Shape From Motion of Nonrigid Objects: The Case of Isometrically Deformable Flat Surfaces

This paper deals with the reconstruction of smooth, flexible, flat surfaces isometrically embedded in 3D when observed from uncalibrated camera images. It provides a cost function which captures the global geometry of the problem. The input data consists of a sequence of matched feature points (i.e. known correspondence), but the algorithm allows for missing data so that all points do not need to be visible in all images. Its performance under these conditions is analyzed. A way of inferring the bend radius at each point is provided which can be used back in the cost function, providing a higher order fitting. The performance is validated using both synthetic data and real image examples, where the reconstruction is compared to ground truth and reference points.