Construction of Autostereograms Taking into Account Object Colors and its Applications for Steganography Yusuke Tsuda Yonghao Yue Tomoyuki Nishita The University of Tokyo ftsuday,yonghao,[email protected] Abstract Information on appearances of three-dimensional ob- jects are transmitted via the Internet, and displaying objects q plays an important role in a lot of areas such as movies and video games. An autostereogram is one of the ways to represent three- dimensional objects taking advantage of binocular paral- (a) SS-relation (b) OS-relation lax, by which depths of objects are perceived. In previous Figure 1. Relations on an autostereogram. methods, the colors of objects were ignored when construct- E and E indicate left and right eyes, re- ing autostereogram images. In this paper, we propose a L R spectively. (a): A pair of points on the screen method to construct autostereogram images taking into ac- and a single point on the object correspond count color variation of objects, such as shading. with each other. (b): A pair of points on the We also propose a technique to embed color informa- object and a single point on the screen cor- tion in autostereogram images. Using our technique, au- respond with each other. tostereogram images shown on a display change, and view- ers can enjoy perceiving three-dimensional object and its colors in two stages. Color information is embedded in we propose an approach to take into account color variation a monochrome autostereogram image, and colors appear of objects, such as shading. Our approach assign slightly when the correct color table is used. Our technique can also different colors to a pair of points on the screen, which are be used for steganography to hide color information. More- seen as the same point on the object when performing stere- over, file size gets smaller than that of an original autostere- opsis. The images constructed using our method can be ogram image because indexed colors are used. Therefore, used for amusement. the 3D images constructed using our method are useful for In an autostereogram, a virtual screen S is placed be- tranmission through the cyberworld. tween viewer and the object, and an autostereogram image is constructed by placing points on S. There are two rela- 1. Introduction tions to be considered in constructing autostereogram im- ages. Firstly, in performing stereopsis, since viewer sees Three-dimensional objects are displayed for many pur- a pair of points on S with left and right eyes, and perceive poses such as research about human vision and represen- them as a single point on the object, these three points corre- tation of virtual objects in movies, and there are a lot of spond with each other (Figure 1(a)). We define the relation- ways to display objects. Depth information is important for ship between these three points as a relationship in screen three-dimensional impression, and is usually represented by space (SS-relation). Secondly, since a single point on S is displaying the objects on the screen using perspcetive pro- not only seen by just one eye, but by two eyes, so a sin- jection. An autostereogram is one of the ways to represent gle point on S and a pair of points on the object correspond three-dimensional objects by ordinary display devices tak- with each other (Figure 1(b)). We define the relationship ing advantage of binocular parallax which plays an impor- between such three points as relationship in object space tant role in depth perception. (OS-relation). Autostereogram images are constructed tak- In the previous methods, color autostereogram images ing into account these relations alternately. Because of OS- have not taken into account the objects' colors. Therefore, relation, the color of a single point on S is related to colors of two corresponding points on the object, however is as- signed irrelevant to the colors of the points on the object in previous methods. In this paper, we propose a method to determine the color of points on S. Although a pair of points on S has an SS- relation with a point on the object, such points on S also (a) (b) have OS-relations with other points on the object. There- fore, in our method, slightly different colors are assigned to Figure 2. Random Dot Stereograms showing a pair of points on S which have SS-relation. The allowable a teapot: (a) a stereo pair, and (b) an au- differences of colors are determined by an user test. We also tostereogram. Methods to perform stereop- consider the limitation of representation of colors because it sis are explained in Section 3.2. is expected that object colors with wide variety are difficult to be represented in autostereogram images. tograph with three-dimensional information recorded in. We also propose a method to apply color autostereogram Holograms were first created by Denisyuk [4] in 1962, and images to the amusement of color emergence. Two-stage later by Leith and Upatnieks [8] in 1962. Except for stereo perceptions of three-dimensional object and its colors are pairs, all the methods discussed above need special devices amusing. In the first stage, a sand storm like autostereogram to record information or to view three-dimensional objects. image is displayed. This image has color information in Julesz [6] invented Random Dot Stereogram (RDS), color index, but colors are not displayed because a dummy which is a technique to construct a pair of images consisting color table is embedded in. In the second stage, color au- of random dots (Figure 2(a)). Tyler et al. [13] combined tostereogram image is displayed by using correct color ta- a pair of random dot images into a single image, and cre- ble. It is amusing that monochrome object and color object ated Single Image Random Dot Stereogram (SIRDS) (Fig- can be perceived in two stages. In addition, our technique is ure 2(b)). SIRDS is a form of autostereogram or single- a kind of steganography in the sense that the existence of in- image stereogram (SIS), and view angles of autostereogram formation about object colors are hidden. Color information images can be wide. Kinsman [7] showed a method to cre- can be transmitted only to those who should receive color ate colored autostereograms from a depth map and a pattern information by taking advantage of our method. Moreover, image. His method was based on orthogonal projection. In since indexed colors are used to encode the autostereogram his method, pattern images are distorted according to depth images, file size is reduced from original file size. maps and are tiled horizontally, and colors of the objects are The rest of this paper is composed as follows. Related out of consideration. In the previous autostereograms, ex- work is described in Section 2. Section 3 reviews pre- actly the same color is assigned to a correlated pair of points vious methods constructing monochrome autostereograms. on the image. This is because, in autostereograms, two or We describe the algorithm to determine colors of autostere- more horizontal points on the image tend to have correlation ogram images in Section 4. An algorithm to embed color in- with each other due to the SS-relation and the OS-relation, formation in autostereogram images, and to construct color and two of the correlated points on the image are thought to tables used as encryption keys is described in Section 5. We be seen as the same point on the object only when they share show the results in Section 6, and describe conclusion and the same color. Our method improves autostereograms to future work in Section 7. take into account color variation of objects. Recently, a lot of methods are researched to improve the 2. Related work performance in the construction of SIRDS. Thimbleby et al. [12] showed an algorithm based on the perspective pro- Wheatstone [14] invented stereoscopes, by which two jection. Yu et al. [15] created a fast and memory saving images drawn or taken from slightly different angles are re- algorithm based on ray-tracing. Petz et al. [11] introduced spectively projected to each eye. David Brewster [1] built an algorithm which is suited for hardware-acceleration and stereo cameras, by which two pictures of scenes can be succeeded in constructing SIRDS images at real time. taken. Stereogram images, which consist of a pair of pho- Applications of stereograms are also searched. Omori tographs or images are called stereo pair, and view angles et al. [10] analyzed the recognition of stereoscopic images of the images can not be wide because it becomes diffi- among elderly people using stereogram images on liquid cult to perform stereopsis when two points on the image, crystal display and papers. Dadson [3] described the tools which are to be seen as the same point on the object, are for evaluation of stereoscopic camera systems using RDS too separated. Gabor [5] invented holography taking ad- built with ray tracing. Liu et al. [9] developed a system vantage of the interference between beams. Holography is to display trajectories of particles on stereogram images. a technique to produce a hologram, which is a kind of pho- Stereograms also appear on books for amusement [2]. 3. Constructing and viewing autotereograms squares are seen to be four squares, the two of which are seen from the left eye, and the others are seen from the In this section, we first review the methods to con- right eye. By adjusting eyes so that the center two of these struct autostereogram images, and then review the viewing four squares are seen at the same position, the eyes are fo- method to perform stereopsis.