We present a model of morphological segmentation that jointly learns to segment and restore orthographic changes, e.g., funniest 7 → fun-y-est. We term this form of analysis canonical segmentation and contrast it with the traditional surface segmentation, which segments a surface form into a sequence of substrings, e.g., funniest 7 → funn-i-est. We derive an importance sampling algorithm for approximate inference in the model and report experimental results on English, German and Indonesian.