opencv透视变换

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 = &not_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 = &not_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。

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