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Intersection of two images

I have two images of equal size -

image description

and

image description

Is there any way that I can get the intersection of the two images such that the final image is

image description

The size of the final image is the same as the size of the ellipse..Maybe pictorally the size doesnt look the same here. The center of the images coincide.

Intersection of two images

I have two images of equal unequal size -

image description

and

image description

Is there any way that I can get the intersection of the two images such that the final image is

image description

The size of the final image is the same as the size of the ellipse..Maybe pictorally the size doesnt look the same here. The center of the images coincide.