Created attachment 228
Squares with the same area but different rotations

The computation of the perimeter for particle analyzer is not consistent when you analyze particles with edges that are not parallel, perpendicular, or do not have a 45 degree inclination.

The issue can be reproduced as follows:

1 - With an external program, generate an 8-bit image with a series of squares with the same area but different rotation from 0 to 45° (example is provided)

2 - Threshold the image (Image->Adjust->Threshold)

3 - Apply particle analysis to the image (Analyze->Analyze Particles)

The results will show same area but different perimeter.
The problem is inherited by shape descriptors based on Perimeter quantity and plugins (e.g. Shape Descriptor1u).

The issue seems to be related to on edge detection because the outlined profile is stepped and not continuous. Increase of image resolution does not improve.

Fiji ImageJ 2.0.0-rc-15/1.49k
Java 1.7.0_67
Windows 7 (64 bit)

The bug was found on ImageJ 1.44 as well.