Shape analysis based on feature-preserving Elastic Quadratic Patch Modeling

An explicit shape representation, which is robust to noise and feature-preserving, is important to various tasks such as shape analysis and image processing. Elastic Quadratic Wire (EQW) is a recently proposed spline based shape representation model. It is particularly highlighted for good capacity in eliminating shape noises and preserving salient shape features, but is limited in representing only 2D planar shapes. In this study, we extend the EQW model into an Elastic Quadratic Patch (EQP) model to represent 3D parametric surfaces. In our model, we construct a planar overlapping parameterization space and represent all the surface points by quadratic patches. We then form the 0th and 1st order discontinuities between the neighboring patches into a quadratic energy function with an analytic minimal value. Therefore, the shape can be gradually fitted using an efficient iterative style. In experiments, we validate the EQP model in terms of efficient computation, effects on the adjustable parameter selection and performance in de-noising and preserving features. Experimental results on 3D facial surfaces demonstrate that our EQP model inherits all the strong points of the seminal EQW model, and is comparable or better than other frequently-used models in the shape smoothing task.