improve circle detection with a priori information?

Dear all, for my work i have some circle detection going. most of the time it works, but I ask myself if i could improve the results by using a-priori information of the location of the circles. Here is one image (i have 1000's) where i need to find the 4 circle centers:

using imfindcircles() with a few parameter tweaks and a black white converted image, i find the red circles:

the ideal locations are marked green. obviously the upper two circles are more or less correct, but the bottom two are grossly wrong. Now I do know that the four circle centers form a square of known size which is centered at the symmetry point in the middle of the image.

How can i use this informatino to improve my ciclre finding? Thanks!