空间二次曲线代数不变量的几何解释

Geometrical Interpretation of the Algebraic Invariant of Space Conics

利用不变量进行物体识别、形状描述是计算机视觉中非常活跃的一个研究领域。以往关于代数不变量和几何特征方面的研究,主要是利用点、直线等几何元素来计算单视图中平面物体的不变量。本文从实际计算的角度出发,研究了两个未校焦图像中一对不共面空间二次曲线的不变量,利用四元二次型不变量给出了空间两条二次曲线代数不变量的定义,并对其进行了相应的几何解释。在此基础上通过实验验证,证明文中所给公式的正确性。

The recognition of objects and description of shapes are very important in computer vision. The conventional studies of algebraic invariants and geometrical properties are that these invariants are derived for planar objects using points, lines from one single image. The invariants of a pair of non-coplanar conics in space from two uncalibrated images are studied from the perspective of computational processes. The algebraic invariants is defined from the algebra of invariants of quaternary quadratic forms, and the geonietrieal interpretation is proposed in this paper. The result of example shows that this formula is correct.