OpenCV 透视变换的两个实例

参考文献：

/article/7125554.html

http://opencv-code.com/tutorials/automatic-perspective-correction-for-quadrilateral-objects/

透视变换：

/article/1357493.html

具体流程为：

a)载入图像→灰度化→边缘处理得到边缘图像（edge map）

cv::Mat im = cv::imread(filename);

cv::Mat gray;

cvtColor(im,gray,CV_BGR2GRAY);

Canny(gray,gray,100,150,3);

b)霍夫变换进行直线检测，此处使用的是probabilistic Hough transform（cv::HoughLinesP）而不是standard Hough transform（cv::HoughLines）

std::vector<Vec4i> lines;

cv::HoughLinesP(gray,lines,1,CV_PI/180,70,30,10);

for(int i = 0; i < lines.size(); i++)

line(im,cv::Point(lines[i][0],lines[i][1]),cv::Point(lines[i][2],lines[i][3]),Scalar(255,0,0),2,8,0);

c)通过上面的图我们可以看出，通过霍夫变换检测到的直线并没有将整个边缘包含，但是我们要求的是四个顶点所以并不一定要直线真正的相交，下面就要求四个顶点的坐标，公式为：



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cv::Point2f computeIntersect(cv::Vec4i a, cv::Vec4i b) { int x1 = a[0], y1 = a[1], x2 = a[2], y2 = a[3]; int x3 = b[0], y3 = b[1], x4 = b[2], y4 = b[3]; if ( float d = (( float )(x1-x2) * (y3-y4)) - ((y1-y2) * (x3-x4))) { cv::Point2f pt; pt.x = ((x1*y2 - y1*x2) * (x3-x4) - (x1-x2) * (x3*y4 - y3*x4)) / d; pt.y = ((x1*y2 - y1*x2) * (y3-y4) - (y1-y2) * (x3*y4 - y3*x4)) / d; return pt; } else return cv::Point2f(-1, -1); }

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std::vector<cv::Point2f> corners; for ( int i = 0; i < lines.size(); i++) { for ( int j = i+1; j < lines.size(); j++) { cv::Point2f pt = computeIntersect(lines[i], lines[j]); if (pt.x >= 0 && pt.y >= 0) corners.push_back(pt); } }

d）检查是不是四边形

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std::vector<cv::Point2f> approx; cv::approxPolyDP(cv::Mat(corners), approx, cv::arcLength(cv::Mat(corners), true ) * 0.02, true ); if (approx.size() != 4) { std::cout << "The object is not quadrilateral!" << std::endl; return -1; }

e)确定四个顶点的具体位置（top-left, bottom-left, top-right, and bottom-right corner）→通过四个顶点求出映射矩阵来.

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void sortCorners(std::vector<cv::Point2f>& corners, cv::Point2f center) { std::vector<cv::Point2f> top, bot; for ( int i = 0; i < corners.size(); i++) { if (corners[i].y < center.y) top.push_back(corners[i]); else bot.push_back(corners[i]); } cv::Point2f tl = top[0].x > top[1].x ? top[1] : top[0]; cv::Point2f tr = top[0].x > top[1].x ? top[0] : top[1]; cv::Point2f bl = bot[0].x > bot[1].x ? bot[1] : bot[0]; cv::Point2f br = bot[0].x > bot[1].x ? bot[0] : bot[1]; corners.clear(); corners.push_back(tl); corners.push_back(tr); corners.push_back(br); corners.push_back(bl); }

下面是获得中心点坐标然后利用上面的函数确定四个顶点的坐标

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for ( int i = 0; i < corners.size(); i++) center += corners[i]; center *= (1. / corners.size()); sortCorners(corners, center);

定义目的图像并初始化为0

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cv::Mat quad = cv::Mat::zeros(300, 220, CV_8UC3);

获取目的图像的四个顶点

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std::vector<cv::Point2f> dst_pt; dst.push_back(cv::Point2f(0,0)); dst.push_back(cv::Point2f(quad.cols,0)); dst.push_back(cv::Point2f(quad.cols,quad.rows)); dst.push_back(cv::Point2f(0,quad.rows));

计算映射矩阵

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cv::Mat transmtx = cv::getPerspectiveTransform(corners, quad_pts);

进行透视变换并显示结果

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cv::warpPerspective(im, quad, transmtx, quad.size()); cv::imshow( "quadrilateral" , quad);

// affine transformation.cpp : 定义控制台应用程序的入口点。
//
#include "stdafx.h"
/**
* Automatic perspective correction for quadrilateral objects. See the tutorial at
* http://opencv-code.com/tutorials/automatic-perspective-correction-for-quadrilateral-objects/ */
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <iostream>
#pragma comment(lib,"opencv_core2410d.lib")
#pragma comment(lib,"opencv_highgui2410d.lib")
#pragma comment(lib,"opencv_imgproc2410d.lib")
cv::Point2f center(0,0);
cv::Point2f computeIntersect(cv::Vec4i a, cv::Vec4i b)
{
int x1 = a[0], y1 = a[1], x2 = a[2], y2 = a[3], x3 = b[0], y3 = b[1], x4 = b[2], y4 = b[3];
float denom;
if (float d = ((float)(x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4)))
{
cv::Point2f pt;
pt.x = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / d;
pt.y = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / d;
return pt;
}
else
return cv::Point2f(-1, -1);
}
void sortCorners(std::vector<cv::Point2f>& corners,
cv::Point2f center)
{
std::vector<cv::Point2f> top, bot;
for (int i = 0; i < corners.size(); i++)
{
if (corners[i].y < center.y)
top.push_back(corners[i]);
else
bot.push_back(corners[i]);
}
corners.clear();
if (top.size() == 2 && bot.size() == 2){
cv::Point2f tl = top[0].x > top[1].x ? top[1] : top[0];
cv::Point2f tr = top[0].x > top[1].x ? top[0] : top[1];
cv::Point2f bl = bot[0].x > bot[1].x ? bot[1] : bot[0];
cv::Point2f br = bot[0].x > bot[1].x ? bot[0] : bot[1];
corners.push_back(tl);
corners.push_back(tr);
corners.push_back(br);
corners.push_back(bl);
}
}
int main()
{
cv::Mat src = cv::imread("image.jpg");
if (src.empty())
return -1;
cv::Mat bw;
cv::cvtColor(src, bw, CV_BGR2GRAY);
cv::blur(bw, bw, cv::Size(3, 3));
cv::Canny(bw, bw, 100, 100, 3);
std::vector<cv::Vec4i> lines;
cv::HoughLinesP(bw, lines, 1, CV_PI/180, 70, 30, 10);
// Expand the lines
for (int i = 0; i < lines.size(); i++)
{
cv::Vec4i v = lines[i];
lines[i][0] = 0;
lines[i][1] = ((float)v[1] - v[3]) / (v[0] - v[2]) * -v[0] + v[1];
lines[i][2] = src.cols;
lines[i][3] = ((float)v[1] - v[3]) / (v[0] - v[2]) * (src.cols - v[2]) + v[3];
}
std::vector<cv::Point2f> corners;
for (int i = 0; i < lines.size(); i++)
{
for (int j = i+1; j < lines.size(); j++)
{
cv::Point2f pt = computeIntersect(lines[i], lines[j]);
if (pt.x >= 0 && pt.y >= 0)
corners.push_back(pt);
}
}
std::vector<cv::Point2f> approx;
cv::approxPolyDP(cv::Mat(corners), approx, cv::arcLength(cv::Mat(corners), true) * 0.02, true);
if (approx.size() != 4)
{
std::cout << "The object is not quadrilateral!" << std::endl;
return -1;
}
// Get mass center
for (int i = 0; i < corners.size(); i++)
center += corners[i];
center *= (1. / corners.size());
sortCorners(corners, center);
if (corners.size() == 0){
std::cout << "The corners were not sorted correctly!" << std::endl;
return -1;
}
cv::Mat dst = src.clone();
// Draw lines
for (int i = 0; i < lines.size(); i++)
{
cv::Vec4i v = lines[i];
cv::line(dst, cv::Point(v[0], v[1]), cv::Point(v[2], v[3]), CV_RGB(0,255,0));
}
// Draw corner points
cv::circle(dst, corners[0], 3, CV_RGB(255,0,0), 2);
cv::circle(dst, corners[1], 3, CV_RGB(0,255,0), 2);
cv::circle(dst, corners[2], 3, CV_RGB(0,0,255), 2);
cv::circle(dst, corners[3], 3, CV_RGB(255,255,255), 2);
// Draw mass center
cv::circle(dst, center, 3, CV_RGB(255,255,0), 2);
cv::Mat quad = cv::Mat::zeros(300, 220, CV_8UC3);
std::vector<cv::Point2f> quad_pts;
quad_pts.push_back(cv::Point2f(0, 0));
quad_pts.push_back(cv::Point2f(quad.cols, 0));
quad_pts.push_back(cv::Point2f(quad.cols, quad.rows));
quad_pts.push_back(cv::Point2f(0, quad.rows));
cv::Mat transmtx = cv::getPerspectiveTransform(corners, quad_pts);
cv::warpPerspective(src, quad, transmtx, quad.size());
cv::imshow("image", dst);
cv::imshow("quadrilateral", quad);
cv::waitKey();
return 0;
}

实现结果：



opencv透视变换

实现透视变换

目标：

在这篇教程中你将学到：

1、如何进行透视变化

2、如何生存透视变换矩阵

理论：

什么是透视变换：

1、透视变换(Perspective
Transformation)是将图片投影到一个新的视平面(Viewing Plane)，也称作投影映射(Projective Mapping)。

2、换算公式



u,v是原始图片左边，对应得到变换后的图片坐标x,y,其中

。

变换矩阵

可以拆成4部分，

表示线性变换，比如scaling，shearing和ratotion。

用于平移，

产生透视变换。所以可以理解成仿射等是透视变换的特殊形式。经过透视变换之后的图片通常不是平行四边形（除非映射视平面和原来平面平行的情况）。

重写之前的变换公式可以得到：



所以，已知变换对应的几个点就可以求取变换公式。反之，特定的变换公式也能新的变换后的图片。简单的看一个正方形到四边形的变换：

变换的4组对应点可以表示成：


根据变换公式得到：



定义几个辅助变量：




都为0时变换平面与原来是平行的，可以得到：




不为0时，得到：



求解出的变换矩阵就可以将一个正方形变换到四边形。反之，四边形变换到正方形也是一样的。于是，我们通过两次变换：四边形变换到正方形+正方形变换到四边形就可以将任意一个四边形变换到另一个四边形。



代码:

#include "opencv2/highgui.hpp"

#include "opencv2/imgproc.hpp"

#include <iostream>

#include <stdio.h>

using namespace cv;

using namespace std;

/** @function main */

int main( int argc, char** argv )

{

cv::Mat src= cv::imread( "test.jpg",0);

if (!src.data)

return 0;

vector<Point> not_a_rect_shape;

not_a_rect_shape.push_back(Point(122,0));

not_a_rect_shape.push_back(Point(814,0));

not_a_rect_shape.push_back(Point(22,540));

not_a_rect_shape.push_back(Point(910,540));

// For debugging purposes, draw green lines connecting those points

// and save it on disk

const Point* point = ¬_a_rect_shape[0];

int n = (int )not_a_rect_shape.size();

Mat draw = src.clone();

polylines(draw, &point, &n, 1, true,
Scalar(0, 255, 0), 3, CV_AA);

imwrite( "draw.jpg", draw);

// topLeft, topRight, bottomRight, bottomLeft

cv::Point2f src_vertices[4];

src_vertices[0] = not_a_rect_shape[0];

src_vertices[1] = not_a_rect_shape[1];

src_vertices[2] = not_a_rect_shape[2];

src_vertices[3] = not_a_rect_shape[3];

Point2f dst_vertices[4];

dst_vertices[0] = Point(0, 0);

dst_vertices[1] = Point(960,0);

dst_vertices[2] = Point(0,540);

dst_vertices[3] = Point(960,540);

Mat warpMatrix = getPerspectiveTransform(src_vertices, dst_vertices);

cv::Mat rotated;

warpPerspective(src, rotated, warpMatrix, rotated.size(), INTER_LINEAR, BORDER_CONSTANT);

// Display the image

cv::namedWindow( "Original Image");

cv::imshow( "Original Image",src);

cv::namedWindow( "warp perspective");

cv::imshow( "warp perspective",rotated);

imwrite( "result.jpg",src);

cv::waitKey();

return 0;

}

代码解释：

1、获取图片，如果输入路径为空的话程序直接退出

cv::Mat
src= cv::imread( "test.jpg",0);

if (!src.data)

return 0;

2、定义边界点，输入到std::vector数据结构中。注意这里的顺序如上图。

vector<Point> not_a_rect_shape;

not_a_rect_shape.push_back(Point(122,0));

not_a_rect_shape.push_back(Point(814,0));

not_a_rect_shape.push_back(Point(22,540));

not_a_rect_shape.push_back(Point(910,540));

并将这几个点标注出来

const Point* point = ¬_a_rect_shape[0];

int n = (int )not_a_rect_shape.size();

Mat draw = src.clone();

polylines(draw, &point, &n, 1, true,
Scalar(0, 255, 0), 3, CV_AA);

imwrite( "draw.jpg", draw);

3、生成透视变换矩阵

cv::Point2f
src_vertices[4];

src_vertices[0] = not_a_rect_shape[0];

src_vertices[1] = not_a_rect_shape[1];

src_vertices[2] = not_a_rect_shape[2];

src_vertices[3] = not_a_rect_shape[3];

Point2f dst_vertices[4];

dst_vertices[0] = Point(0, 0);

dst_vertices[1] = Point(960,0);

dst_vertices[2] = Point(0,540);

dst_vertices[3] = Point(960,540);

Mat warpMatrix = getPerspectiveTransform(src_vertices, dst_vertices);

4、执行转换

cv::Mat
rotated;

warpPerspective(src, rotated, warpMatrix, rotated.size(), INTER_LINEAR, BORDER_CONSTANT);

5、显示并保存结果

// Display the image

cv::namedWindow( "Original Image");

cv::imshow( "Original Image",src);

cv::namedWindow( "warp perspective");

cv::imshow( "warp perspective",rotated);

imwrite( "result.jpg",src);

结果：

原始图片



标注四个边界点



透视变换后的图片



需要注意的是，这里变化后的图像丢失了一些边界细节，这在具体实现的时候是需要注意的。