Image analysis – Image transformation or preprocessing – Changing the image coordinates
Reexamination Certificate
1999-09-08
2003-04-08
Mehta, Bhavesh (Department: 2625)
Image analysis
Image transformation or preprocessing
Changing the image coordinates
C358S525000
Reexamination Certificate
active
06546157
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a number-of-pixels conversion apparatus and a display apparatus using the same. More particularly, the invention relates to a number-of-pixels conversion apparatus that interpolates digital data (i.e., pixel data) corresponding to an arbitrary number of pixels, respectively, to display a number-of-pixels-converted version of an image that is represented by the pixel data as well as to a display apparatus using the conversion apparatus.
The above number-of-pixels conversion apparatus and the display apparatus are useful in displaying a number-of-pixels-converted version of an image on a matrix display device in which a number of pixels are arranged two-dimensionally, such as a liquid crystal panel, a plasma display panel (PDP), or a digital micromirror device (DMD).
2. Description of the Related Art
A description will be made of a pixel data conversion method for enlarging or reducing an image at an arbitrary ratio by increasing or decreasing the number of pixels. In the following description, the xy orthogonal coordinate system is used in which the x-coordinate and the y-coordinate correspond to the horizontal direction and the vertical direction, respectively.
FIG. 1
schematically shows a relationship between a pre-conversion image (i.e, on original image) and a post-conversion image. In
FIG. 1
, mark “◯” represents pixel data of the original image and mark “&Circlesolid;”represents image regions after the conversion that correspond to the pixel data “◯” of the original image. It is assumed that the original image is represented by pixel data that have been obtained by sampling in both of the horizontal and vertical directions and that includes m pixels in the horizontal direction and n pixels in the vertical direction. Consideration will be given to a case of enlarging the original image of m×n pixels to pixel data of M×N pixels that includes M(>m) pixels in the horizontal direction and N (>n) pixels in the vertical direction. In this case, the horizontal enlargement magnification factor is M/m and the vertical enlargement magnification factor is N
.
In a pixel data interpolation method for the above conversion in the number of pixels, first, inverse mapping is performed which maps post-conversion coordinates to pre-conversion coordinates.
FIG. 2
shows how a pixel D of a post-conversion image is inversely mapped to coordinates in an original image. In
FIG. 2
, “◯” represents pixels of the original and “&Circlesolid;” represents pixels of the inversely-mapped post-conversion image. To simplify the description, it is assumed that adjacent pixels of the original image have an interval of a distance “1” in each of the horizontal and vertical directions. Further, a pixel of the original image having coordinates (x, y) is denoted by d(x, y) and its density value is also denoted by d(x, y), where x and y are integers.
As shown in
FIG. 2
, the pixel D is inversely-mapped to coordinates that divide the region defined by four pixels d(x, y), d(x+1, y), d(x, y+1), and d(x+1, y+1) at a ratio p:(1−p) in the horizontal direction and at a ratio q:(1−q) in the vertical direction. The inversely-mapped pixel D of the post-conversion image has coordinates (x+p, y+q). It is noted that 0≲p<1 and 0≲q<1.
In the following description, the pixel D for which interpolation is performed based on density values of the original image is called an interpolation pixel and the four pixels d(x, y), d(x+1, y), d(x, y+1), and d(x+1, y+1) of the original image that are used to determine the density value of the interpolation pixel D are called reference pixels.
The density value of the inversely-mapped interpolation pixel D(x+p, y+q) (in the following description, its density value will also be represented by the same symbol D(x+p, y+q) ) is given by Equation (1) below by using the density values of the pixels d(x, y), d(x+1, y), d(x, y+1), and d(x+1, y+1) of the four reference pixels d(x, y), d(x+1, y), d(x, y+1), and d(x+1, y+1) located at the four corners around the interpolation pixel D and interpolation coefficients Hx(p), Gx(p), Hy(q) and Gy(q). The interpolation coefficient is a coefficient that indicates to what extent the associated reference pixel contributes to the interpolation pixel.
D(x+p, y+q)=Hx(p)·Hy(q)·d(x, y)+Gx(p)·Hy(q)·d(x+, y) (1)
+Hx(p)·Gy(q)·d(x, y+1)+Gx(p)·Gy(q)·d(x+1, y+1)
where 0≲p<1 and 0≲q<1. Hx(p) and Gx(p) are functions of the distance p in the x-direction and Hy(q) and Gy(q) are functions of the distance q in the y-direction. Further, Hx(p)=1−Gx(p) and Hy(q)=1−Gy(q).
An interpolation method satisfying Equation (1) has a feature that the above-described interpolation can easily be performed by combining horizontal interpolation and vertical interpolation, which will be described with reference to
FIGS. 3 and 4
.
As shown in
FIG. 3
, first, an imaginary pixel t(y) is assumed that is located from the pixel d(x, y) by a distance p in the horizontal direction. The density value of the pixel t(y) (the density value will be represented by the same symbol t(y) in the following description) can be determined by interpolation based on the density values d(x, y) and d(x+1, y). Similarly, a density value t(y+1) can be determined based on the density values d(x, y+1) and d(x+1, y+1).
Then, as seen from
FIG. 4
, the density value D(x+p, y+q) of the interpolation pixel that is located from t(y) by a distance q from t(y) in the vertical direction can be determined from the above values t(y) and t(y+1).
This is apparent from the fact that Equation (1) can be modified into Equation (2) below.
D(x+p, y+q)=Hy(q)·t(y)+Gy(q)·t(y+1) . . . (2)
where
t(y)=Hx(p)·d(x, y)+Gx(p)·d(x+1, y), and
t(y+1)=Hx(p)·d(x,y+1)+Gx(p)·d(x+1, y+1).
In the interpolation method satisfying Equation (1), since the horizontal interpolation and the vertical interpolation are performed in the directions of the coordinate axes that are perpendicular to each other, they can be processed independently of each other. Therefore, the interpolation characteristics of an interpolation method that is a combination of horizontal interpolation and vertical interpolation can be discussed by independently considering a horizontal interpolation characteristic and a vertical interpolation characteristic. For this reason, in the following description, the interpolation characteristic in each of the horizontal and vertical directions is referred to simply as an interpolation characteristic.
An interpolation method called a linear interpolation method will be described below as a first conventional example that satisfies Equation (1). According to the linear interpolation method, the density value of the pixel D can be determined by multiplying the density values d(x, y), d(x+1, y), d(x, y+1), and d(x+1, y+1) of the four corner pixels of the original image around the pixel D by the complements of their distances in the x and y-directions from the pixel D (i.e., values obtained by subtracting those distances from 1) and adding up resulting products. That is, in the linear interpolation method, the density value D of the pixel D is given by Equation (3).
D=(1−q)·(1−p)·d(x, y)+(1−q)·p·d(x+1,y) (3)
+q·(1−p)·d(x, y+1)+q·p·d(x+1, y+1)
Equation (3), which represents the density value of the interpolation pixel according to the linear interpolation method, is modified into Equation (4) below.
D=(1−q){(1−p)·d(x, y)+p·d(x+1, y)}
+q{(1−p)·d(x, y+1)+p·d(x+1, y+1)} (4)
By substituting 1&minu
Okuno Yoshiaki
Someya Jun
Mehta Bhavesh
Mitsubishi Denki & Kabushiki Kaisha
Patel Kanji
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