将极坐标应用于UIImage

Question

我想将常规的全景照片转换为极坐标以创建“微小的地球”效果，但是我不知道该如何解决。我会假设有一些有用的Core Graphics过滤器或第三方库，但我找不到任何库。

例：

Answer 1

这实际上很简单，您只需要应用极坐标即可。这是一个完整注释的示例（在C ++中实现，并且仅将OpenCV用于数据结构以及图像加载和显示）：

#include <opencv2/highgui.hpp>

// Function returning the bilinear interpolation of the input image at input coordinates
cv::Vec3b interpolate(const cv::Mat &image, float x, float y)
{
    // Compute bilinear interpolation weights
    float floorx=std::floor(x), floory=std::floor(y);
    float fracx=x-floorx, fracy=y-floory;
    float w00=(1-fracy)*(1-fracx), w01=(1-fracy)*fracx, w10=fracy*(1-fracx), w11=fracy*fracx;

    // Read the input image values at the 4 pixels surrounding the floating point (x,y) coordinates
    cv::Vec3b val00 = image.at<cv::Vec3b>(floory, floorx);
    cv::Vec3b val01 = (floorx<image.cols-1 ? image.at<cv::Vec3b>(floory, floorx+1) : image.at<cv::Vec3b>(floory, 0));       // Enable interpolation between the last right-most and left-most columns
    cv::Vec3b val10 = image.at<cv::Vec3b>(floory+1, floorx);
    cv::Vec3b val11 = (floorx<image.cols-1 ? image.at<cv::Vec3b>(floory+1, floorx+1) : image.at<cv::Vec3b>(floory+1, 0));   // Enable interpolation between the last right-most and left-most columns

    // Compute the interpolated color
    cv::Vec3b val_interp;
    val_interp.val[0] = cv::saturate_cast<uchar>(val00.val[0]*w00+val01.val[0]*w01+val10.val[0]*w10+val11.val[0]*w11);
    val_interp.val[1] = cv::saturate_cast<uchar>(val00.val[1]*w00+val01.val[1]*w01+val10.val[1]*w10+val11.val[1]*w11);
    val_interp.val[2] = cv::saturate_cast<uchar>(val00.val[2]*w00+val01.val[2]*w01+val10.val[2]*w10+val11.val[2]*w11);
    return val_interp;
}

// Main function
void main()
{
    const float pi = 3.1415926535897932384626433832795;

    // Load and display color panorama image
    cv::Mat panorama = cv::imread("../panorama_sd.jpg", cv::IMREAD_COLOR);
    cv::namedWindow("Panorama");
    cv::imshow("Panorama", panorama);

    // Infer the size of the final image from the dimensions of the panorama
    cv::Size result_size(panorama.rows*2, panorama.rows*2);
    float ctrx=result_size.width/2, ctry=result_size.height/2;

    // Initialize an image with black background, with inferred dimensions and same color format as input panorama
    cv::Mat tiny_earth_img = cv::Mat::zeros(result_size, panorama.type());
    cv::Vec3b *pbuffer_img = tiny_earth_img.ptr<cv::Vec3b>();   // Get a pointer to the buffer of the image (sequence of 8-bit interleaved BGR values)

    // Generate the TinyEarth image by looping over all its pixels
    for(int y=0; y<result_size.height; ++y) {
        for(int x=0; x<result_size.width; ++x, ++pbuffer_img) {

            // Compute the polar coordinates associated with the current (x,y) point in the final image
            float dx=x-ctrx, dy=y-ctry;
            float radius = std::sqrt(dx*dx+dy*dy);
            float angle = std::atan2(dy,dx)/(2*pi); // Result in [-0.5, 0.5]
            angle = (angle<0 ? angle+1 : angle);    // Result in [0,1[

            // Map the polar coordinates to cartesian coordinates in the panorama image
            float panx = panorama.cols*angle;
            float pany = panorama.rows-1-radius;    // We want the bottom of the panorama to be at the center

            // Ignore pixels which cannot be linearly interpolated in the panorama image
            if(std::floor(panx)<0 || std::floor(panx)+1>panorama.cols || std::floor(pany)<0 || std::floor(pany)+1>panorama.rows-1)
                continue;

            // Interpolate the panorama image at coordinates (panx, pany), and store this value in the final image
            pbuffer_img[0] = interpolate(panorama, panx, pany);
        }
    }

    // Display the final image
    cv::imwrite("../tinyearth.jpg", tiny_earth_img);
    cv::namedWindow("TinyEarth");
    cv::imshow("TinyEarth", tiny_earth_img);
    cv::waitKey();
}

样本输入全景图（来源）：

结果图像：

编辑：

要回答有关黑色边框的评论，您可以调整映射功能（将最终图像中的像素坐标映射到全景图像中的像素坐标）以实现所需的功能。这里有些例子：

来源全景图：

1）原始贴图：半径> panorama.rows / 2的像素保持不变（因此，您可以在此处显示任何背景图像）

float panx = panorama.cols*angle;
float pany = panorama.rows-1-radius;

结果：

2）最近点映射：将半径> panorama.rows / 2的像素映射到全景图中最接近的有效像素。

float panx = panorama.cols*angle;
float pany = std::max(0.f,panorama.rows-1-radius);

结果：

3）放大映射：放大了地球图像，以便将半径> panorama.rows / 2的像素映射到有效的全景像素，但是全景的某些部分现在已映射到地球图像的外部（在顶部/底部/左侧/右侧）

float panx = panorama.cols*angle;
float pany = panorama.rows-1-0.70710678118654752440084436210485*radius;

结果：

4）对数映射：包含对数函数的非线性映射用于最小化在小地球图像外部映射的全景图区域（您可以调整100常数以或多或少地缩放）。

const float scale_cst = 100;
float panx = panorama.cols*angle;
float pany = (panorama.rows-1)*(1-std::log(1+scale_cst*0.70710678118654752440084436210485*radius/panorama.rows)/std::log(1+scale_cst));

结果：