JPH01113878A - Linear density transformation system - Google Patents

Abstract

PURPOSE:To reduce the capacity of a working table by forming a partial interpolation table based on the objective properties of the intra-grid address of a picture element to be mapped. CONSTITUTION:For intra-grid coordinates corresponding to each other via respective quadrants R1-R4, a transformed picture element value can be obtained just by rearranging the permutations of original picture elements of a grid area. With a notice given to this fact, a table corresponding to the intra- grid addresses is prepared for one of those quadrants R1-R4. In case the quadrant R1, for example, is defined as an objective area, values 0-3 are sufficient with the intra-grid addresses in both the raster direction and the direction vertical to the raster direction. Thus the most significant bits u2 and v2 can be omitted in each direction of the intra-grid coordinates. In such a way, the conventional (2<3>X2<3>) ways of combinations can be cut down to (2<2>X2<2>) combinations for the intra-grid coordinates. Thus the table capacity can be cut down to 1/4.

Description

[Detailed description of the invention] [Industrial application field] The present invention relates to a linear density conversion method for digital images.

[Conventional technology]

Conventionally, as linear density conversion of digital images, for example, Information Processing Society of Japan's Journal Vol. 24, No. 6 (Nov,
(1983) titled ``A high-speed processing method for image scaling using the periodicity of lattice coordinates,'' in which pixels before conversion are converted using the pixel values of the end points of the lattice that include the points to be moved after conversion, and the positions within the lattice. A method for determining subsequent pixel values is known.

The above conventional technology focuses on the fact that when an original image is subjected to linear density transformation, the pixel position after the transformation changes periodically within the lattice of the original image. Each time the table address is given, the in-lattice coordinates are determined by updating the table address, and the converted pixel value is determined based on the in-lattice coordinates and the pixel values of the four end points forming the grid. In this case, the density calculation is also uniquely determined by the four end points and the grid coordinates, so by storing the calculation results in a table (hereinafter referred to as the density calculation table), arithmetic operations can be omitted and images can be imaged at high speed. can be processed.

[Problem that the invention seeks to solve]

However, in the above-mentioned conventional technology, it is necessary to store a concentration calculation method for each lattice coordinate point, and this table requires a large memory capacity.

An object of the present invention is to provide a linear density conversion method that can reduce the capacity of tables used.

[Means for solving problems]

In order to achieve the above object, the present invention divides the grid into two parts vertically and horizontally from the center line, has a table for only one of the divided areas, and calculates the other part using the table and logical operations. It is characterized by

[Effect]

In the present invention, the most significant bit of the lattice coordinates is used to rearrange the four pixels constituting the lattice area, which is a factor in density calculation. Therefore, the same address in the table will not be referenced repeatedly from different grid coordinate points, and grid coordinates that cannot be calculated will not exist.

〔Example〕

Hereinafter, one embodiment of the present invention will be described with reference to the drawings.

FIG. 1 shows the main parts of an image data processing system, and in FIG. 1, 1 and 2 are line memories. Here, the reason why the line memory is divided into two is that when performing density calculation, the processed data is obtained by using the pixel data of the grid point that includes the pixel after density calculation from two adjacent rasters. This is to distinguish between the line memory of the previous raster and the line memory of the subsequent raster. When calculating density using pixel data of three or more rasters, line memories equal to the number of rasters to be referenced are required. 3 is a shift register, which is controlled by a shift controller 5. That is, when moving the grid used for density calculation, one pixel of data is input from the line memories 1 and 2 to the shift register 3 using the shift clock 4, and one pixel of data is input from each shift register to the density calculation section 6. Output.

The density calculation section 6 performs density calculation based on the pixel values output from the shift register 3.

In image scaling processing, the coordinates of grid points after mapping have periodicity (Information Processing Society of Japan Journal Vol. 124)
Na6. Nov1983 p754 to p763 "High-speed processing method for image scaling using periodicity of lattice coordinates". In Figure 2, the lattice spacing of the original image is A, B, the original pixel in the i-th row and j column (xt J is a natural number) is represented by Pig, and the lattice coordinates after scaling the image are Q (IIll). The relationship between the original image lattice and the converted lattice is shown below. If the lattice spacing after conversion is a, b, then the scaling ratio is.

α=A/a and β=t3/b hold true. Also, pixel Q(,,,) after conversion is P Cxwrg 'Iv) g P (xm”ty
Y+m') P(xme Ym"l)vP (xm+
x, Y11+1) (hereinafter referred to as the lattice region of Q an), then X.

The relationship between , and Y n g n is:
Y o= INTEGER [(m −1)・b/B] −
The distance from the upper left point of the grid in the +1 grid area can be expressed as um=(m-1)a, mcdA vn"(m-1)b, mcdB. In this example, the distance from the upper left point of the grid in the grid area can be expressed as: Concentration calculation is performed using the four points and grid coordinates in the grid area.

In Figure 3, suppose that the point P (1,.) of the original image moves to Q (p, q) due to transformation.

The pixels constituting the grid area are P (at n) vP (
m+t+nLP (me n”l)y P (m+t*
n+z). The pixel value of Q (,, q) is
It is calculated using the lattice coordinates u (pt q), v (p, 'q) and the above four points, but when performing such interpolation, 1. For example, the converted pixel is at the position shown in Figure 3. If there is a point PC-+ Appropriate. When defining the distance between each pixel in the grid area by the distance from the point after conversion, the calculation formula has the following characteristics. That is, the calculation formula for Q Cp, q) is as follows.

Q(p=q)=P(--11)・D(u(p,q)-
v(p, q)) + P(, ◆z, n)・D(A-u (p
pqLv(ptq))+P(m@n+t)'D(u(p
tq)tB V(Ptq))+P(,÷1.n+t)
・D(A-u(p, q)tB v(p, J) −・・
a) (where D (Xs y) is a function of the distance components x, y between the conversion point and the corresponding original pixel), and the grid distance in the same grid area is u' (pt q) = A u (pt q )V
' (p, q) = B-v (p, 慴) The pixel calculation formula for the conversion point is Q' (p, q) = P (-n) · D (A u (p, q
), B−v(p,J)+P(m+ttn)・D(
A-u (pyq)t V (prq))+P(-2n
÷n)・D(u(p, J, B−v(p, q))+P
(m+1.net)・D(u(ppq)ev (ptJ
) - (2), and equations (1) and (2) become equivalent by switching the relationship between the distance function and the corresponding pixels. Similarly, as shown in Figure 3, the lattice area is defined as the rask direction.

When the rask is equally divided into two in the vertical direction, the generated grid area is divided into four regions (R1e Rz, Ra e R
By changing the distance function and the corresponding pixels for each step a), there is always one position where the converted pixel can be found.

The above formula (1) is 4 pixels P (at n)-e P Cm
+xpn)tP(nt net)@P (m+z*n
Since it is a function determined by ``i) and u (psqLV(pyq)), Q(P, q)=f(P(,,n),P(,÷1.n)p
P (mym”t)tP (+a+11n÷1).

u (Fyq) * V (Fyq)
...(3), each point Q Rt to QR4 corresponding to R1 to R4 in FIG. 4 can be expressed as follows.

In this embodiment, the coordinate points in the grid are digitized, the calculated values D (u, v) corresponding to each coordinate point are stored in advance in a memory such as a ROM, and the four end pixels of the grid area and the coordinate points in the grid are The calculated value is selected from the ROM.

For example, as shown in FIG. 5, the table setting method will be explained with reference to FIG. 6 in the case where grid coordinate positions exist only at the intersections of straight lines dividing the rask direction and the rask perpendicular direction into eight parts. The grid area original pixels are the four end points that make up the grid area. For simplicity, a binary image is taken as an example, but the same applies to multi-valued images. The grid coordinates are the values obtained by digitizing u and v. In this example, the grid is divided into 8 parts, so the values in the table are INTEGER (8 parts u/A) and INTEGER (8 parts v/B). ) and 0 to 7
It can be expressed as

Therefore, it is expressed by 3 bits in the rask direction and 3 bits in the rask vertical direction. Using the above 10 bits, formula (1)
The pixel value Q Cp, q) calculated by is stored in the memory in advance. In the conventional method, Q (,, q) is set for the combination of the original pixel value of the entire grid area and the entire case preliminary coordinate, so the amount of memory required is: 21OX 1 bit = 1024 words x 1 Becomes a bit.

(However, this is for a binary image, and in the case of 2' gradation, the grid point original pixel is 4Xnbit, and the output pixel value is nbit.
Therefore, 2 e+in words X nbits of memory are required.

1 for the corresponding grid coordinates in each quadrant R1” Ra
From Equation (4), the converted pixel value can be obtained by simply rearranging the permutations of the grid area original pixels.

Taking note of this, in the present invention, a table corresponding to addresses within the lattice is prepared for only one of the quadrants R1 to R4.For example, when R1 is the target area, the address within the lattice is , a value of 0 to 3 in each of the rask direction and the rask perpendicular direction is sufficient, and the most significant bits uz and vx in each direction of the lattice coordinates in FIG. 6 can be omitted. In other words.

The above table shows that in the conventional case, the combination of lattice coordinates is
Whereas there used to be 2s x 28 pieces, according to the present invention, 2" x 2" is sufficient, so the capacity of the table is reduced to 1/4
That's enough.

The recombination of the grid point original pixels according to the region can be determined by the most significant bits ul and v2 in each direction of the grid coordinates.

FIG. 7 shows a block diagram of a system using the above-mentioned simplified table, with four pixels D1 to D4 used for calculation.
The combination changes as follows for each region of R1-R4.

D1=R1・P(,,Il)+R2・P(lI+1.n
) 10R3・P(,,.+1)+R4・P (m+11n
÷1) D2=R1'P(m+xtn)+R2''P(+a+it
n+t)+R3'P(m,n)+R4・P(mym"
t) D3=R1・P(ll, Il+1)×R2・P(,,n
)+R3・P (sjl+n÷1)+R4・P (m”
xpn) D4=R1-P(@+1.i+1)+R2-P(++v
n+1)+R3-P(m÷1.n)+R4・P (,,
rl) These four points D1 to D4 and the grid coordinates Lliy uo,
Data corresponding to Vatvo is output from the concentration calculation table and stored in the data buffer 7 in FIG.

The region Rs''Ra can be expressed by the following formula using uz and vz.

As described above, the concentration calculation table 61 in FIG.

By adding the peripheral circuit shown in FIG. 7, the capacity can be reduced to 1/4 of the conventional one, as shown in the concentration calculation table 72.

〔Effect of the invention〕

In the present invention, the capacity of the interpolation table can be reduced to 1/4 of the rows, so memory efficiency can be improved.

[Brief explanation of the drawing]

Fig. 1 is a schematic block diagram of an embodiment of the present invention, Fig. 2 is an explanatory diagram of the relationship between the lattice after density conversion and the lattice of the original image, and Fig. 3 is an illustration of the relationship between the pixel position and the lattice area after density conversion. Figure 4 shows the positional relationship of corresponding points in each quadrant, Figure 5 shows the grid area when the grid circular coordinate points are digitized, and Figure 6 shows the density calculation before abbreviation. Diagram showing the table, No. 7
The figure is a diagram showing an abbreviated concentration calculation table and peripheral circuits. 1.2... Line memory, 3... Shift register,
4... Shift blocker, 5... Shift controller, 6... Concentration calculation section, 7... Output data buffer,
8...Clock counter, 9...Grid coordinate table address, 61...Concentration calculation table that is not abbreviated, 71...Comparator, 72...Abbreviated concentration calculation tape v, 1 Figure Figure 3 of the rod

Claims (1)

[Claims] 1. A digital image linear density conversion device using an interpolation table, which is characterized in that it includes a partial interpolation table based on the symmetry of addresses within a grid of pixels to be mapped.