Should the execution time change when I am running MOG2 extractor on image in GPU?

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Ah, berak? https://docs.opencv.org/3.3.0/df/d23/classcv_1_1cuda_1_1BackgroundSubtractorMOG2.html

As to your question, it is important to know how the GPU works. The 640x480 image is 307200 pixels, which is far more than the number of cores on the GPU. In the ideal case, where each pixel is operated upon once, for example, adding one to every pixel. If you had a GPU with 640 cores, each core would operate on 480 pixels. If you resized the image to be 4 times larger (2x width 2x height), then each core would operate on 4x480 pixels, taking about 4x as long.

So, as you can see, MOG2, which is much more complicated than simple addition, will definitely take longer if you use larger images like you say.