基于VisualApplets仿真的Zernike算法
一、Zernike正交矩模板计算
对于7X7模板，即由7*7=49个小方格分割单位圆的面积。
①小方格面积：
②边缘小方格面积:
由圆的中心对称性可得
1、M00mask
|
0 |
0.0287 |
0.0686 |
0.0807 |
0.0686 |
0.0287 |
0 |
|
0.0287 |
0.0815 |
0.0816 |
0.0816 |
0.0816 |
0.0815 |
0.0287 |
|
0.0686 |
0.0816 |
0.0816 |
0.0816 |
0.0816 |
0.0816 |
0.0686 |
|
0.0807 |
0.0816 |
0.0816 |
0.0816 |
0.0816 |
0.0816 |
0.0807 |
|
0.0686 |
0.0816 |
0.0816 |
0.0816 |
0.0816 |
0.0816 |
0.0686 |
|
0.0287 |
0.0815 |
0.0816 |
0.0816 |
0.0816 |
0.0815 |
0.0287 |
|
0 |
0.0287 |
0.0686 |
0.0807 |
0.0686 |
0.0287 |
0 |
2、M11实数mask
|
0 |
-0.015 |
-0.019 |
0 |
0.019 |
0.015 |
0 |
|
-0.0224 |
-0.0466 |
-0.0233 |
0 |
0.0233 |
0.0466 |
0.0224 |
|
-0.0573 |
-0.0466 |
-0.0233 |
0 |
0.0233 |
0.0466 |
0.0573 |
|
-0.069 |
-0.0466 |
-0.0233 |
0 |
0.0233 |
0.0466 |
0.069 |
|
-0.0573 |
-0.0466 |
-0.0233 |
0 |
0.0233 |
0.0466 |
0.0573 |
|
-0.0224 |
-0.0466 |
-0.0233 |
0 |
0.0233 |
0.0466 |
0.0224 |
|
0 |
-0.015 |
-0.019 |
0 |
0.019 |
0.015 |
0 |
3、M11虚数mask
|
0 |
-0.0224 |
-0.0573 |
-0.069 |
-0.0573 |
-0.0224 |
0 |
|
-0.015 |
-0.0466 |
-0.0466 |
-0.0466 |
-0.0466 |
-0.0466 |
-0.015 |
|
-0.019 |
-0.0233 |
-0.0233 |
-0.0233 |
-0.0233 |
-0.0233 |
-0.019 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0.019 |
0.0233 |
0.0233 |
0.0233 |
0.0233 |
0.0233 |
0.019 |
|
0.015 |
0.0466 |
0.0466 |
0.0466 |
0.0466 |
0.0466 |
0.015 |
|
0 |
-0.0224 |
-0.0573 |
-0.069 |
-0.0573 |
-0.0224 |
0 |
4、M20mask
|
0 |
0.0225 |
0.0394 |
0.0396 |
0.0394 |
0.0225 |
0 |
|
0.0225 |
0.0271 |
-0.0128 |
-0.0216 |
-0.0128 |
0.0271 |
0.0225 |
|
0.0394 |
-0.0128 |
-0.0528 |
-0.0661 |
-0.0528 |
-0.0128 |
0.0394 |
|
0.0396 |
-0.0261 |
-0.0661 |
-0.0794 |
-0.0661 |
-0.0261 |
0.0396 |
|
0.0394 |
-0.0128 |
-0.0528 |
-0.0661 |
-0.0528 |
-0.0128 |
0.0394 |
|
0.0225 |
0.0271 |
-0.0128 |
-0.0216 |
-0.0128 |
0.0271 |
0.0225 |
|
0 |
0.0225 |
0.0394 |
0.0396 |
0.0394 |
0.0225 |
0 |
5、M31实数mask
|
0 |
-0.0103 |
-0.0073 |
0 |
0.0073 |
0.0103 |
0 |
|
-0.0153 |
-0.0018 |
0.0162 |
0 |
-0.0162 |
0.0018 |
0.0153 |
|
-0.0223 |
0.0324 |
0.0333 |
0 |
-0.0333 |
-0.0324 |
0.0223 |
|
-0.0190 |
0.0438 |
0.0390 |
0 |
-0.0390 |
-0.0438 |
0.0190 |
|
-0.0223 |
0.0324 |
0.0333 |
0 |
-0.0333 |
-0.0324 |
0.0223 |
|
-0.0153 |
-0.0018 |
0.0162 |
0 |
-0.0162 |
0.0018 |
0.0153 |
|
0 |
-0.0103 |
-0.0073 |
0 |
0.0073 |
0.0103 |
0 |
6、M31虚数mask
|
0 |
-0.0152 |
-0.0223 |
-0.019 |
-0.0223 |
-0.0152 |
0 |
|
-0.0103 |
-0.0018 |
0.0324 |
0.0438 |
0.0324 |
-0.0018 |
-0.0103 |
|
-0.0073 |
0.0162 |
0.0333 |
0.039 |
0.0333 |
0.0162 |
-0.0073 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0.0073 |
-0.0162 |
-0.0333 |
-0.039 |
-0.0333 |
-0.0162 |
0.0073 |
|
0.0103 |
0.0018 |
-0.0324 |
-0.0438 |
-0.0324 |
0.0018 |
0.0103 |
|
0 |
0.0153 |
0.0223 |
0.019 |
0.0223 |
0.0153 |
0 |
7、M40mask
|
0 |
0.013 |
0.0056 |
-0.0018 |
0.0056 |
0.013 |
0 |
|
0.0130 |
-0.0186 |
-0.0323 |
-0.0239 |
-0.0323 |
-0.0186 |
0.0130 |
|
0.0056 |
-0.0323 |
0.0125 |
0.0406 |
0.0125 |
-0.0323 |
0.0056 |
|
-0.0018 |
-0.0239 |
0.0406 |
0.0751 |
0.0406 |
-0.0239 |
-0.0018 |
|
0.0056 |
-0.0323 |
0.0125 |
0.0406 |
0.0125 |
-0.0323 |
0.0056 |
|
0.0130 |
-0.0186 |
-0.0323 |
-0.0239 |
-0.0323 |
-0.0186 |
0.0130 |
|
0 |
0.013 |
0.0056 |
-0.0018 |
0.0056 |
0.013 |
0 |
二、程序仿真
1、程序总流程图
分别计算，并用计算的模板分别对图像进行卷积操作得到
。根据公式：
以及阈值判断条件，计算条纹中心线。
2、计算四个模板M11,M20,M31,M40
3、阈值判断
三、计算结果
1、原始图像
2、条纹中心线