将极坐标应用于 UIImage

Question

我想将常规全景照片转换为极坐标以创建 "tiny earth" 效果，但我不知道如何解决这个问题。我假设有一些有用的 Core Graphics 过滤器或第三方库，但我找不到。

示例：

Answer 1

这个其实很简单，只要应用极坐标就可以了。这是一个完整注释的示例（用 C++ 实现，仅使用 OpenCV 用于数据结构和图像加载和显示）：

#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();
}

示例输入全景图（source）：

结果图像：

编辑:

要回答你关于黑色边框的评论，你可以调整映射函数（将最终图像中的像素坐标映射到全景图像中的像素坐标）来实现你想要做的。以下是一些示例：

来源全景图：

1) 原始映射：半径 > 全景图的像素。rows/2 被留下 un-touched（因此你可以在那里显示任何背景图像）

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

结果：

2）Closest-point映射：半径>全景图的像素。rows/2映射到全景图中最近的有效像素。

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

结果：

3) Zoomed-in 映射：tiny-earth 图像被放大，使半径 > 全景图的像素。rows/2 映射到有效的全景图像素，但是全景图的某些部分现在映射到 tiny-earth 图像之外（在 top/bottom/left/right）

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

结果：

4) 对数映射：涉及对数函数的non-linear映射用于最小化映射到tiny-earth图像之外的全景图区域（您可以调整100常数以缩放或多或少）。

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：

将极坐标应用于 UIImage

Apply Polar Coordinates to UIImage

image-processing

uiimage

core-graphics

polar-coordinates