Characterizing the distribution of completion shapes with corners using a mixture of random processes

摘要

We derive an analytic expression for the distribution of contours x(t) generated by fluctuations in ẋ(t)=∂x(t)/∂t due to random impulses of two limiting types. The first type are frequent but weak while the second are infrequent but strong. The result has applications in computational theories of figural completion and illusory contours because it can be used to model the prior probability distribution of short, smooth completion shapes punctuated by occasional discontinuities in orientation (i.e., corners). This work extends our previous work on characterizing the distribution of completion shapes which dealt only with the case of frequently acting weak impulses.