Shape-from-intrinsic operator

Shape-from-X is an important class of problems in the fields of geometry processing, computer graphics, and vision, attempting to recover the structure of a shape from some observations. In this paper, we formulate the problem of shape-from-operator (SfO), recovering an embedding of a mesh from intrinsic differential operators defined on the mesh. Particularly interesting instances of our SfO problem include synthesis of shape analogies, shape-from-Laplacian reconstruction, and shape exaggeration. Numerically, we approach the SfO problem by splitting it into two optimization sub-problems that are applied in an alternating scheme: metric-from-operator (reconstruction of the discrete metric from the intrinsic operator) and embedding-from-metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem).