Description
There are many methods which fit a surface to a noisy point cloud 'as good as possible', but this does not guarantee conformance to the actual physical object. For the sensing device which generates these points, we can assume a noise model, based on the manufacturer's specifications, or measure its properties to a certain extent from that data. Then we can say that the surface passes at a specific location close to such a point with certain confidence depending on such a probability density function.Use the constraints of this model to pose surface fitting as an energy minimization problem, with a property of the surface (e.g. absolute mean curvature, longest-edge-in-triangle) as the objective to be minimized.
Task
- Model a probability density function, e.g. for the Kinect device, including handling of outliers.
- Decide the types of geometric primitives to used for surface fitting (triangles, quadrangles, triangular or quad patches) and formulate the optimization problem.
- Implement an efficient solver for the above problem.
- Incorporate sharp features into the problem.
