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I think this shouldn't necessarily change the extrinsic parameters, since this parameters basically defines a transform between two "rigid" bodies(e.g you use this parameters to transform a LIDAR point to camera frame, all in 3D space). However this should change the intrinsic parameters. If you look at, what parameters are regraded as intrinsic ones; From wiki;

So from here one will expect the change in size of your image should effect principal point(u_0,v_0). Principal point would/should be multiplied by the factor you divide your image.