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Today, many phones can process images to imitate the effect of large aperture on professional lens, to blur the background and achieve small depth of field (DOF).

My question is: is that algorithm available on some separate software (not the camera app)?

The tutorials I have seen includes instructions to select manually the object we want to be in focus; this seems to be an unnecessary use of time, since computers can do this for us.

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If you know the coordinates of the object in your picture, you can apply a clipping path or mask to it, and then a blur filter.

Google Cloud has an image recognition service which would give you back the coordinates of the bounding boxes of the objects in the picture.
This API is called Vision API. It can do various things. Most interesting would be the services "Detect Crop Hints" and "Detect multiple Objects".

I haven't tried it, but obviously this will have difficulties to clip detail-rich objects, such as a model's long hair. For simple objects it might work.

I think other Cloud Providers have similar offerings.

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