Starting with R2014a, the regionprops function in the Image Processing Toolbox calculates the perimeter with a new method. In their release notes, they state:
"The regionprops function uses a new algorithm to calculate a perimeter, when used with the ‘Perimeter’ option. Because of this change, regionprops returns different results for the perimeter calculations than it did in earlier releases... While the new algorithm used with regionprops returns more accurate perimeter calculation, you can get the same return value as previous releases by specifying the ‘perimeterold’ option."
Unfortunately, that is the only documentation I've found. It doesn't describe the differences between the new and old methods.