﻿ 基于Charlier矩的图像分析 Image Analysis by Charlier Moments

Computer Science and Application
Vol.07 No.04(2017), Article ID:20263,10 pages
10.12677/CSA.2017.74044

Image Analysis by Charlier Moments

Guanghui Shi, Xuan Wang

School of Physics and Information Technology, Shaanxi Normal University, Xi’an Shaanxi

Received: Apr. 10th, 2017; accepted: Apr. 23rd, 2017; published: Apr. 27th, 2017

ABSTRACT

The existing methods for extracting the translation and scale invariants from the discrete orthogonal moments are via a linear combination of the corresponding invariants of geometric moments or image normalization, which led to calculational errors. In this paper, a novel kind of discrete orthogonal moments named as Charlier moment is proposed based on the discrete Charlier polynomials, and then an approach to directly derive the translation and scale invariants from Charlier moments is also presented. Experimental results show the high classification and representation accuracy of these invariants as a result of direct calculation instead of the image normalization or a linear combination of the corresponding invariants of geometric moments. It is also shown that these invariants are relatively robust in the presence of image noise and are potentially useful as a kind of invariant descriptors in some image analysis and pattern recognition.

Keywords:Discrete Orthogonal Moments, Charlier Polynomials, Translation, Scale Invariants, Pattern Recognition

1. 引言

1962年Hu [1] 提出的图像几何矩理论受到广泛关注。图像几何矩不变描述量具有平移、旋转和尺度不变的特性，而且计算效率较高，可以应用于图像不变分析与机器视觉的各个领域。然而，几何矩的基函数是非正交的，导致了较大的信息冗余，所以基于几何矩重构图像是非常困难的，而且该类矩对图像噪声非常敏感，带来一定的表示误差与分类错误率。针对以上问题，一些研究工作者基于连续正交基函数提出了Zernike [2] [3] [4] 和Legendre [5] 等连续正交矩。由于连续正交矩的基函数是正交的连续函数，所以可以具有较小的信息冗余，基于连续正交矩可以对图像精确重构，此外，与几何矩相比，对噪声有更好的稳定性。但是，由于连续正交矩的定义涉及到二维连续积分形式，而数字图像是定义在离散域的数字矩阵，所以计算过程中需要进行坐标转换和积分近似，所以存在数值积分近似误差与几何误差 [4] 。这些误差会严重影响图像的重构精度与分类精度。

Mukundan [6] 在2001年提出一种基于离散Tchebichef多项式的离散正交矩。随后，Yap [7] 提出另一种基于Krawtchouk多项式的离散正交矩。离散正交矩的基函数与数字图像域完全匹配，定义与计算过程消除了由坐标转换和近似误差引起的数值积分近似误差与几何误差，具有良好的图像表征能力与分类精度，而且与连续正交矩相比，抵抗噪声的干扰能力也明显增强，然而，离散正交矩缺乏本质上的平移与尺度变换不变性，平移和尺度不变量是通过图像平移与尺度归一化方法或者借助几何矩不变量的线性组合间接获取通，这一过程会引入新的计算误差，从而影响离散正交矩的优良性能。本文基于Charlier离散正交多项式 [8] ，提出了一种新的离散正交矩，并基于该离散正交多项式的特殊性质，提出一种直接计算该矩的平移和尺度不变量的方法。实验结果验证了该方法所获得的Charlier离散正交矩尺度和平移不变量具有很好的表示与分类性能。

2. Charlier离散正交矩

(1)

(2)

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(17)

3. Charlier矩不变量的快速计算

3.1. Charlier矩的平移不变量

(18)

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3.2. 尺度不变量

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， (34)

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4. 仿真实验

4.1. 平移不变量的稳定性

4.2. 尺度不变量

Table 1. Selected orders of Charlier central moments for an English letter “Z”

Table 2. Selected orders of Charlier central moments for a Chinese letter “幕”

Table 3. The scale invariant descriptors of Charlier moments for “Fortune Cat”

Table 4. The scale invariant descriptors of Tchebichef moments for “Fortune Cat”

4.3. 分类性能

(39)

(40)

(41)

Figure 1. Part of the first testing set

Figure 2. Part of the second testing set

Table 5. Classification results of uppercase letters

Table 6. Classification results of butterfly images

5. 结论

Image Analysis by Charlier Moments[J]. 计算机科学与应用, 2017, 07(04): 359-368. http://dx.doi.org/10.12677/CSA.2017.74044

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