Clustering algorithm with defined global proportions?

Hi,

I'm currently working on an image segmentation problem with a very large set of photos of drill core from a mining property. On of the first steps in my image processing sequence is to separate the actual stone from the boxes they sit in, sample tags etc with K-Means clustering. For the most part, it has been working very well. There are some situations; however, when it fails and does not classify well enough.

I'm converting the images into Lab color space then clustering them based on the a and b values. I've found that 3 clusters is the most robust. In most cases, cluster 1 is stone, cluster two is box and cluster 3 is anything dark in the photo.

Is there anyway to force cluster proportions? In my case, no two pictures are identical but for the most part, the stone occupies between 50 and 60% of the photo. I'm wondering if I could improve my clustering reliability by enforcing this?

Thanks,

Cole