1. A method, comprising: at a source computing device, receiving, from a recipient computing device, a request for a computer resource; at the source computing device, after receiving the request for the computer resource from the recipient computing device, receiving a recipient image from the recipient computing device, wherein the recipient image comprises a two-dimensional arrangement of random elements; automatically generating a challenge image based on a recognizable image and the recipient image, wherein the challenge image comprises a stereogram with first and second images, each of which includes random elements, and wherein the first and second images are configured to allow a human viewer to perceive the recognizable image as a result of stereopsis only when the human viewer sees the first and second images together; transmitting the challenge image from the source computing device to the recipient computing device; receiving, from the recipient computing device, recipient input associated with the transmitted challenge image; automatically determining, at the source computing device, whether the received recipient input signifies correct recognition of the recognizable image; and in response to a determination of correct recognition of the recognizable image, automatically allowing the recipient computing device to access the computer resource; wherein the operation of automatically generating the challenge image comprises using the recipient image to generate the second image by changing positions of multiple random elements in the second image, relative to the recipient image, based on the recognizable image, wherein the changes of position are adapted to cause the recognizable image to appear to the human viewer when the recipient image and the second image are observed together at the same time; and wherein the operation of transmitting the challenge image comprises transmitting the second image to the recipient computing device.