A vision-based operating system is provided in which a computer-based system accepts visual inputs and takes appropriate actions in a wide variety of environments. One environment is a security environment in which the vision-based operating system acquires an image of a face and determines, with an arbitrarily small probability of a false positive, whether the face is of a person who is authorized to enter the environment. The method employed may include acquiring a digital image for comparison to a reference image and identifying a group of pixels in the acquired image. A pixel group in the reference image that is the best match for the pixel group in the acquired image is selected. These steps are repeated for at least one more group of pixels. The relative locations of the selected pixel groups in the reference images and the pixel groups in the acquired image are compared, and the probability that the relative locations occurred randomly is determined.