perimeter

04/29/2008

Perimeter

The perimeter is an 'iffy' sort of measurement - it often changes dramatically with image resolution. Given that you want to use perimeter anyway, here are some notes on how Lispix measures it.

The blob perimeter is measured as the sum of the distance between the centers of the outer edges of the pixels (connect the *'s in diagram below).

-----*-----.------*-----|
. |
pixel a . pixel b *
. |
. |
.........................-----*-----
inside of . |
blob . . |
. . *
. . |
. . |
.....................................

. . .

This is more accurate than counting pixels or edges. (and between the two in magnitude).

Note on perimeter length from Joseph Barba, Kin S. Chan and Joan Gil,

'Quantitative Perimeter and Area Measurements of Digital Images'
Microscopy Research and Technique 21:300-314, 1992, page 304
Freman and Glass were the first to use the root-2 scheme above.

Freeman, H. and Glass, J.M., 1969 'On the quantitization of line-drawing data.'
IEEE Trans Syst Sci Cybern SSC-5:70-79

Kulpa, Z. 1977,
'Area and perimeter measurement of blobs indiscrete binary pictures.'
Computer Graphics and Image processing 6:434-451

For polygons with uniformly distributed slopes, the length is over estimated by 1.055.

Perimeter estimator - +2.5% for squares, -5.3% for circles.