In this article, we show how to extend the multi-view stereo technique when the object to be reconstructed is inside a transparent but refractive medium, which causes distortions in the images. We provide a theoretical formulation of the problem accounting for a general non-planar shape of the refractive interface, and then a discrete solving method. We also present a pipeline to recover precisely the geometry of the refractive interface, considered as a convex polyhedral object. It is based on the extraction of visible polyhedron vertices from silhouette images and matching across a sequence of images acquired under circular camera motion. These contributions are validated by tests on synthetic and real data.