JPH02236685A - Two-dimensional data interpolation device - Google Patents

Abstract

PURPOSE:To contrive the high speed of an interpolation processing by selecting the addresses of three points by means of a decimal part address value, preparing a coefficient for the selected three points, reading the data of the three points, and obtaining the inner product of the three point data and coefficient. CONSTITUTION:Two-dimensional real number coordinates (X, Y) are separated into integer part addresses (x, y) and decimal part addresses (Kx, Ky), and based on the value of the decimal part addresses (Kx, Ky), the three point addresses to be used for interpolation are selected out of (x, y), (x+1, y), (x, y+1) and (x+1, y+1). Next, the coefficient for the selected three points is prepared, and the inner product of the three point data and the three point coefficient is obtained. That is, the two-dimensional real number coordinates are separated to the integer part addresses and the decimal part addresses, the three point addresses are selected based on the value of the decimal part addresses, the coefficient for the selected three points is prepared, the three point data are read, and the inner product of the three point data and coefficient is obtained. Thus the two-dimensional data of the real number coordinates can be interpolation-processed at high accuracy and at high speed.

Description

[Detailed Description of the Invention] [Objective of the Invention] (Industrial Application Field) The present invention is a method for interpolating two-dimensional data of real coordinates that do not lie on the integer coordinates where two-dimensional data exists in digital image processing, for example, in affine transformation. The present invention relates to a two-dimensional data interpolation device.

(Prior Art) This type of conventional two-dimensional data interpolation device uses the nearest neighbor interpolation method of allocating the data of the two-dimensional integer coordinate closest to the two-dimensional real number coordinate, or
4 of the integer coordinates around the two-dimensional real number coordinates as shown in the figure.
There are mainly methods that use a 4-neighbor linear interpolation method in which distances between a point and real coordinates in the X and Y directions are temporarily interpolated.

The conventional four-neighbor linear interpolation method shown in FIG. 11 will be explained. In the figure, P (X, Y) is the two-dimensional real number coordinate to be determined, and there are four integer coordinates A (x, y) around this real number coordinate P (X, Y). B (x+ y+
1), C (x-t-1, y+1). D(x+1.y)
It is shown. Also, as shown in the same figure, integer coordinate A
(x, y) and real number coordinates P (X, Y), if kx is a real number smaller than 1 in the X direction, then real number coordinates p (x,
A real number smaller than 1 in the X direction between y) and integer coordinate D(x+1.y) is 1-kx, and integer coordinate A(x,y)
If ky is a real number smaller than 1 in the Y direction between real number coordinates P (X, Y) and real number coordinates P (X, Y), then the real number smaller than 1 between real number coordinates P (X, Y) and integer coordinates B (x.y+1) is 1-
It becomes ky.

The data value of the real number coordinate P (X, Y) to be determined is f
(X, Y), the data value of integer coordinate A (x, y) is r (x, y), the data value of integer coordinate B (cross, y + 1) is f (x, y + 1), integer coordinate C ( x +1.
y +1) as f(x+1, y +1), and the data value of integer coordinate D (X +1, y) as r(x+1
．． y), but the data value r of real number coordinates P (X, Y)
(X, Y) becomes as follows.

r (X, Y) − (1 − kx) ( (
1 -ky) ・r(x.y)+ky・r(x,y+
1)! +kx ((1 −ky) ・ r (
x +1. y)+ky・r(x+
1. y +1) 1 (Problems to be Solved by the Invention) Among the conventional two-dimensional data interpolation devices described above, those that use the nearest neighbor interpolation method have problems with data accuracy;
Furthermore, the method using the 4-neighbor linear interpolation method has a problem in that it takes a long time to process data for 4 pixels, making it impossible to increase the speed.

The present invention has been made in view of the above, and an object thereof is to provide a two-dimensional data interpolation device that interpolates two-dimensional data of real coordinates at high speed with high data accuracy.

[Structure of the Invention] (Means for Solving the Problems) In order to achieve the above object, a two-dimensional data interpolation device of the present invention is a two-dimensional data interpolation device that interpolates two-dimensional data of real number coordinates. The real number coordinates (X, Y) of the dimension are expressed as the integer part address (x.y) and the decimal part address (kx,
ky), and three-point addresses used for interpolation based on the value of the fractional part address (kx, ky) separated by the separating means as (x+y)+(
x+1. y). Cx,y +1). (x +1.
y + 1), coefficient creation means for creating coefficients for the three points selected by the selection means, and data for reading the data of the three points from the addresses of the three points selected by the selection means. The gist of the present invention is to include a reading means, and a product-sum means for calculating the inner product of the three points of data read by the data reading means and the three points of coefficients created by the coefficient creating means.

(Function) The two-dimensional data interpolation device of the present invention separates two-dimensional real number coordinates into integer part addresses and decimal part addresses, selects three points of addresses according to the value of the small loss address, and selects three points from the selected three points. At the same time, the coefficients for the data are created, data at three points are read out, and the inner product of the data at these three points and the coefficients is determined.

(Example) Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of a two-dimensional data interpolation device according to an embodiment of the present invention. The two-dimensional data interpolation device shown in the figure converts the address of two-dimensional real number coordinates (X, Y) into three
2-bit fixed point value X. A real number coordinate address latch 11 that latches as Y, and the real number coordinate address latch 1
The integer part address latch 13 latches the integer part address (x.y) of the upper 16 bits of the 32-bit value starting from 1, and the decimal part address (kx) of the lower 16 bits of the 32-bit value from the real number coordinate address latch 11. , ky)
The decimal address latch 15 latches the decimal address latch 15, and the decimal address latch 15 latches the decimal address latch 15.
a comparator 17 that compares kx and ky of an address addition value creator 19 that sequentially creates address addition values (ΔX, Δy), which will be described later, based on the comparison of kx and ky with 0.5 in step 17, and an address addition value created by the address addition value creation device 19; The value (ΔX, △y) is set to the integer part address (x
. latch 23 and the integer coordinate address latch 2
An image memory 25 that stores coordinate data values r1, r2, r3 for the addresses of the three points latched in
Based on the comparison of kx and ky with 0.5 in the comparator 17, three-point creation coefficients kl, k 2 will be described later.
, k3, and the data values r1., k3 read from the image memory 25. ``2, ``3 and the coefficients k l, k 2 output from the coefficient generator 27
, k 3 inner product k1・rl+k2・r 2+k 3
・Product-sum adder 29 that calculates r3; and the product-sum adder 29
an output data latch 31 that latches the inner product calculated by;
It has a sequence control section 33 that controls the overall operation.

The real number coordinate address latch 11 has two-dimensional real number coordinates (
32-bit fixed point coordinates (X, Y)
,Y), and these 32 bits are divided into 16 bits as shown in Figure 2.
It is divided into a bit integer part address (x, y) and a 16-bit fraction part address (kx, ky). Therefore, real numbers X, Y representing two-dimensional real number coordinates (X, Y) are integers x
, y and real numbers kx, ky smaller than 1 are expressed as follows.

X-x+kx Y-y+ky Here, 0≦kx<1.0≦ky<l.

FIG. 3 is an explanatory diagram of the three-neighborhood image data linear interpolation method used in the two-dimensional data interpolation device of this embodiment. In the figure, the integer coordinates of four points around the two-dimensional real number coordinate p (x, y), that is, the integer coordinates A ('', y), B (x, y +1), as shown in FIG. C (x
+1, y +1) and D (! +1, y) as described below. For example, in Figure 3, integer coordinates ASB and C are selected, and the two-dimensional real number coordinate p (
The data value r(x, y) of x, y) is calculated. That is, in FIG. 3, kx>0.5 and ky≦0.
5, so the integer coordinates A (X, y), B (x,
y +1) and C (x +1, y +1) are selected, and two-dimensional real coordinates P (X,
The data value r(x, y) of Y) is given by the following equation.

r (X, Y) − (1 −ky) ●r
(x. y) + (ky-kx) 11r (
X, y + 1) + kx-r (x + 1. y
+1) Next, the operation will be explained with reference to the flowchart in FIG.

First, the 32-bit two-dimensional real number coordinate (
A 16-bit integer part address (x, y) and a 16-bit decimal part address (kx, ky) are created separately from X, Y) and latched into the integer part address latch 13 and the decimal part address latch 15, respectively (step 11
o).

Next, the comparator 17 compares the decimal addresses kx and ky latched in the decimal address latch 15 with 0.5, and determines where the real coordinates (X, Y) are located in the area shown in FIG. judge.

As can be seen from FIG. 5, the method for determining this area is as follows.

1) Area 1 if 0≦kx≦0.5 and 0≦ky≦0.5 2) Area 2 if O<kx<0.5 and 0≦ky≦0.5 3) 0≦kx≦0.5 and Q<ky<0. 5 (7
), then area 3 1) If O<kx<0.5 and O<ky<0.5, area 4 In this way, the area where the real coordinates (X, Y) exist is determined. Then, the two-dimensional integer coordinates of three grid points near this area, that is, the three points near the area are determined.

That is, as shown in FIG. 6, when area 1 is selected, integer coordinates A, D, B, i.e. A (x, y
), D (x + 1. y) and B (X, y + 1) are selected, and if area 2 is selected, the integer coordinates A,
D, C, i.e. A(x.y), DC! +1. y) and C (x +1. y +1) are selected and area 3
is selected, the integer coordinates A, B, C, i.e. A(X+y), B(x,y+1) and C(x
+1, )' +1) is selected and area 4 is selected, integer coordinates D, B, C1, that is, D(x+
1. y), B(x.y+1) and C(x+1.
Y +1) is selected.

In order to create the integer coordinates of the three points selected in this way, the address addition value generator 19 creates address addition values ΔX and Δy according to the mode of the selected area. These address addition values 8X and Δy are shown in the table of FIG. 6 for each area.

By adding these address addition values △X, △y to the integer part addresses x, y from the integer part address latch 13 in the adder 21, the integer coordinates of the four points A (x, F), B
(!, y+1), C (x+1, y + 1) s
Integer coordinate addresses of the three selected points of D (x + 1, y) are created and latched in the integer coordinate address latch 23 (step 120).

The two-dimensional integer coordinate addresses of the three points latched by the integer coordinate address latch 23 in this way are supplied to the image memory 25, and the data r 1 , f 2 , r 3 corresponding to each address are read from the image memory 25 ( Step 130).

In addition, 3
The coefficients k l, k 2, k 3 of the points are the coefficient generator 27
(step 14o). This coefficient k
l, k2, k3 are as shown in FIG.

Data r1. read from the image memory 25. r 2,
r 3 and the coefficient k l created by the coefficient creator 27
．． k2. k3 is supplied to the product-sum adder 29,
Inner product of both k 1-f 1+k 2-r 2+k 3"
r3 is calculated as a data value of two-dimensional real number coordinates (X, Y) and latched into the output data latch 31 (step 150).

Next, as described above, the coefficients k l, k 2 . Calculation of the data value r(x,y) of the two-dimensional real number coordinates (X,Y) from k3 and the inner product of the data will be explained with reference to FIGS. 7 to 10.

First, in the case of area 1, as shown in FIG.
, y+l) passing through P (X, Y) is A(x, y
) to D(x+1,y) is the point Q,
Letting the lengths between this point Q and A(x, y) and D(x+1., y) be r, 1-r, the following will be obtained.

r-kx:ky-san':1 r-kx鴫kyr r-kx/ (1-ky) Therefore, ding-k>1-neck+(1-ky)y-ky-b+
(1-ky) ((1-r) T+'d}-ky-''M (1-kx-ky) M+kxΦ
d The result is as follows.

rCx. y) - (1-kx-ky)t (X
, y)+ky-r Cx, y +1) +kx-r (! +1, y) Next, in the case of area 2, as can be seen from Figure 8, kx-r: ky-1-r: 1kx
- r - ky - rky r (1 - ky) = kx - ky r - (kx - ky)/ (1 - ky
) Therefore, p -ky-c + (1 -ky) Q-ky●c
+ (1 -ky) ((1-r) ma + 'd} -ky-c + (1 -kx) a + (kx-
ky)d The result is as follows.

r (!. y) = (1 − kx) r Cx
, y)+ky-r D +1,y+1)+
(kx-ky) r (x゛+1.y)
Next, in the case of area 3, as can be seen from Fig. 9, r −kx: 1 −ky−r : 1r
-kx-r -rky r -kx/ky Therefore, p-(1-ky) ・a+ky-q - (1-ky)a+ky((1-r)b+ rcl (ky-kx)b -(1-ky ) a+ + k!e As a result, 1'(x, y becomes as follows.

) − (1 −ky) r (x. y) + (k
y−kx) r (x, y+1)+kx・r(x+1, y+1) Next, in the case of area 4, as can be seen from FIG. 10, kx−r: 1 −ky − 1−r:
1kx-r − 1 −ky-r +r @
kyr − (kx+ ky − 1) /
ky Therefore, +re) + (kx+ky- 1)c As a result, the following is obtained.

r (x, F)= (1-ky)r (x
+1. y ) + (1 − kx) f
(X.F +1)+ (kx+ky-1)
t (X +1, y+ 1) In the above embodiment, two-dimensional image data is used, but the present invention is not limited to this.
It can be similarly applied to other two-dimensional interpolations.

[Effects of the Invention] As explained above, according to the present invention, two-dimensional real number coordinates are separated into integer part addresses and decimal part addresses, three-point addresses are selected according to the value of the decimal part addresses, and this selection is performed. In addition to creating coefficients for the three points, we also read the data of the three points and find the inner product of the data and coefficients of these three points.
Compared to the neighborhood linear interpolation method, data readout time can be reduced to 3/4 while maintaining the same level of data accuracy.
In addition to speeding up the interpolation process, the hardware configuration can be simplified because coefficients are multiplied only once, compared to twice in four-neighbor linear interpolation.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing the configuration of a two-dimensional data interpolation device according to an embodiment of the present invention, and FIG. 2 is a two-dimensional real number coordinate (
Figure 3 is a diagram for explaining the configuration of the integer part address (x, y) and the fractional part address (km, ky) that make up the data (x, y).
A diagram for explaining the neighborhood linear interpolation method, Figure 4 is a flowchart showing the operation of the two-dimensional data interpolation device in Figure 1, Figure 5 is a diagram showing areas, and Figure 6 is a diagram showing three integers for each area. Table showing coordinates, address addition values, and coefficients, Figure 7~
Figure 10 is a diagram for explaining the calculation of the data value f(x.y) of two-dimensional real number coordinates (X, Y) in areas 1.2 and 3.4, respectively, and Figure 11 is a diagram for explaining the calculation of the data value f(x.y) of the two-dimensional real number coordinates (X, Y) in areas 1.2 and 3.4, respectively. FIG. 3 is a diagram for explaining an interpolation method. 11... Real number coordinate address latch 13... Integer part address latch 15... Decimal part address latch 17... Comparator 19... Address addition value creator 21... Adder 23... Integer Coordinate address latch 25...image memory 27...coefficient generator 29...product-sum adder 31...output data latch 33...sequence control section

Claims (1)

[Claims] A two-dimensional data interpolation device that interpolates two-dimensional data of real number coordinates, which separates two-dimensional real number coordinates (X, Y) into integer part addresses (x, y) and decimal part addresses (kx, ky). and three-point addresses to be used for interpolation based on the value of the fractional part address (kx, ky) separated by the separation means (x, y), (x+1, y), (x
, y+1), (x+1, y+1); coefficient creation means for creating coefficients for the three points selected by the selection means; and coefficient creation means for creating coefficients for the three points selected by the selection means. The method is characterized by comprising a data reading means for reading point data, and a product-sum means for calculating an inner product of the data of the three points read by the data reading means and the coefficient of the three points created by the coefficient creating means. Two-dimensional data interpolation device.