The staircase illusion, in which many staircase-like planes appear when a dot matrix pattern is tilted in depth and observed binocularly from the horizontal direction, is a visual phenomenon ever known in the field of psychology/psychophysics on binocular vision. We studied and formulated the mechanism that generated the phenomenon, and could visualize the whole shape of 3D staircases through a binocular vision model in computer. Our formulation was carried out, based on a hypothesis called "the nearest-neighbor rule." Moreover, we found two types of new staircase illusions induced by a vertical square-wave gratings pattern tilted around horizontal/vertical axis. One is a round-edged staircase illusion, and the other is a vertical strip type staircase illusion. We also constructed a new binocular vision model to formulate the mechanism, adopting the concept of horizontal horopter, and applied it into these new phenomena, and succeeded to visualize the whole shape of their 3D structures. Our computed and visualized results were very similar to those ones human observed in the real world. Our computer model not only verified the results of psychophysical experiments but also showed the possibility to discover/forecast new unknown phenomena that have not ever been referred in previous psychological trials.