I hope this falls within the \"programming question\" category. Im all lightheaded from Googling (and reading every post in here on the subject) on the subject \"Computer Vi
I do shape recognition in my iPhone app Instaviz and the routines are actually packaged into a library I call "Recog". Only problem is that it is meant for finger or mouse gesture recognition rather than image recognition. You pass the routines a set of points representing the gesture and it tells you whether it's a square, circle etc.
I haven't yet decided on a licensing model but probably use a minimal per-seat royalty.
Have a look at at OpenCV's SURF feature extraction (they also have a demo which uses it to detect objects). Surf features are salient image features which are invariant to rotation and scale. Many algorithms detect objects by extracting such features from an image, and then use simple "bag of words" classification (comparing the set of extracted image features to the features of your "shapes". Even without referring to their spacial alignment you can have good detection rates if you only have 6 shapes).
While not a library, Chris Greening explains how iPhone Sudoku Grab does its image recognition of puzzles in his post here. He does seem to recommend OpenCV, and not just for jailbroken devices.
Also Glen Low talks a bit about how Instaviz does its shape recognition in an interview for the Mobile Orchard podcast.