Five types of anomalous perceptions created by the same mirror-reflection process

The real world and its mirror image are plane symmetric to each other with respect to a mirror surface, but mirror images are often perceived differently due to optical illusions. This paper shows that there are at least five types of different illusory perceptions of mirror images of pictures, although they arise from the same optical process. In all five illusions, we place a 2D picture of a 3D object horizontally, and see its image reflected by a vertical mirror. In some cases, the left and the right are reversed (left-right reversal illusion), sometimes horizontal planes change their heights (height reversal illusion), sometimes a lying object rises up (lying-standing illusion), sometimes the object turns upside down as if having done a somersault (somersault illusion), and sometimes the object is replaced by a rather different object (replacement illusion). This paper examines why these illusions occur from geometrical and psychological points of view.