Computer graphics processing and selective visual display system – Computer graphics processing – Attributes
Reexamination Certificate
1999-04-21
2002-07-23
Brier, Jeffery (Department: 2672)
Computer graphics processing and selective visual display system
Computer graphics processing
Attributes
C345S427000
Reexamination Certificate
active
06424351
ABSTRACT:
TECHNICAL FIELD
The present invention relates to methods and systems for producing three-dimensional images of a scene. More particularly, the present invention relates to modeling a scene using relief textures, pre-warping the relief textures into two-dimensional textures that are perspectively correct from a desired viewpoint, and texture mapping the two-dimensional textures to polygons used to model the scene.
RELATED ART
In computer graphics, conventional textures are two-dimensional patterns or arrays of pixels used to add detail to computer-generated images. In other words, each pixel in a conventional texture has a row coordinate in texture space, a column coordinate in texture space, and a color value. Texture mapping is the process of mapping two-dimensional textures onto polygons used to model objects displayed on a computer screen. For example, the front of a building may be represented by a rectangle in computer graphics. A texture for the front of the building may include the windows. Texture mapping is utilized to map the pixels in the texture from texture space to screen space. The most common form of texture mapping is inverse mapping. In inverse mapping, the color of each pixel in the rectangle is determined projecting the footprint of each pixel in screen space to texture space and integrating the pixel colors in the texture that fall within the footprint.
One problem with conventional texture mapping is that images created using conventional methods appear flat when viewed from different viewpoints.
FIG. 1
illustrates computer images of a photograph viewed from different viewpoints. In
FIG. 1
, a first image
100
is a photograph shown from a viewpoint orthogonal to the plane of the page. A second image
106
is the same photograph shown from a viewpoint below the viewpoint of the image
100
. In images
104
and
102
, the photograph is shown from viewpoints shifted to the left and right of the viewpoint of the image
100
. Because the photograph is flat, and the corresponding image is flat, occluded objects in the photograph cannot be seen when the viewpoint changes. For example, additional features of the person in the photograph do not become visible when the viewpoint changes. If, however, the actual scene is viewed, different things could be seen from the different viewpoints. For example, if the actual scene were viewed from the viewpoints of the images
104
and
102
, left and right side views of the profiles of the person in the scene would be visible.
In computer graphics, the images of the photograph in
FIG. 1
are the same as conventional textures, i.e., each image is a set of pixels, each having a row coordinate, a column coordinate, and a color value. The mapping of the images in
FIG. 1
onto different viewing planes illustrates the limitations of conventional texture mapping. Thus, like the images of the photograph in
FIG. 1
, surfaces represented by two-dimensional textures appear flat when the viewpoint changes.
FIG. 2
is an example of a scene represented with three polygons using conventional texture mapping. The red lines represent the borders of the polygons. Textures
200
,
202
, and
204
are mapped to the polygons and represent faces of buildings from the original scene. Because the textures do not convey depth information with regard to the actual surfaces they represent, the reproduction of the scene appears flat.
FIG. 3
illustrates conventional texture mapping in the one-dimensional domain. In
FIG. 3
, a first image
300
may represent a horizontal section through a two-dimensional texture. A second image
302
is a projection of the image
300
onto a projection plane
304
. A third image
306
is a projection of the image
300
onto a projection plane
308
. A fourth image
310
is a projection of the first image onto a projection plane
312
. Because of the viewing angles between the original image and the projection planes
308
and
312
, non-uniform contraction of the original image may occur. For example, in
FIG. 3
, the original image includes a red area
314
, a green area
316
, and a blue area
318
. In the image
310
, the red area
314
maps to red area
320
. The green area
316
maps to green area
322
, and the blue area
318
maps to blue area
324
. Because of the viewing angle, the contraction of the red area between images
300
and
310
is greater than the contraction of the blue area. Despite the non-uniform contraction of the projected image, there is a one-to-one mapping between points of the original image
300
and points of the projected image
310
. Because the mapping from original to projected images is one-to-one, the mapping can be easily inverted, i.e., given coordinates on the projected image, the computation of the corresponding coordinates on the original image is straightforward. When the projection plane is a computer screen and the original image is a texture image, this mapping is referred to as texture mapping. When pixels are mapped from the texture coordinates to the screen coordinates, the mapping is referred to as a forward mapping. When pixels are mapped from screen coordinates back to texture coordinates, the mapping is referred to as an inverse mapping. Because there is a one-to-one correspondence between pixels in the original and projected images in texture mapping, inverse mapping requires only simple calculations. The simple nature of the inverse formulation of texture mapping is known, presents several filtering advantages over the forward mapping, and is a standard operation in most computer graphics hardware.
Texture Mapping and Three-Dimensional Image Warping
Three-dimensional image warping is a mapping from a sampled three-dimensional model of a scene to a two-dimensional image from a given viewpoint. Texture mapping is a special case of three-dimensional image warping for which the input image is planar, as in the examples illustrated in
FIGS. 1 and 2
. Thus, for conventional two-dimensional images, both techniques produce exactly the same results. The difference between texture mapping and three-dimensional image warping is primarily in the type of input images, rather than the process, as will be explained in more detail below. Because conventional texture mapping only handles planar images, its equations are simpler than those used for three-dimensional image warping. Equations (1)-(4) shown below illustrate the relationship between texture mapping and three-dimensional image warping. Equations (1) and (2) define forward texture mapping; whereas, equations (3) and (4) define forward three-dimensional image warping. Each of the equations express how elements (pixels) of the input image represented by the coordinates (u
1
, v
1
) are mapped to elements of the projected image represented by the coordinates (u
2
, v
2
). In Equations (3) and (4), displ(u
1
, v
1
) represents the height of each pixel in an image measured from a basis plane of the image. If displ(u
1
, v
1
) is constant for all elements of the input image (i.e., the image is planar), equations (3) and (4) reduce to an instance of equations (1) and (2), respectively.
u
2
=
Au
1
+
Bv
1
+
C
Iu
1
+
Jv
1
+
K
(
1
)
v
2
=
Eu
1
+
Fv
1
+
G
Iu
1
+
Jv
1
+
K
(
2
)
u
2
=
Au
1
+
Bv
1
+
C
+
Ddispl
(
u
1
,
v
1
)
Iu
1
+
Jv
1
+
K
+
Ldispl
(
u
1
,
v
1
)
(
3
)
v
2
=
Eu
1
+
Fv
1
+
G
+
Hdispl
(
u
1
,
v
1
)
Iu
1
+
Jv
1
+
K
+
Ldispl
(
u
1
,
v
1
)
(
4
)
Images with Depth
Images with depth are images in which each pixel has an associated depth value representing a distance between the sample and the center of projection of a real or imaginary camera used to define the image. Images can be spherical, cylindrical, etc., but such images are not within the type of images referred to herein as non-planar images or images with depth. Due to the two-dimensional nature of the film and paper used to acquire and print pictures, images are commonly thought of as two-dimensional entities. In fact, an image is a mapping from a two-dimensional support to a multidimensional space. Such space is usually a color space
Bishop Thomas G.
Oliveira Neto Manuel M. de
Brier Jeffery
Jenkins & Wilson, P.A.
The University of North Carolina at Chapel Hill
Yang Ryan
LandOfFree
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