find the distance to the moon in an image in matlab

There are different ways to find the distance to the moon in an image in Matlab, but one way is to use the known size of the moon and its angular diameter.

First, you need to estimate the angular diameter of the moon in the image. You can use imtool or imshow to display the image and manually measure the diameter using a ruler tool. Alternatively, you can use image processing techniques to automatically detect the moon and estimate its diameter. For example, you can use the imfindcircles function to detect a circle in the image that corresponds to the moon and estimate its radius.

Once you have the angular diameter of the moon, you can compute the distance to the moon using the formula:

distance = size / 2 * tan(alpha)

where size is the known size of the moon (e.g., its average radius), and alpha is the estimated angular diameter of the moon in radians.

Note that this formula assumes that the moon is at the zenith (i.e., directly overhead). If the moon is at an angle, you need to adjust the formula accordingly.

Here's an example code snippet that demonstrates how to estimate the distance to the moon in an image:

main.m
% Load the image
img = imread('moon.jpg');

% Estimate the radius of the moon
[centers, radii] = imfindcircles(img, [50 100]);
radius = radii(1);

% Compute the angular diameter of the moon
angularDiameter = 2 * atan(radius / (2 * focalLength));
angularDiameterDegree = rad2deg(angularDiameter);

% Compute the distance to the moon
size = 3474.8; % km
distance = size / 2 * tand(angularDiameterDegree / 2);
fprintf('Distance to moon: %.2f km\n', distance);
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Note that the focalLength parameter needs to be calibrated for your specific camera and lens setup. You can measure it by taking a photo of an object with a known size and distance, and then computing the focal length from the resulting image. For example:

main.m
% Take a photo of an object with a known size and distance
objectDistance = 100; % cm
objectSize = 10; % cm
img = snapshot(cam);
imshow(img);

% Manually select two points on the object with the known size
[x1, y1] = ginput(1);
[x2, y2] = ginput(1);

% Compute the distance and size of the object in pixels
distancePixels = norm([x1 y1] - [x2 y2]);
sizePixels = sqrt(objectSize ^2 * distancePixels^2 / (focalLength * objectDistance));

% Compute the focal length in pixels
focalLengthPixels = focalLength * sizePixels / objectSize;
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