Manipulating and modifying surface while preserving geometric details has been an active area of research in geometric modeling due to their applications in design (e.g. computer graphics, animation), but also in biomedical imaging (e.g. deforming surface based atlas).
Here, we present one surface-based technique, as opposed to free-form deformations which deform the ambient 3D space, and based on differential representations (i.e. gradient based representation, Laplacian based representation, local frame representation). These techniques are becoming more and more popular over the last past years, most likely due to their robustness, speed and ease of implementation. The main idea behind these approaches relies on the use of a representation that focus on local differential properties and on preserving these ones when deforming. These approaches remain quite intuitive and preserve local details throughout the deformation. In the rest of the paper, we will focus on Laplacian based representation and will focus on methods as described in [3]