贝塞尔-傅里叶矩的快速精确计算

FAST AND ACCURATE CALCULATION OF BESSEL-FOURIER MOMENTS

贝塞尔-傅里叶矩作为一种重要的径向正交矩,具有本质上的旋转不变性,因此被广泛应用于图像处理与模式分类中。但是,其存在的计算复杂度较高、数值稳定性差的问题严重限制了其应用扩展。针对此问题,提出一种贝塞尔-傅里叶矩的快速精确计算方法,该方法采用多采样点近似计算降低积分误差对贝塞尔矩数值稳定性的影响,并且在计算过程中利用其角度基函数的递归关系与贝塞尔多项式的空间对称性有效降低了计算成本。仿真实验表明,该方法较原方法在有效降低计算成本的同时,提升了贝塞尔-傅里叶矩的重构精度与分类性能。

Bessel-Fourier moments, an important kind of radial orthogonal moment, is natively rotation invariant and thus it has been widely used in image processing and pattern classification. However, the two existing drawbacks namely high computational complexity and low numerical stability, limiting the application extension. Therefore, a fast and accurate calculation algorithm using Bessel-Fourier moments is proposed to solve the problem. The proposed approach is able to lower the influence that integral error brings to the Bessel-Fourier moments numeric by using multi sampling point approximation, and then the computational cost is reduced by using the recursive relation of the circular basis functions and the spatial symmetrical characteristic of the radial basis functions in the computational process. Experimental results demonstrate that this approachnot only reduces computational expense but also has higher reconstruction accuracy and better classification performance compared with the original method.