Count shapes in image

I have an image which has a number of shapes, all are the same color and on a white background. Is there a quick way of counting how many shapes there are?

I don't want to know what shape they actually are (polygon, circle or whatever), I just want to know how many isolated shapes are present. Other than some kind of brute force method, I can't find any other way of doing this.

Use a paint-bucket fill algorithm -- there's plenty to find on the web. Scan the image for the first coloured pixel you find, do a paint fill to get all the connected pixels, add 1 to your shape count and delete those pixels. Repeat until there are no coloured pixels left. Or does this count as brute force?

BB