Computer graphics processing and selective visual display system – Computer graphics processing – Attributes
Reexamination Certificate
2000-05-16
2004-07-20
Bella, Matthew C. (Department: 2676)
Computer graphics processing and selective visual display system
Computer graphics processing
Attributes
C345S610000
Reexamination Certificate
active
06765587
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an image processing apparatus for processing a digital image signal, specifically for processing a luminance signal and chrominance signals of the digital image signal by using respectively different interpolation techniques.
2. Description of the Related Art
Computer graphics and image processing occasionally require geometric transformation of images, such as enlargement and reduction, rotation and deformation. Geometric transformation of vector-type data requires only coordinate transformation of each vector, but geometric transformation of raster images requires other processing in addition to coordinate transformation. Geometric transformation of raster images refers to projection of an existing image to a different coordinate systems based on a given coordinate transformation equation, and requires the following three stages of processing.
1. Coordinate Transformation
Based on a given coordinate transformation equation, an image coordinate of an input image is transformed into an image coordinate of an output image, or an image coordinate of an output image is transformed into an image coordinate of an input image.
2. Rearrangement of an Image
Image data of the input image is rearranged so as to correspond to a lattice arrangement of the output image obtained by the coordinate transformation.
3. Interpolation of Image Data
Image data of pixels (at the intersections of the lattice) which is required for rearrangement is obtained by interpolation. This is performed since post-coordinate transformation image data is not arranged in a lattice in general.
The rearrangement of image data will be described in more detail. Rearrangement of image data can be performed in two different methods. One method is based on the concept of forward transformation. By the concept of forward transformation, the position on the post-coordinate transformation output image coordinate system which corresponds the position of each pixel of an input image is calculated, and the image data of each pixel of the input image is projected onto the calculated position on the post-coordinate transformation output image coordinate system. The other method is based on the concept of reverse transformation. By the concept of reverse transformation, the position on an input image coordinate system which corresponds the position of each pixel of an output image is calculated, and the image data of the calculated position is obtained. Geometric transformations of raster images generally adopt the concept of reverse transformation. In either method, the coordinate of the position obtained by either method is not an integer in general, and thus interpolation is required.
2-1. Method Based on the Concept of Forward Transformation
The position on the post-coordinate transformation output image coordinate system which corresponds the position of each pixel of an input image is calculated. The image data of each pixel of the input image is projected onto the calculated position on the post-coordinate transformation output image coordinate system. Interpolation processing is performed on an output image coordinate system. The image data of each of pixels on the output image is obtained based on the image data of each pixel of the projected input image.
2-2. Method Based on the Concept of Reverse Transformation
The position on an input image coordinate system which corresponds the position of each pixel of an output image is calculated. The image data of the calculated position is obtained. Interpolation processing is performed on the input image coordinate system. The image data of each pixel of the output image is obtained based on the image data of each of the pixels of the input image arranged in a lattice.
In accordance with geometric transformation of raster images, a forward lattice is set on the post-coordinate transformation output image coordinate system, and the input image is transformed into the arrangement of the image data corresponding to the pixels. Whether the method based on the concept of forward transformation or the method based on the concept of reverse transformation is adopted, the coordinate of the corresponding position obtained by calculation (i.e., the coordinate in the output image in the case of forward transformation, and the coordinate in the input image in the case of reverse transformation) is not an integer in general. Accordingly, the image data of the pixel to be interpolated needs to be obtained by interpolation from the image data of other pixels in the vicinity of the pixel to be interpolated.
There are many interpolation techniques usable for geometric transformation of raster images. Hereinafter, the three main techniques (i.e., nearest neighbor interpolation, bi-linear interpolation, and cubic convolution interpolation) will be generally described.
Herein, the three main techniques will be described when rearrangement is performed based on the reverse transformation, which is common to geometric transformations of raster images. In the following description, the input image coordinate of the pixel to be interpolated is represented by (u, v); and the image data of the pixel is represented by P. A pixel having a pixel number of i and a line number of j is represented by (i,j), and the image data of an input image at pixel (i,j) is represented by P
i,j
. Symbol [ ] is a Gaussian symbol and represents that decimals are omitted.
3-1. Nearest Neighbor Interpolation
The image data at pixel P
i,j
, which is closest to pixel P to be interpolated is used as the image data of pixel P. The image data at pixel P
i,j
is obtained by expression (1).
P=P
i,j
(1)
where
i=[u
+0.5
], j=[v
+0.5].
This technique generates a positional error of ½ pixel at the maximum, but has advantages that the original data is not destroyed and the processing algorithm is simple.
3-2. Bi-linear Interpolation
The image data of pixel P to be interpolated is obtained using image data of four (2×2) pixels (P
i,j
, P
i,j+1
, P
i+1,j
, P
i+1,j+1
) in the vicinity of pixel P based on expression (2).
P
=[(
i
+1)−
u
][(
j
+1)−
v]P
i,j
+[(
i
+1)−
u][v−j]P
i,j+1
+[u−i
][(
j
+1)−
v]P
i+1,j
+[u−i][v−j]P
i+1,j+1
(2)
where
i=[u], j=[v]
This technique disadvantageously destroys the original data but advantageously obtains the effect of smoothing due to averaging.
3-3. Cubic Convolution Interpolation
The image data of pixel P to be interpolated is obtained using image data of 16 (4×4) pixels (P
1,1
, P
1,2
, . . . P
4,4
) in the vicinity of pixel P, using the cubic convolution function represented by the expression (3).
P
=
[
f
(
y1
)
f
(
y2
)
f
(
y3
)
f
(
y4
)
]
[
P
1
,
1
P
2
,
1
P
3
,
1
P
4
,
1
P
1
,
2
P
2
,
2
P
3
,
2
P
4
,
2
P
1
,
3
P
2
,
3
P
3
,
3
P
4
,
3
P
1
,
4
P
2
,
4
P
3
,
4
P
4
,
4
]
[
f
(
x1
)
f
(
x2
)
f
(
x3
)
f
(
x4
)
]
(
3
)
Conventional interpolation techniques used for enlarging and reducing images include, for example, a digital image interpolation circuit for performing a plurality of interpolation techniques disclosed by Japanese Laid-Open Publication No. 8-251400. It is not described in the document that the plurality of interpolation techniques are used in parallel for one color image.
Japanese Laid-Open Publication No. 1-142879 discloses that the cubic convolution interpolation is used only for a luminance signal separated from a video signal source, but does not describe anything on processing of chrominance signals.
The above-described cubic convolution interpolation processes the data as follows. Pixels in the vicinity of the pixel to be interpolated are each multiplied with a positive coefficien
Kubo Noboru
Obuchi Yasuji
Zhang Xiaomang
Bella Matthew C.
Cunningham G. F.
Sharp Kabushiki Kaisha
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