Cropping a face and removing the background?

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Check out the Face detection module tutorial to detect the face. You should be able to directly apply it to extract the face (along with neck/torso and the surrounding background) as a Mat object.

Are you using a camera with a stationary scene with faces popping in and out? In that case, subtracting a detected face from the background is quite straightforward. You will first need to save template background image Mat background_img without any faces in the scene.

Once you detect a face as Mat roi , find and extract the corresponding sub-region in bgrnd_img to get roi_background_img. Now you can simply perform subtraction: roi - roi_background_img to get only the face (with the neck and parts of the torso).

Note: This will produce poor results if your illumination varies. In this case, you should threshold both roi and roi_background_img before subtraction.

Additionally, you can also check out this module for background subtraction.

Let me know if this helps!