本文研究了能够保持几何特征并且对噪声鲁棒的形状表示方法。根据弹性二次曲线(Elastic Quadratic Wire, EQW)的基本思想,对模型加以推广,提出用于曲面表示的弹性二次曲面(Elastic Quadratic Patch, EQP)模型。通过对曲面上每一点构造在参数平面上彼此重叠的二次曲面片,进而建立相邻曲面片之间0阶与1阶不连续势能函数。由于此势能函数是关于该曲面点的二次型,因而容易求得使其最小的二次曲面参数向量。对整个曲面的逐点迭代,进而获得稳定且保持显著几何特征的形状EQP表示。实验部分以3维人脸成像数据为例,验证了本文模型在平滑与细节保持等方面的性能。在不同噪声水平下,分析了参数变化对EQP模型性能影响。与常见样条与小波方法结果进行定量和定性比较,分析了不同噪声水平下(方差N=1,5,10)整体与局部区域中各方法优劣。在噪声水平较高时,在信噪比和直观效果等定量与定性方面上,EQP模型与对比方法相比具备一定优势。

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^th and 1^st 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 (N=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.