How to use Imagick to merge and mask images?

Question

I know very little of image processing and even less of the terminology used, so please bear with me.

Basically, I want to merge two images together where one of them will act as a mask. That image looks something like this:

Where the blue and yellow background are both transparent in reality.

This image is being used as a mask for regular photo's. Parts of the photo that 'stick out' of the circle need to be 'cropped' (be made invisible) while the inside remains visible.
So everything that comes in the blue area is invisible, everything in the yellow area is visible.

I honestly have no clue how to go about it so any help would be greatly appreciated!

Edit:
I use the API version of Imagick, not the commandline version

Edit:
To get a feel of what I want to achieve, here is an example.

The input images are thus:

This is the mask image, always the same

This is an example of a picture, dynamic

This is what the end result should look like

Answer 1

So, finally, this should do what you need:

Original image:

Opacity mask:

Overlay:

Output:

The code:

<?php
$base = new Imagick('U0R4F.png');
$mask = new Imagick('mask.png');
$over = new Imagick('3ulkM.png');

// Setting same size for all images
$base->resizeImage(274, 275, Imagick::FILTER_LANCZOS, 1);

// Copy opacity mask
$base->compositeImage($mask, Imagick::COMPOSITE_DSTIN, 0, 0, Imagick::CHANNEL_ALPHA);

// Add overlay
$base->compositeImage($over, Imagick::COMPOSITE_DEFAULT, 0, 0);

$base->writeImage('output.png');
header("Content-Type: image/png");

echo $base;
?>

I hope it's right now! Note: In your example it looks like you downscaled the base image, which I didn't (my goal is just to show how the masking is done).