One-shot 3D scanning by combining sparse landmarks with dense gradient information

Scene understanding is one of the most challenging and popular problems in the field of robotics and computer vision and the estimation of 3D information is at the core of most of these applications. In order to retrieve the 3D structure of a test surface we propose a single shot approach that combines dense gradient information with sparse absolute measurements. To that end, we designed a colored pattern that codes fine horizontal and vertical fringes, with sparse corners landmarks. By measuring the deformation (bending) of horizontal and vertical fringes, we are able to estimate surface local variations (i.e. its gradient field). Then corner sparse landmarks are detected and matched to infer spare absolute information about the test surface height. Local gradient information is combined with the sparse absolute values which work as anchors to guide the integration process. We show that this can be mathematically done in a very compact and intuitive way by properly defining a Poisson-like partial differential equation. Then we address in detail how the problem can be formulated in a discrete domain and how it can be practically solved by straight forward linear numerical solvers. Finally, validation experiment are presented.