【图像算法】不变矩
图像算法：不变矩
SkySeraph Mar 29th 2011 HQU
Email：[email protected] QQ：452728574
Latest Modified Date：Mar 29th 2011 HQU
一 工具：VC6.0+OpenCV1.0
语言：CPP
二 原理：http://blog.csdn.net/byxdaz/archive/2009/12/28/5089448.aspx
三 说明：
本源码参考了http://blog.csdn.net/dadaadao/archive/2011/01/04/6114705.aspx，对里面的一些错误(比较多)进行了修正，同时增加了匹配功能，即可以用来实现不变矩匹配，但在匹配中总发现有点点蹊跷，反复查看程序未发现问题，暂时放在博客，如果大家发现了错误，请不吝赐教！
四 源码：
1
/*
===============================================//
2 功能：不变矩匹配
3 时间：3/28/2011 SkySeraph HQU
4 参考：
5 //=============================================== */
6 #include " iostream "
7 using namespace std;
8
9 #include " cv.h "
10 #include " highgui.h "
11
12 #include " math.h "
13
14 #pragma comment(lib,"highgui.lib")
15 #pragma comment(lib,"cv.lib")
16 #pragma comment(lib,"cvaux.lib")
17 #pragma comment(lib,"cxcore.lib")
18
19 const char * filename = " D:\\My Documents\\My Pictures\\Images\\1.bmp " ;
20 const char * filename2 = " D:\\My Documents\\My Pictures\\Images\\2.bmp " ;
21
22 /* ============================================= */
23 double M[ 7 ] = { 0 }; // HU不变矩
24
25 bool HuMoment(IplImage * img)
26 {
27
28 int bmpWidth = img -> width;
29 int bmpHeight = img -> height;
30 int bmpStep = img -> widthStep;
31 int bmpChannels = img -> nChannels;
32 uchar * pBmpBuf = (uchar * )img -> imageData;
33
34 double m00 = 0 ,m11 = 0 ,m20 = 0 ,m02 = 0 ,m30 = 0 ,m03 = 0 ,m12 = 0 ,m21 = 0 ; // 中心矩
35 double x0 = 0 ,y0 = 0 ; // 计算中心距时所使用的临时变量（x-x'）
36 double u20 = 0 ,u02 = 0 ,u11 = 0 ,u30 = 0 ,u03 = 0 ,u12 = 0 ,u21 = 0 ; // 规范化后的中心矩
37 // double M[7]; // HU不变矩
38 double t1 = 0 ,t2 = 0 ,t3 = 0 ,t4 = 0 ,t5 = 0 ; // 临时变量，
39 // double Center_x=0,Center_y=0; // 重心
40 int Center_x = 0 ,Center_y = 0 ; // 重心
41 int i,j; // 循环变量
42
43 // 获得图像的区域重心
44 double s10 = 0 ,s01 = 0 ,s00 = 0 ; // 0阶矩和1阶矩 // 注：二值图像的0阶矩表示面积
45 for (j = 0 ;j < bmpHeight;j ++ ) // y
46 {
47 for (i = 0 ;i < bmpWidth;i ++ ) // x
48 {
49 s10 += i * pBmpBuf[j * bmpStep + i];
50 s01 += j * pBmpBuf[j * bmpStep + i];
51 s00 += pBmpBuf[j * bmpStep + i];
52 }
53 }
54 Center_x = ( int )(s10 / s00 + 0.5 );
55 Center_y = ( int )(s01 / s00 + 0.5 );
56
57 // 计算二阶、三阶矩
58 m00 = s00;
59 for (j = 0 ;j < bmpHeight;j ++ )
60 {
61 for (i = 0 ;i < bmpWidth;i ++ ) // x
62 {
63 x0 = (i - Center_x);
64 y0 = (j - Center_y);
65 m11 += x0 * y0 * pBmpBuf[j * bmpStep + i];
66 m20 += x0 * x0 * pBmpBuf[j * bmpStep + i];
67 m02 += y0 * y0 * pBmpBuf[j * bmpStep + i];
68 m03 += y0 * y0 * y0 * pBmpBuf[j * bmpStep + i];
69 m30 += x0 * x0 * x0 * pBmpBuf[j * bmpStep + i];
70 m12 += x0 * y0 * y0 * pBmpBuf[j * bmpStep + i];
71 m21 += x0 * x0 * y0 * pBmpBuf[j * bmpStep + i];
72 }
73 }
74
75 // 计算规范化后的中心矩
76 u20 = m20 / pow(m00, 2 );
77 u02 = m02 / pow(m00, 2 );
78 u11 = m11 / pow(m00, 2 );
79 u30 = m30 / pow(m00, 2.5 );
80 u03 = m03 / pow(m00, 2.5 );
81 u12 = m12 / pow(m00, 2.5 );
82 u21 = m21 / pow(m00, 2.5 );
83
84 // 计算中间变量。
85 t1 = (u20 - u02);
86 t2 = (u30 - 3 * u12);
87 t3 = ( 3 * u21 - u03);
88 t4 = (u30 + u12);
89 t5 = (u21 + u03);
90
91 // 计算不变矩
92 M[ 0 ] = u20 + u02;
93 M[ 1 ] = t1 * t1 + 4 * u11 * u11;
94 M[ 2 ] = t2 * t2 + t3 * t3;
95 M[ 3 ] = t4 * t4 + t5 * t5;
96 M[ 4 ] = t2 * t4 * (t4 * t4 - 3 * t5 * t5) + t3 * t5 * ( 3 * t4 * t4 - t5 * t5);
97 M[ 5 ] = t1 * (t4 * t4 - t5 * t5) + 4 * u11 * t4 * t5;
98 M[ 6 ] = t3 * t4 * (t4 * t4 - 3 * t5 * t5) - t2 * t5 * ( 3 * t4 * t4 - t5 * t5);
99
100
101 /* cout<<M[0]<<endl;//<<二"<<M[0]<<"三"<<M[0]<<"四"<<M[0]<<"五"<<M[0]<<"六"<<M[0]<<"七"<<M[0]<<endl;
102 cout<<M[1]<<endl;
103 cout<<M[2]<<endl;
104 cout<<M[3]<<endl;
105 cout<<M[4]<<endl;
106 cout<<M[5]<<endl;
107 cout<<M[6]<<endl;
108 cout<<endl; */
109 return true ;
110 }
111
112
113 int main( char argc, char ** argv)
114 {
115 int i;
116 double Sa[ 7 ] = { 0 },Ta[ 7 ] = { 0 };
117
118 /// *源图像
119 IplImage * img = cvLoadImage(filename, 0 ); // 灰度
120 HuMoment(img);
121 for (i = 0 ;i <7 ;i ++ )
122 {
123 Sa[i] = M[i];
124 M[i] = 0 ;
125 }
126 cout << Sa[ 0 ] << endl;
127 cout << Sa[ 1 ] << endl;
128 cout << Sa[ 2 ] << endl;
129 cout << Sa[ 3 ] << endl;
130 cout << Sa[ 4 ] << endl;
131 cout << Sa[ 5 ] << endl;
132 cout << Sa[ 6 ] << endl;
133 cout << endl;
134 // */
135
136
137 /// *模板图
138 IplImage * tpl = cvLoadImage(filename2, 0 ); // 灰度
139 HuMoment(tpl);
140 for (i = 0 ;i <7 ;i ++ )
141 {
142 Ta[i] = M[i];
143 M[i] = 0 ;
144 }
145 cout << Ta[ 0 ] << endl;
146 cout << Ta[ 1 ] << endl;
147 cout << Ta[ 2 ] << endl;
148 cout << Ta[ 3 ] << endl;
149 cout << Ta[ 4 ] << endl;
150 cout << Ta[ 5 ] << endl;
151 cout << Ta[ 6 ] << endl;
152 cout << endl;
153
154
155 // 计算相似度
156 double dbR = 0 ; // 相似度
157 double dSigmaST = 0 ;
158 double dSigmaS = 0 ;
159 double dSigmaT = 0 ;
160 double temp = 0 ;
161
162 for (i = 0 ;i <7 ;i ++ )
163 {
164 temp = Sa[i] * Ta[i];
165 dSigmaST += temp;
166 dSigmaS += pow(Sa[i], 2 );
167 dSigmaT += pow(Ta[i], 2 );
168 }
169 dbR = dSigmaST / (sqrt(dSigmaS) * sqrt(dSigmaT));
170 printf( " %lf\n " ,dbR);
171 // cout<<dbR<<endl;
172
173 cvReleaseImage( & img);
174 cvReleaseImage( & tpl);
175
176 return 0 ;
177 }
2 功能：不变矩匹配
3 时间：3/28/2011 SkySeraph HQU
4 参考：
5 //=============================================== */
6 #include " iostream "
7 using namespace std;
8
9 #include " cv.h "
10 #include " highgui.h "
11
12 #include " math.h "
13
14 #pragma comment(lib,"highgui.lib")
15 #pragma comment(lib,"cv.lib")
16 #pragma comment(lib,"cvaux.lib")
17 #pragma comment(lib,"cxcore.lib")
18
19 const char * filename = " D:\\My Documents\\My Pictures\\Images\\1.bmp " ;
20 const char * filename2 = " D:\\My Documents\\My Pictures\\Images\\2.bmp " ;
21
22 /* ============================================= */
23 double M[ 7 ] = { 0 }; // HU不变矩
24
25 bool HuMoment(IplImage * img)
26 {
27
28 int bmpWidth = img -> width;
29 int bmpHeight = img -> height;
30 int bmpStep = img -> widthStep;
31 int bmpChannels = img -> nChannels;
32 uchar * pBmpBuf = (uchar * )img -> imageData;
33
34 double m00 = 0 ,m11 = 0 ,m20 = 0 ,m02 = 0 ,m30 = 0 ,m03 = 0 ,m12 = 0 ,m21 = 0 ; // 中心矩
35 double x0 = 0 ,y0 = 0 ; // 计算中心距时所使用的临时变量（x-x'）
36 double u20 = 0 ,u02 = 0 ,u11 = 0 ,u30 = 0 ,u03 = 0 ,u12 = 0 ,u21 = 0 ; // 规范化后的中心矩
37 // double M[7]; // HU不变矩
38 double t1 = 0 ,t2 = 0 ,t3 = 0 ,t4 = 0 ,t5 = 0 ; // 临时变量，
39 // double Center_x=0,Center_y=0; // 重心
40 int Center_x = 0 ,Center_y = 0 ; // 重心
41 int i,j; // 循环变量
42
43 // 获得图像的区域重心
44 double s10 = 0 ,s01 = 0 ,s00 = 0 ; // 0阶矩和1阶矩 // 注：二值图像的0阶矩表示面积
45 for (j = 0 ;j < bmpHeight;j ++ ) // y
46 {
47 for (i = 0 ;i < bmpWidth;i ++ ) // x
48 {
49 s10 += i * pBmpBuf[j * bmpStep + i];
50 s01 += j * pBmpBuf[j * bmpStep + i];
51 s00 += pBmpBuf[j * bmpStep + i];
52 }
53 }
54 Center_x = ( int )(s10 / s00 + 0.5 );
55 Center_y = ( int )(s01 / s00 + 0.5 );
56
57 // 计算二阶、三阶矩
58 m00 = s00;
59 for (j = 0 ;j < bmpHeight;j ++ )
60 {
61 for (i = 0 ;i < bmpWidth;i ++ ) // x
62 {
63 x0 = (i - Center_x);
64 y0 = (j - Center_y);
65 m11 += x0 * y0 * pBmpBuf[j * bmpStep + i];
66 m20 += x0 * x0 * pBmpBuf[j * bmpStep + i];
67 m02 += y0 * y0 * pBmpBuf[j * bmpStep + i];
68 m03 += y0 * y0 * y0 * pBmpBuf[j * bmpStep + i];
69 m30 += x0 * x0 * x0 * pBmpBuf[j * bmpStep + i];
70 m12 += x0 * y0 * y0 * pBmpBuf[j * bmpStep + i];
71 m21 += x0 * x0 * y0 * pBmpBuf[j * bmpStep + i];
72 }
73 }
74
75 // 计算规范化后的中心矩
76 u20 = m20 / pow(m00, 2 );
77 u02 = m02 / pow(m00, 2 );
78 u11 = m11 / pow(m00, 2 );
79 u30 = m30 / pow(m00, 2.5 );
80 u03 = m03 / pow(m00, 2.5 );
81 u12 = m12 / pow(m00, 2.5 );
82 u21 = m21 / pow(m00, 2.5 );
83
84 // 计算中间变量。
85 t1 = (u20 - u02);
86 t2 = (u30 - 3 * u12);
87 t3 = ( 3 * u21 - u03);
88 t4 = (u30 + u12);
89 t5 = (u21 + u03);
90
91 // 计算不变矩
92 M[ 0 ] = u20 + u02;
93 M[ 1 ] = t1 * t1 + 4 * u11 * u11;
94 M[ 2 ] = t2 * t2 + t3 * t3;
95 M[ 3 ] = t4 * t4 + t5 * t5;
96 M[ 4 ] = t2 * t4 * (t4 * t4 - 3 * t5 * t5) + t3 * t5 * ( 3 * t4 * t4 - t5 * t5);
97 M[ 5 ] = t1 * (t4 * t4 - t5 * t5) + 4 * u11 * t4 * t5;
98 M[ 6 ] = t3 * t4 * (t4 * t4 - 3 * t5 * t5) - t2 * t5 * ( 3 * t4 * t4 - t5 * t5);
99
100
101 /* cout<<M[0]<<endl;//<<二"<<M[0]<<"三"<<M[0]<<"四"<<M[0]<<"五"<<M[0]<<"六"<<M[0]<<"七"<<M[0]<<endl;
102 cout<<M[1]<<endl;
103 cout<<M[2]<<endl;
104 cout<<M[3]<<endl;
105 cout<<M[4]<<endl;
106 cout<<M[5]<<endl;
107 cout<<M[6]<<endl;
108 cout<<endl; */
109 return true ;
110 }
111
112
113 int main( char argc, char ** argv)
114 {
115 int i;
116 double Sa[ 7 ] = { 0 },Ta[ 7 ] = { 0 };
117
118 /// *源图像
119 IplImage * img = cvLoadImage(filename, 0 ); // 灰度
120 HuMoment(img);
121 for (i = 0 ;i <7 ;i ++ )
122 {
123 Sa[i] = M[i];
124 M[i] = 0 ;
125 }
126 cout << Sa[ 0 ] << endl;
127 cout << Sa[ 1 ] << endl;
128 cout << Sa[ 2 ] << endl;
129 cout << Sa[ 3 ] << endl;
130 cout << Sa[ 4 ] << endl;
131 cout << Sa[ 5 ] << endl;
132 cout << Sa[ 6 ] << endl;
133 cout << endl;
134 // */
135
136
137 /// *模板图
138 IplImage * tpl = cvLoadImage(filename2, 0 ); // 灰度
139 HuMoment(tpl);
140 for (i = 0 ;i <7 ;i ++ )
141 {
142 Ta[i] = M[i];
143 M[i] = 0 ;
144 }
145 cout << Ta[ 0 ] << endl;
146 cout << Ta[ 1 ] << endl;
147 cout << Ta[ 2 ] << endl;
148 cout << Ta[ 3 ] << endl;
149 cout << Ta[ 4 ] << endl;
150 cout << Ta[ 5 ] << endl;
151 cout << Ta[ 6 ] << endl;
152 cout << endl;
153
154
155 // 计算相似度
156 double dbR = 0 ; // 相似度
157 double dSigmaST = 0 ;
158 double dSigmaS = 0 ;
159 double dSigmaT = 0 ;
160 double temp = 0 ;
161
162 for (i = 0 ;i <7 ;i ++ )
163 {
164 temp = Sa[i] * Ta[i];
165 dSigmaST += temp;
166 dSigmaS += pow(Sa[i], 2 );
167 dSigmaT += pow(Ta[i], 2 );
168 }
169 dbR = dSigmaST / (sqrt(dSigmaS) * sqrt(dSigmaT));
170 printf( " %lf\n " ,dbR);
171 // cout<<dbR<<endl;
172
173 cvReleaseImage( & img);
174 cvReleaseImage( & tpl);
175
176 return 0 ;
177 }
五 效果(略)
Author: SKySeraph
Email/GTalk: [email protected] QQ：452728574
From： http://www.cnblogs.com/skyseraph/
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