot
distinguish topological differences of figures that have the same
Euler numbers.  Generally, our theorems about recognition by summing
"diameter-limited features, such as corners and, even, integrals of
boundary curvatures, apply in genral, and not only to the discrete
square retina arrays discussed in that chapter.

However, there is indeed lots more to be learned about this subject. 

By the way, the theorems are exactly the same in the old (1969) and
new (1988) editions. The only differences are in added discussions on
a more general level.

