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Nonlinear scalespace should be based on a hierarchical statistical model of the image intensity function. This model should contain an explicit representation of the multiscale structure of edges and corners. Using this model we can have a non-ad-hoc basis for computing the parameters we need to determine how much smoothing we should do at points that appear to be edge points. We also have a basis for computing the apparent error in our scalespace calculations. Hierarchical statistical modeling is a technique that can be applied to other problems in low-level vision, but in this introductory paper we just present the application of our scalespace theory to image smoothing.