text: 1. Field of the Invention
  The present invention relates to a three-dimensional image display apparatus and a method for displaying a three-dimensional image.
  2. Description of the Related Art
  In recent years, apparatuses have been developed which display three-dimensional images that can be observed with the naked eye. Naked-eye display apparatuses for three-dimensional images are known to be based on a twin lens scheme or a multi-lens scheme. In the twin lens or multi-lens three-dimensional image display apparatus, a beam control element such as a lenticular sheet (a flat protruding rod and lens array having lens properties only in a horizontal direction) or a parallax barrier is arranged opposite a display surface of the display apparatus with a gap between the beam control element and the display surface. With this apparatus, two-dimensional images offering parallaxes are separately incident on the right and left eyes so that an observer can perceive a “three-dimensional image that allows a three-dimensional object to be perceived in only one direction”. With the twin lens display of a three-dimensional image, two two-dimensional images are observed from the observer's eye point in only one direction so that the observer can perceive a three-dimensional object. With the twin lens display of a three-dimensional image, the eye point is fixed, so that the moving observer cannot perceive the three-dimensional image. In contrast, by way of example, with the multi-lens display method for three-dimensional images allowing the three-dimensional image to be observed from eye points in three directions, four two-dimensional images are provided and the observer observes two of these two-dimensional images which correspond to each of the eye points in three directions. The observer can perceive the three-dimensional images from each eye point. Consequently, even the moving observer can be provided with movement parallaxes, which are inconsecutive. Here, the movement parallax is defined as a phenomenon in which an image of the object appears to be moving in a direction opposite to that in which the observer's body is moving.
  A II (Integral Imaging) scheme is known to display three-dimensional images that allow the observer to be more appropriately provided with movement parallaxes. The II scheme is based on what is called an integral photography (IP) scheme proposed by M. G. Lippmann in Comptes Rendus de l'Academie des Sciences, Vol. 146, pp. 446-451 (1908), which relates to techniques for taking and reproducing three-dimensional photographs. The integral photography (IP) scheme is also called an integral imaging (II) scheme. With the integral imaging scheme, such a lens array as correspond to pixels in a three-dimensional photograph is provided. A film is then placed at the position of the focal distance of the lens array, and an image of the subjected is picked up. The lens array used for the image pickup is placed on the film subjected to the image pickup. The image of the subject is then three-dimensionally reproduced. With the II scheme, beam information recorded on the film via the lenses contains beam traveling directions during the image pickup. Consequently, during display, the beam traveling directions during the image pickup are reversed to emit beams to a space through the film, allowing a three-dimensional image to be reproduced. As is apparent from this process, provided that an observation position in the space is not fixed and that the film has a sufficient resolution, a perfect spatial image can be reproduced as in the case of holography. The II scheme is considered to be an ideal display scheme that allows three-dimensional images to be spatially displayed without limiting the observation position.
  A three-dimensional image display apparatus based on the II scheme uses a liquid crystal display (LCD) as a flat panel display, in place of the film. A lens array is located in front of the liquid crystal display as a beam control element with a gap between the lens array and the liquid crystal display. Beams emitted by pixels in the liquid crystal display are incident on a lens, which limits the traveling direction of the beams. The beams are thus emitted toward the space, allowing a three-dimensional image to be displayed in the space in front of the display or behind the display. With the three-dimensional image display apparatus based on the II scheme, as disclosed in H. Hoshino, F. Okano, H. Isono, and I. Yuyama, Opt. Soc. Am. A., Vol. 15, pp. 2059-2065 (1998). NHK, an increase in the number of pixels arranged behind the lens, that is, the number of pieces of parallax image information (parallax component images that are differently viewed depending on viewing angle) increases the display range in front of or behind (rear surface side) the display, where a three-dimensional image is displayed. However, with the resolution of LCD fixed, lens pitch increases to reduce the resolution of the three-dimensional image. In particular, a one-dimensional IT (1D-II) scheme which provides parallax information only in a horizontal direction and which is different from the multi-lens scheme may be confused with the multi-lens scheme, which is considered to belong to the same category as that of the 1D-II scheme owing to the use of a lenticular sheet.
  However, the II scheme is characterized by increasing the number of parallaxes to as large a value as possible taking a decrease in the definition of eye point images, and avoiding assuming the observer's position for beam design, that is, avoiding providing beam converging points at positions corresponding to the respective eyes during observation. This characteristic is definitely different from that of the multi-lens design in which the number of parallaxes is set at a smaller value between 2 and 4 in order to inhibit a decrease in the definition of parallax images and in which the beam converging points are provided at the positions corresponding to the respective eyes to allow a three-dimensional image to be perceived.
  Specifically, according to the multi-lens scheme, the lens pitch (Ps) along the horizontal direction is designed to be smaller than an integral multiple of horizontal pixel pitch (Pp) (m×Pp: m is a natural number equal to or greater than 3). The ratio of the lens pitch to the horizontal pixel pitch is determined by the ratio of the focal distance g of the lens array to observing visual distance L. That is, the following formula (1) is given,Ps:m×Pp=L:(L+g)  (1)
  wherein m denotes an integer equal to or greater than 3.
  Owing to the relationship expressed by Formula (1), m converging points are generated at the observing visual distance L. The distance between the adjacent beam converging points is equal to the inter-eye distance. This necessarily determines the value of g.
  On the other hand, with the II scheme, the lens pitch (Ps) along the horizontal direction or an integral multiple of the lens pitch (Ps) (n×Ps: n denotes an integer equal to or greater than 1) is designed to be equal to an integral multiple of horizontal pixel pitch (Pp) (m×Pp: m is a natural number equal to or greater than 3). That is, the following formula (2) is given,Ps=m/n×Pp  (2)
  wherein n denotes an integer equal to or greater than 1. m denotes an integer equal to or greater than 3.
  Since the relationship expressed by Formula (1) is established, beams are emitted from a plurality of lenses so as to establish a parallel relationship. That is, no such special beam converging points on which beams are converged are provided at the visual distance. Thus, at any observation position, the observer can view a three-dimensional image that is to be substantially viewed from that position on the basis of the sum of beams incident on the eye. That is, consecutive movement parallaxes can be realized. Similar effects are expected to be exerted when the beam converging points are arranged at a distance sufficiently farther than the observing distance.
  Thus, with the II scheme, beams are reproduced so as to be discretely extracted from a surface on which an object is actually present. Consequently, when the number of parallaxes increases to and above a certain value, the observer can view a binocular eye point image that can be substantially viewed from the observation position within the observation range. The observer can also obtain consecutive movement parallaxes. With the multi-lens scheme, importance is attached to the definition of the eye point image, resulting in incomplete movement parallaxes. In contrast, with the 1D-II scheme, which does not provide any special beam-converging points, the balance between the binocular parallax and the movement parallax is taken into account for design. This allows the display of more natural images that prevent the observer from feeling fatigued.
  Thus, the large number of parallaxes is one of the characteristics of the display apparatus displaying three-dimensional images on the basis of the II scheme. The large number of parallaxes means (A) the long distance between adjacent lenses corresponding to pixels in a three-dimensional image, that is, the lens pitch set at a large value, and (B) the large number of directions in which parallax information required to display a three-dimensional image is acquired. For the former (A), as described in JP-A 2004-040722 (KOKAI), the horizontal pitch at which parallax information is presented is set equal to the distance between sub-pixels (an R pixel, a G pixel, and a B pixel), to reduce the distance between the adjacent lenses. For the latter (B), as described in JP-A 2003-288612 (KOKAI), the design in which beams are emitted substantially parallel to one another is adopted to efficiently acquire parallax information while preventing beam converging points from being generated in an observation area. With this design, parallel-projection eye point images can be used to efficiently acquire pieces of parallax information to be displayed at pixels for which beam directions are in a parallel relationship.
  In connection with the parallel-projection II scheme, JP-A 2004-212666 (KOKAI) discloses a method for optimizing the layout of a group of display pixels at which element images corresponding to lenses are displayed and pieces of parallax information displayed at the grouped display pixels, depending on the positions of the lenses on a display surface of the three-dimensional image display apparatus, in order to enlarge an area in which a three-dimensional image can be observed at a finite visual distance, that is, a viewing area. Here, the element images mean a set of parallax component images each corresponding to a single lens. A problem with the display apparatus disclosed in JP-A 2004-212666 (KOKAI) is an increase in the number of directions in which parallax images are acquired. The increase in the number of directions in which multi-eye-point images are acquired may increase the amount of rendering loads if each eye point image is rendered by CG. This may affect scenes that require a high processing speed such as in real-time rendering. Also for live action, the increase in the number of directions in which multi-eye-point images may disadvantageously increase the amount of image pickup loads.
  As a method for reducing the number of parallaxes, JP-A 2005-331844 (KOKAI) proposes a method of replacing some of the parallax component images in accordance with the II scheme with twin lens or multi-lens images. That is, according to the method disclosed in JP-A 2005-331844 (KOKAI), the grouped display pixels at which the element images are displayed, parallax information from the same projection eye point image is assigned to at least three pixels arranged at the same position. However, with this method, strictly speaking, the direction of each beam does not match the corresponding parallax information, unavoidably degrading image quality. In general, whether the lenses or slits are arranged in front of the display panel, it is difficult to limit the number of pixels observed by the observer via one exit pupil, that is, the number of pieces of parallax information, to one, in connection with the curvature of an image surface or the aperture. That is, disadvantageously, the observer may actually view at least two pixels via the one exit pupil. The phenomenon in which the observer views at least two pixels via the one exit pupil is called cross talk in the II scheme. The proposal in JP-A 2005-331844 (KOKAI) assigns the same piece of parallax information to at least three pixels taking the cross talk into account.
  Another problem is that an image exceeding a protrusion or depth limit as defined in H. Hoshino, F. Okano, H. Isono, and I. Yuyama, J. Opt. Soc. Am. A., Vol. 15, pp. 2059-2065 (1988). NHK is viewed as a multiple image. This problem occurs because the intervals (angles) at which parallax information is presented needs to be reduced in order to display a three-dimensional image with a significant protrusion or depth but because the intervals (angles) are insufficient. However, because of the above-described cross talk, significant parallaxes may make the three-dimensional image appear multiplied.
  As described above, the method for displaying three-dimensional images utilizing multiple parallaxes on the basis of the II scheme disadvantageously imposes the heavy burden of creating two-dimensional images to be displayed on the display panel. The three-dimensional image display apparatus offering multiple parallaxes so as to enable three-dimensional viewing with the naked eye disadvantageously makes an image appear multiplied when the image is displayed with the protrusion or depth display limit exceeded. That is, with the three-dimensional image display apparatus based on the II scheme, beams are set to have a substantially parallel relationship, increasing the number of directions in which eye point images are acquired as well as the amount of rendering loads.