Ricerc@Sapienza

In this paper we show that the introduction of an attenuation factor in the brightness equations relative to various perspective shape-from-shading models allows us to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solutions and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton–Jacobi equations associated to these models.

In this paper we study the well-known family of Random Utility Models, developed over 50 years ago to codify rational user behavior in choosing one item from a finite set of options. In this setting each user draws i.i.d. from some distribution a utility function mapping each item in the universe to a real-valued utility. The user is then offered a subset of the items, and selects theone of maximum utility. A Max-Dist oracle for this choice model takes any subset of items and returns the probability (over the distribution of utility functions) that each will be selected.