图像椭圆扁度不变性及其在仿射不变量构造中的应用

Invariance of image ellipse oblateness degree and its application to construction of affine invariants

针对传统基于面积比不变的仿射不变量方法具有的特征点选取不稳定且有冗余以及区域面积误差累积等特点,提出了一种基于图像椭圆扁度划分策略的仿射不变量构造方法。介绍了图像仿射变换模型,得到了图像仿射近似条件。结合图像椭圆扁率定义,依据不变矩理论证明了仿射变换下图像扁率的不变性。给出了图像扁度的定义及其物理含义,并以此作为图像同心圆划分依据,选取三阶以下仿射不变矩作为图像特征量,通过计算各同心圆区域的仿射不变量描述图像目标。将提出的方法应用于实际舰船图像并结合离散系数对其稳定性进行了分析。结果表明:同一舰船目标各种仿射变换图像计算所得扁度相同,所在划分特征圆区域仿射不变量离散系数最大为1.55%。得到的结果显示该方法对目标图像的特征区域划分具有唯一性,构造的仿射不变特征稳定性较好。

As the traditional affine invariants based on the invariant of area ratio are characterized by unstable and redundant feature points, error accumulation, this paper proposes a novel method based on the division strategy of image ellipse oblateness degree for construction of affine invariants. The af- fine transformation model was presented, and the condition of affine approximation was obtained. In combination of the definition of image ellipse oblateness degree and the invariant moment theory, the invariance of image ellipse oblateness under affine transformation was verified. Meanwhile, the defini- tion of image oblateness degree and its physical meaning were given. Then, on the basis of the image ellipse oblateness degree, the affine invariant moments below the 3rd order were selected as the fea- ture descriptors, the image target was described by calculation of the affine invariants of each concen- tric region. Finally, the proposed method was applied to the actual ship images and its stability was analyzed by discrete coefficients. Experimental results indicate that all kinds of the target images for the same ship under different affine transformations have the same oblateness degree, and the maxi-mum discrete coefficient in the divided feature region is 1. 550//00. It concludes that the proposed method is unique for the image division and constructed affine invariants have good stability.