Height reversal generated by rotation around a vertical axis

• Height reversal property common to pictures drawn on a horizontal plane.
• Height reversal generated by 3D rotation instead of 2D rotation.
• Anomalous objects that change the appearances in a mirror.

This paper presents a mathematical framework for explaining “height reversal”, a class of depth-reversal phenomena that occur when interpreting images. In particular, it is proved that, if a picture on a horizontal plane evokes an impression of depth for a viewer who sees it from an oblique direction, then when that same picture is rotated by 180°around a vertical axis, it evokes an impression of reversed height. Visual effects caused by this 3D rotation are different from the 2D rotation of turning a picture upside down, because additional objects outside the horizontal plane are also rotated. Examples of height-reversing scenes are constructed, and their relations with known depth-reversal phenomena are discussed.

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