基于椭圆傅里叶描述子的形状表示的研究

Study on shape representation based on elliptic Fourier descriptor

形状表示是模式识别和计算机视觉中最重要的研究内容之一。针对传统形状表示算法对形状的整体特征和细节信息不能同时描述、通用性不高的问题,提出了一种基于高斯多尺度分析下的椭圆傅里叶描述算子。提出的算法利用高斯函数与目标形状的复坐标函数进行卷积,通过选择高斯曲线的参数,将形状的边界信息呈现到不同的尺度空间之中;利用椭圆傅里叶变换将其展开得到表示该形状的特征向量。实验结果表明,该方法的优点在于描述同类形状时,特征向量之间的相关系数高,具有很好的平移、旋转以及尺度不变性;在描述不同类形状时,相关系数低,有很强的形状区分能力。该方法在形状分类实验中也有较高的检索准确率。

Shape representation is one of the most important research contents in the field of pattern recognition and com- puter vision. Considering that the traditional shape representation algorithm cannot describe the whole characteristics and the detail information well at the same time and the versatility is also not desired, a new elliptic Fourier descriptor based on the Gaussian multiscale analysis is proposed in this paper. This algorithm makes convolution between Gauss function and complex coordinate function of the target object. Through the choice of parameters of Gaussian curve, the boundary information can be presented into different scale spaces. And then it can get a shape characteristic vector through elliptic Fourier transform. When this method is used to describe the shapes of a same kind, the correlation coefficients between the characteristic vectors are very high. On the contrary, the coefficients are very low when describing the shapes of different kinds. The experimental results show that this method has good translation, rotation and scale invariance, strong shape dis- crimination ability and more accurate results in the shape classification and recognition experiment.