If we have an object in a digital image (see Objects in binary images and Objects in gray scale images), then the perimeter of the object is the length of its boundary = the number of edges in its contour.
If you are prepared to assume that the object is a circle you can go: area->radius->perimeter and avoid the inaccuracy altogether. Similar for squares.
The perimeter appears in Pixcavator's output table.
To experiment with the concepts, download the free Pixcavator Student Edition.
To see how this can be applied, browse our numerous image analysis examples.