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