Room-size illusion and recovery of the true appearance.

It is widely known among photographers that photographing a room with a wide-angle lens exaggerates the size of the room; nevertheless, such images are commonly found on hotel-reservation web sites. The present paper points out that the size exaggeration is a kind of optical illusion caused by an inappropriate viewpoint from which the image is seen, and presents a method we developed for removing the illusion and thus recovering the true appearance of the room. This method requires only a single image together with the lens center at which the image is taken. From this information, we can generate images that would be obtained if we stand at the same point as the camera and pan around the original scene, changing the view direction. The validity of the method is shown by examples. Possible applications to size-exaggerated images posted on web sites are also discussed.

BetaCavityWeb: a webserver for molecular voids and channels.

Molecular cavities, which include voids and channels, are critical for molecular function. We present a webserver, BetaCavityWeb, which computes these cavities for a given molecular structure and a given spherical probe, and reports their geometrical properties: volume, boundary area, buried area, etc. The server's algorithms are based on the Voronoi diagram of atoms and its derivative construct: the beta-complex. The correctness of the computed result and computational efficiency are both mathematically guaranteed. BetaCavityWeb is freely accessible at the Voronoi Diagram Research Center (VDRC) (http://voronoi.hanyang.ac.kr/betacavityweb).

BetaVoid: molecular voids via beta-complexes and Voronoi diagrams.

Molecular external structure is important for molecular function, with voids on the surface and interior being one of the most important features. Hence, recognition of molecular voids and accurate computation of their geometrical properties, such as volume, area and topology, are crucial, yet most popular algorithms are based on the crude use of sampling points and thus are approximations even with a significant amount of computation. In this article, we propose an analytic approach to the problem using the Voronoi diagram of atoms and the beta-complex. The correctness and efficiency of the proposed algorithm is mathematically proved and experimentally verified. The benchmark test clearly shows the superiority of BetaVoid to two popular programs: VOIDOO and CASTp. The proposed algorithm is implemented in the BetaVoid program which is freely available at the Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

Rectangularity Is Stronger Than Symmetry in Interpreting 2D Pictures as 3D Objects.

It is known that the human brain has a strong preference for rectangularity in interpreting pictures as 3D shapes. Symmetry is also considered to be a factor that the human vision system places high priority on when perceiving 3D objects. Thus, a question is raised: which is more basic, the rectangularity preference or the symmetry preference? To answer this question, we carried out experiments using pictures that have at least two interpretations as 3D objects, one of which was rectangular but not symmetric, and the other of which was symmetric but not rectangular. We found that the preference for rectangularity is stronger than that for symmetry. This observation will help us to understand various 3D optical illusions, including the room-size illusion and the ambiguous object illusion.

A single solid that can generate two impossible motion illusions.

We discovered three-dimensional solids that can generate two different impossible motion illusions. When such a solid is seen from two particular viewpoints, two different shapes are perceived. In both cases the perceived physical motion appears to be impossible.