Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ames!pasteur!ucbvax!agate!eos!glenn
From: glenn@eos.UUCP (Glenn Meyer)
Newsgroups: comp.graphics
Subject: Re: How do I find the area of a non-polygonal bounded region?
Message-ID: <2674@eos.UUCP>
Date: 19 Feb 89 04:54:59 GMT
References: <5532@homxc.ATT.COM>
Distribution: na
Organization: NASA Ames Research Center, California
Lines: 34

From article <5532@homxc.ATT.COM>, by jackson@homxc.ATT.COM (B.JACKSON):
> Here's the problem:  I've got a bitmapped display 
> that has an image of a ragged-edged closed perimeter surrounding an
> open area.  I need to know the area of the opening.  The
> boundry of the area looks like someone spray-painted a
> circle of pixels on the screen -- I can guarentee a closed
> boundry of connected pixels, but there are some individual
> pixels (and groups of pixels) 'floating' around out in the
> area I want to measure (I don't want to count the 'floaters'
> in the area).  The perimeter has, as you might
> guess, thousands of small inclusions.


How about a "scan-line fill" of the area? If you can define a simple
geometric bounding primitive (box, circle or ellipse, for instance) that
doesn't include other such bounded regions, then, for each pixel row, you
should be able to count the number of pixels between the first and last
perimeter pixel in that row, within the bounding primitive.  Unlike the
pixel or scan-line seed fill, this would count all interior pixels that
are part of either the boundary or of a "floater". The sum of these
pixel-row counts should give you the correct area, unless you're trying to
exclude interior pixels with the same property (gray-scale?) as the outer
perimeter pixels. In that case, count only the pixels that don't have the
perimiter property. If, in addition, you're trying to exclude from the
area calculation all holes ("floaters" that themselves form a region),
look in the book "Computer Graphics: A Programming Approach" for the
algorithm that scan-converts polygons with concave boundaries and holes.
(Sorry, I don't have the complete reference for the algorithm.)

-- 
Glenn Meyer (glenn%carma@{io,aurora,eos,pioneer}.arc.nasa.gov)
CARMA, Sterling Software
NASA-Ames, M.S. 233-14
Moffett Field, Ca.  94035