二次曲面体中的斜对称面检测

Skewed Symmetry Detection of Quadric Surface Solids

为了扩大3D重建实体的覆盖域,通过对Sugi moto等[7]的斜对称面检测算法(Sugi moto K,Tomita F.Detection of skewed-symmetrical shape.Proceedings of the IEEE International Conference on I mage Processing,Austin,1994:696-700)进行改进,实现了包括双曲线、抛物线等在内的所有类型的二次曲线的斜对称检测.在曲面的重建过程中,采用参数化方法实现了空间二次曲线的投影匹配,利用斜对称检测算法检测出投影曲线的斜对称轴,并由检测到的斜对称轴生成相应的平面即二次曲面体的斜对称面;同时研究了错解产生的原因.算例验证表明,采用该算法能够对含有对称部分的二次曲面体进行精确的斜对称面检测.

Skewed symmetry detection is of great importance in 3D solid reconstruction. The detected symmetry can reduce the complexity of reconstruction process. The method described in this paper is based on Sugimoto, et al^[13]（Sugimoto K, Tomita F. Detection of skewed-symmetrical shape // Proceedings of the IEEE International Conference on Image Processing, Austin, 1994. 696-700） which proposed a 2D skewed symmetry detection technique that includes ellipse. However, the more general cases involving quadric curve such as hyperbola and parabola are still unsolved. In order to enlarge the reconstruction coverage, this paper extends the Sugimoto＇s technique to further include quadric curves such as hyperbola and parabola. With the help of parametric detection, the 3D quadric curve projection matching is automatically accomplished. Finally, the skewed symmetry surface of quadric solid is obtained. Several examples are presented to demonstrate the algorithm＇s feasibility.