如何在该相机拍摄的图像中找到相机与像素点（x 和 y 坐标）之间的真实距离？

Question

So I tried to implement logic by first considering that camera is placed on ground and captured image, I first calculated distance between bottom most pixel on image along y axis and px and py coordinates on image then I translated that distance into real life by multiplying resulted value with real life distance covered in a pixel of that image. Now my task was to re calculate distance when now camera is lifted above at some height (making angle of 90 deg from ground). Now how can I re calculate distance between new camera position (ie, at some height) and a point on image taken by that camera at new position?

// point of image along y-axis until ground is visible 
const int groundY = 50;
// real life distance from origin (i.e. from where camera is placed and image bottom most point along y-axis) to point where ground is visible in image 
const int realLifeGroundDist = 200;
const int cameraHeight = 40;

void geoLocation(int ***a, int x, int y, int z, int px, int py){

    double onePixelDistance = realLifeGroundDist/groundY;
    // double distBtwPixels = sqrt(pow(px - ((x/2)-1), 2) + pow(py - (y-1), 2) * 1);

    // Distance formula to calculate dist btw origin and (px,py) pixel
    double distBtwPixels = sqrt(pow(px - (x-1), 2) + pow(py - ((y/2)-1), 2) * 1);
    
    //translating pixel distance to real life distance
    double h = distBtwPixels * onePixelDistance;

    //considering that camera is placed above ground at some height i.e. cameraHeight variable at angle = 90deg and calculating distance btw that point and camera i.e. hypteneuse
    double realLifeDist = sqrt(pow(h, 2) + pow(cameraHeight, 2));
    
    cout<<"Distance between camera and px and py coordinates in image = "<<realLifeDist;
}

According to my logic realLifeDist holds distance between point on image captured by camera placed on new location ie at some height from ground making angle of 90 deg from ground. Is my logic correct? If not, then how can I calculate it?

Answer 1

The short answer is, as long as you do not know the distance of your measured points from the camera, you can't.

Imagine the image as a plane between the focus point of the camera and the objects you want to capture. When light is coming from an object (red points) to the focus point, they intersect the image plane. That intersection point is the location of the object on the image.

As you can see, objects that are further away from the camera appear closer together on the image plane. In this sketch, the close points have the same pixel distance as the far away points. So unless you know the distance between each point you want to measure and the camera, you cannot calculate the distance between these points from one image.