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;
}
# 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;
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));
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);
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);
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);
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);
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。
2017年4月30日09:03:03 感谢 网友
CHEN Tian-hua 指出一处错误，已经将 最后的a12修改成a23
