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The Ponzo illusion uses converging lines and/or other depth cues to suggest distance in a picture. Our eyes image the world through a view angle, as seen in the diagram to the left. The farther away something is, the wider the angle of view. As an object moves away from us, it will take up less of the field of view, and so appears smaller. But this is just an optical illusion, and our brain compensates for apparent distance so that distant objects don't appear small, just far away.
The Ponzo illusion uses this compensation against us. To the right we see two lines that are the same size. When the converging grey lines appear, the upper line appears further away, and our brain compensates for its apparent depth, making it seem larger. The more cues available in the scene, the stronger the illusion. The strength of the illusion is also influenced by past experience.
Another factor contributing to the illusion is the framing effect: Objects that seem to fill an enclosing border appear larger than the same object in a larger frame.