It is important for shape processing and analysis to have a noise-robust and detail-preserving shape representation. In this paper

we propose an Elastic Quadratic Patch (EQP) model

which is extended from the basic idea of Elastic Quadratic Wire (EQW)

for robustly representing three-dimensional shapes. In the model

energy function quantifying 0 and 1 discontinuity is constructed based on overlapping quadratic patches for each point and its neighborhood on the surface. This function is in quadratic form and can be easily minimized through a specific vector of quadratic surface parameters. The EQP representation

which is stable and geometry preserving

can be then obtained through a point-wise iteration. In experiments

we mainly take facial depth image as experimental data to evaluate EQP’s performance on smoothing and detail preserving. Model parameters are first analyzed under different noise levels (=1

5

10). Global and local comparisons with splines and wavelets are then presented

which demonstrate

under relatively large noise

the superiority of EQP both on quantitative SNR and qualitative visual effects.