OpenCV中積分圖函數(shù)與應(yīng)用

一：圖像積分圖概念

積分圖像是Crow在1984年首次提出，是為了在多尺度透視投影中提高渲染速度。隨后這種技術(shù)被應(yīng)用到基于NCC的快速匹配、對(duì)象檢測(cè)和SURF變換中、基于統(tǒng)計(jì)學(xué)的快速濾波器等方面。積分圖像是一種在圖像中快速計(jì)算矩形區(qū)域和的方法，這種算法主要優(yōu)點(diǎn)是一旦積分圖像首先被計(jì)算出來(lái)我們可以計(jì)算圖像中任意大小矩形區(qū)域的和而且是在常量時(shí)間內(nèi)。這樣在圖像模糊、邊緣提取、對(duì)象檢測(cè)的時(shí)候極大降低計(jì)算量、提高計(jì)算速度。第一個(gè)應(yīng)用積分圖像技術(shù)的應(yīng)用是在Viola-Jones的對(duì)象檢測(cè)框架中出現(xiàn)。

上圖左側(cè)四個(gè)點(diǎn)的矩形區(qū)域像素求和，只要根據(jù)每個(gè)點(diǎn)左上方所有像素和表值，進(jìn)行兩次減法與一次加法即可=》46 – 22 – 20 + 10 = 14

二：OpenCV中積分圖函數(shù)

OpenCV中通過(guò)integral()函數(shù)可以很容易的計(jì)算圖像的積分圖，該函數(shù)支持和表積分圖、平方和表積分圖、瓦塊和表積分圖計(jì)算。integral函數(shù)與參數(shù)解釋如下：

1. void cv::integral(

2. InputArray src, // 輸入圖像

3. OutputArray sum, // 和表

4. OutputArray sqsum, // 平方和表

5. OutputArray tilted, // 瓦塊和表

6. int sdepth = -1, // 和表數(shù)據(jù)深度常見(jiàn)CV_32S

7. int sqdepth = -1 // 平方和表數(shù)據(jù)深度 常見(jiàn) CV_32F

8. )

三：使用積分圖函數(shù)

通過(guò)代碼演示計(jì)算積分圖實(shí)現(xiàn)任意窗口大小的盒子模糊與垂直邊緣提取，完整的代碼實(shí)現(xiàn)如下：

1. #include

2. #include

4. using namespace cv;

5. using namespace std;

7. void blur_demo(Mat &image, Mat &sum);

8. void edge_demo(Mat &image, Mat &sum);

9. int getblockSum(Mat &sum, int x1, int y1, int x2, int y2, int i);

10. int main(int argc, char** argv) {

11. Mat src = imread("D:/vcprojects/images/yuan_test.png");

12. if (src.empty()) {

13. printf("could not load image... ");

14. return -1;

15. }

16. namedWindow("input", CV_WINDOW_AUTOSIZE);

17. imshow("input", src);

19. namedWindow("output", CV_WINDOW_AUTOSIZE);

21. // 計(jì)算積分圖

22. Mat sum, sqrsum;

23. integral(src, sum, sqrsum, CV_32S, CV_32F);

25. // 積分圖應(yīng)用

26. int type = 0;

27. while (true) {

28. char c = waitKey(100);

29. if (c > 0) {

30. type = (int)c;

31. printf("c : %d ", type);

32. }

34. if (c == 27) {

35. break; // ESC

36. }

37. if (type == 49) { // 數(shù)字鍵 1

38. blur_demo(src, sum);

39. }

40. else if (type == 50) { // 數(shù)字鍵 2

41. edge_demo(src, sum);

42. }

43. else {

44. blur_demo(src, sum);

45. }

46. }

48. waitKey(0);

49. return 0;

50. }

52. void blur_demo(Mat &image, Mat &sum) {

53. int w = image.cols;

54. int h = image.rows;

55. Mat result = Mat::zeros(image.size(), image.type());

56. int x2 = 0, y2 = 0;

57. int x1 = 0, y1 = 0;

58. int ksize = 5;

59. int radius = ksize / 2;

60. int ch = image.channels();

61. int cx = 0, cy = 0;

62. for (int row = 0; row < h + radius; row++) {

63. y2 = (row + 1)>h ? h : (row + 1);

64. y1 = (row - ksize) < 0 ? 0 : (row - ksize);

65. for (int col = 0; col < w + radius; col++) {

66. x2 = (col + 1)>w ? w : (col + 1);

67. x1 = (col - ksize) < 0 ? 0 : (col - ksize);

68. cx = (col - radius) < 0 ? 0 : col - radius;

69. cy = (row - radius) < 0 ? 0 : row - radius;

70. int num = (x2 - x1)*(y2 - y1);

71. for (int i = 0; i < ch; i++) {

72. // 積分圖查找和表，計(jì)算卷積

73. int s = getblockSum(sum, x1, y1, x2, y2, i);

74. result.at<Vec3b>(cy, cx)[i] = saturate_cast(s / num);

75. }

76. }

77. }

78. imshow("output", result);

79. imwrite("D:/result.png", result);

80. }

82. /**

83. * 3x3 sobel 垂直邊緣檢測(cè)演示

84. */

85. void edge_demo(Mat &image, Mat &sum) {

86. int w = image.cols;

87. int h = image.rows;

88. Mat result = Mat::zeros(image.size(), CV_32SC3);

89. int x2 = 0, y2 = 0;

90. int x1 = 0, y1 = 0;

91. int ksize = 3; // 算子大小，可以修改，越大邊緣效應(yīng)越明顯

92. int radius = ksize / 2;

93. int ch = image.channels();

94. int cx = 0, cy = 0;

95. for (int row = 0; row < h + radius; row++) {

96. y2 = (row + 1)>h ? h : (row + 1);

97. y1 = (row - ksize) < 0 ? 0 : (row - ksize);

98. for (int col = 0; col < w + radius; col++) {

99. x2 = (col + 1)>w ? w : (col + 1);

100. x1 = (col - ksize) < 0 ? 0 : (col - ksize);

101. cx = (col - radius) < 0 ? 0 : col - radius;

102. cy = (row - radius) < 0 ? 0 : row - radius;

103. int num = (x2 - x1)*(y2 - y1);

104. for (int i = 0; i < ch; i++) {

105. // 積分圖查找和表，計(jì)算卷積

106. int s1 = getblockSum(sum, x1, y1, cx, y2, i);

107. int s2 = getblockSum(sum, cx, y1, x2, y2, i);

108. result.at<Vec3i>(cy, cx)[i] = saturate_cast(s2 - s1);

109. }

110. }

111. }

112. Mat dst, gray;

113. convertScaleAbs(result, dst);

114. normalize(dst, dst, 0, 255, NORM_MINMAX);

115. cvtColor(dst, gray, COLOR_BGR2GRAY);

116. imshow("output", gray);

117. imwrite("D:/edge_result.png", gray);

118. }

120. int getblockSum(Mat &sum, int x1, int y1, int x2, int y2, int i) {

121. int tl = sum.at<Vec3i>(y1, x1)[i];

122. int tr = sum.at<Vec3i>(y2, x1)[i];

123. int bl = sum.at<Vec3i>(y1, x2)[i];

124. int br = sum.at<Vec3i>(y2, x2)[i];

125. int s = (br - bl - tr + tl);

126. return s;

127. }

這里最重要的是要注意到上面的圖示，積分圖對(duì)象的Mat(1,1)對(duì)應(yīng)實(shí)際圖像Mat（0，0），如果不加處理的話會(huì)導(dǎo)致結(jié)果有明顯的中心遷移。edge_demo實(shí)現(xiàn)了積分圖查找提取圖像邊緣、blur_demo函數(shù)實(shí)現(xiàn)積分圖查找圖像均值模糊，getblockSum函數(shù)實(shí)現(xiàn)和表查找功能，運(yùn)行顯示：

原圖：

模糊效果

邊緣效果

審核編輯 ：李倩