JP4862747B2 - Data interpolation method and image scaling method Image processing apparatus - Google Patents

Description

The present invention relates to a data interpolation method for estimating data of an interpolation point at an arbitrary position by interpolating data at each position of a plurality of points arranged at equal intervals, an image scaling method using the data interpolation method, and an image processing device About.

  A digital image is usually represented by a set of a large number of pixels arranged at regular intervals. When the digital image is enlarged / reduced, as shown in FIG. 7, the interval between adjacent pixels changes in accordance with the enlargement / reduction rate, and the original pixel positions at regular intervals (sample points of the original image data... There is a deviation between the pixel position after enlargement / reduction (circled with hatching in the figure). Therefore, when enlarging / reducing a digital image, an interpolation process for representing the enlarged / reduced image with interpolation data (black circles in the drawing) obtained by matching the original pixel positions (sample points) at regular intervals is performed. Done.

In the interpolation process, as shown in FIG. 8, the density or luminance (interpolation data) of the interpolation point f (x) is estimated with reference to the densities of the peripheral pixels (f ₋₁ , f ₀ , f ₁ , f ₂ ). . Typical pixel interpolation methods include a linear interpolation method and a cubic convolution method.

  In such an interpolation method, there is a large difference in the degree of smoothing action (smoothness) of the original data between the case where the interpolation point coincides with the position of the original data and the case where the interpolation point is located between them. In particular, in linear interpolation, as shown in FIG. 9A, one point of original data is directly used as interpolation data, and as shown in FIG. 9B, an average of two points of original data is adopted as interpolation data. Obviously, the smoothness increases in the latter case (b).

  The difference in smoothness affects the image in terms of density and sharpness. For example, when the image is micro-magnified (enlargement or reduction at a magnification slightly deviated from 1), the difference between the pixel interval in the original image and the pixel interval after enlargement / reduction is very small. As shown in FIG. 5, the region B (a portion with a high degree of smoothness) in which the amount of positional deviation between the sample point and the pixel after enlargement / reduction is large or the region A (a portion with a low degree of smoothness) with little or no positional displacement Continuous, changes in smoothness appear on the image with a relatively large period. For this reason, when micro-magnification is performed, a difference in density and sharpness based on a difference in smoothness appears as a periodic pattern (moire) on the image, and the image quality is significantly deteriorated.

  In order to suppress the occurrence of such moire near the scaling factor of 1.0, the condition that the sum of squares of the interpolation coefficient is constant (the condition that the smoothness is almost constant regardless of the position of the interpolation point) is satisfied. A method of interpolating with reference to surrounding pixels has been proposed (for example, see Patent Document 1).

  By the way, in recent document reading apparatuses such as a digital copying machine and a multi-function peripheral, so-called “double-sided one-pass reading” is performed in which two image sensor units are used to read both front and back surfaces of a document at one time. Is starting to be equipped. In this reading method, there is a slight difference in the reading system such as the optical system between the front side and the back side, and therefore a minute magnification difference in the main scanning direction tends to occur on the front and back sides. Therefore, it is desired to correct the difference between the front and back magnifications by applying a minute enlargement / reduction process in the main scanning direction to the read data.

JP 2001-43356 A

  In the interpolation method described in Patent Document 1, it is accompanied by a minute enlargement / reduction near a scaling factor of 1.0 by interpolating with reference to surrounding pixels so as to satisfy a condition that the square sum of interpolation coefficients is constant. The effect of suppressing moire is obtained. However, since the calculation of the interpolation coefficient includes a square root calculation, the calculation becomes complicated. For this reason, it is difficult to derive the interpolation data by sequentially calculating the interpolation coefficient by the arithmetic circuit. When high-speed processing is desired, for example, the relationship between the interpolation coefficient and the reference data is stored in a table in advance. The method of interpolating by referring to becomes realistic.

  On the other hand, a device such as a digital multi-function peripheral has a large amount of processed image data per unit time, and further needs to execute image input / output in real time. Therefore, high-speed interpolation processing by hardware is desired. However, in the configuration holding the table, many memory resources are required in the integrated circuit, and the device price increases.

  The present invention is intended to solve the above-described problem, and provides a data interpolation method, an image scaling method, and an image processing apparatus capable of suppressing moire at the time of minute scaling without causing complicated computation. It is an object.

  The gist of the present invention for achieving the object lies in the inventions of the following items.

[1] data definitive in each of a plurality of positions arranged at equal intervals in a specific direction with the reference data, a data interpolation method to estimate the data of the interpolation points at an arbitrary position in the specific direction from the value of these reference data,
The value of the data of the interpolation point is represented by a product sum of each reference data and a weight coefficient for the reference data,
The weighting coefficient of each reference data is represented by a high-order function of the position of the interpolation point , and the sum of squares of the weighting coefficient for the reference data is set to be substantially constant regardless of the position of the interpolation point. A data interpolation method characterized by being performed.

In the above invention, the interpolation point data is obtained as a product sum of a plurality of reference data and the weighting coefficient, and the weighting coefficient is represented by a high-order function of the position of the interpolation point . The coefficient of this higher order function is determined in consideration of the condition that the sum of squares of the weighting coefficients for each reference data is substantially constant regardless of the position of the interpolation point . By adding the condition that the square sum of the weighting coefficients is constant, the occurrence of moiré is suppressed even when the magnification is slightly changed. In addition, since the weighting coefficient is expressed by a high-order function at the position of the interpolation point , complicated arithmetic operations such as a square root are not included, and high-speed interpolation processing by an arithmetic circuit is possible.

[2] In the higher-order function , when the sum of squares of the weighting factors of the respective reference data matches the position of the interpolation point with the position of the nearest reference data and the two references where the position of the interpolation point is the nearest The data interpolation method according to [1], wherein the data interpolation method is set so as to coincide with a case in the middle of the data.

In the above-described invention, in the normal interpolation, the value of the sum of squares of the weighting coefficient is most different between the case where the interpolation point is at the position coincident with the reference data and the position between the two reference data. Therefore, if a higher-order function for deriving the weight coefficient of each reference data is determined so that the square sums of the weight coefficients at these two interpolation points match, the sum of the squares of the weight coefficients can be obtained regardless of the position of the interpolation point. It is controlled to a substantially constant value.

[3] In the higher-order function , when the sum of squares of the weighting factors of the respective reference data matches the position of the interpolation point with the position of the nearest reference data, and the two references where the position of the interpolation point is the nearest The data interpolation method according to [1], wherein the data interpolation method is set so as to coincide with a case where the data exists at a plurality of predetermined positions between the data.

In the above invention, by increasing the satisfying interpolation points square sum when the weighting coefficient at the position interpolation point coincides with the reference data are the same value, with less errors even in interpolation points which position The sum of squares of the weight coefficient can be made constant.

[4] In the higher-order function , when the position of the interpolation point is changed between the two most recent reference data, the sum of squares of the weighting coefficient at the position of each interpolation point and the position at the position of each interpolation point The data interpolation method according to [1], wherein the sum of squares of the difference from the average value of the sum of squares of the weighting coefficients is minimized.

  In the above invention, by determining the coefficient of the weighting function under the condition that minimizes the variation in the sum of squares of the weighting coefficient, the sum of the squares of the weighting coefficient is controlled to a substantially constant value regardless of the position of the estimated data. The

[5] the high-order function, the maximum value and the minimum value of the square sum of the weighting factors at the position of each interpolation point in the case of changing the position of the interpolation point between the last two reference data The data interpolation method according to [1], wherein the difference is set so as to minimize.

In the above invention, the conditions of the original to the difference between the maximum value and the minimum value of the sum of the squares of the weighting factors to minimize, by determining the high-order function to derive the weighting factors for each reference data, the position of the interpolation point Regardless, the sum of squares of the weight coefficients is controlled to a substantially constant value.

[6] The data interpolation method according to [1], wherein the data of the interpolation point is represented by convolution of the reference data and a weighting function represented by the higher order function.

[7] The data interpolation method according to [1], wherein the interpolation point data is obtained by a cubic convolution method.

In the above invention, cubic convolution method, remains undefined coefficient higher function for obtaining a weighting factor even after including such boundary conditions, there is a degree of freedom, the substantially constant sum of the squares of the weighting factors Additional conditions for doing so can be easily reflected.

[8] The indefinite coefficients of the cubic convolution method, the is the sum of the squares of the weighting factors for each reference data, the position of the interpolation point and if the position of the interpolation point coincides with the position of the most recent reference data for the most recent 2 The data interpolation method according to [7], wherein the setting is made so as to coincide with a case in which the reference data is in the middle.

[9] When the indefinite coefficient of the cubic convolution method is changed, the sum of squares of the weighting coefficient at the position of each interpolation point and the position of each interpolation point when the position of the interpolation point is changed between the two nearest reference data . The data interpolation method according to [7], wherein the sum of squares of the difference from the average value of the sum of squares of the weighting coefficients at the position is minimized.

[10] When the position of the interpolation point is changed between the two most recent reference data, the difference between the maximum value and the minimum value in the square sum of the weighting coefficient at the position of each interpolation point is minimized. The data interpolation method according to [7], wherein the data interpolation method is set as follows.

[11] The data interpolation method according to any one of [1] to [10] is used only for scaling processing when the scaling factor is in a very small area centered at 1.0. Data interpolation method.

  In the above invention, the data interpolation method to which the condition that the sum of squares of the weighting coefficients is made constant is used only at the time of minute scaling that is likely to cause moire.

[12] An image scaling method, wherein the data interpolation method according to any one of [1] to [11] is applied to each of horizontal scaling and vertical scaling of an image.

  In the above invention, when the image is enlarged or reduced in the two directions of the horizontal direction and the vertical direction, the data interpolation method according to any one of [1] to [11] is applied to each of the horizontal direction and the vertical direction. The Moire during micro-magnification is prevented in both the vertical and horizontal directions.

[13] Data at a plurality of positions arranged at equal intervals in a specific direction is used as reference data, and the image is enlarged or reduced by generating interpolation point data at an arbitrary position in the specific direction from the values of the reference data. An image processing apparatus,
An interpolation point position deriving unit that obtains the position of the interpolation point according to the specified magnification;
A weighting factor for each of the plurality of reference data to be referred to when generating the data of the interpolation point is derived by a high-order function using the position of the interpolation point as a variable, and the derivation for each of the reference data and each reference data. An interpolation calculation unit for calculating a product sum with the weighting factor as data of the interpolation point;
An enlargement / reduction processing unit having
The higher-order function is set so that the sum of squares of the weighting factors for each reference data is substantially constant regardless of the position of the interpolation point.
An image processing apparatus.

  In the above-described invention, it is preferable to perform an operation related to the interpolation by the arithmetic circuit.

[14] and a second image sensor for reading a front side of the document to the back surface of the document and the first image sensor optically reads the optically
The image on the front side of the document obtained by reading with the first image sensor and the image on the back side of the document obtained by reading with the second image sensor are enlarged or reduced by the enlargement / reduction processing unit, and The image processing apparatus according to claim 13, wherein the images on the front and back surfaces are made equal.

  In the above invention, both the front and back sides of the document are read at once using two image sensors, and the front and back images having a magnification difference due to individual differences in the optical system are minutely processed by the data interpolation method according to the present invention. The same magnification is corrected by scaling.

  According to the data interpolation method of the present invention, it is possible to suppress moire at the time of minute zooming without causing complication of calculation.

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

<Principle of data interpolation method according to this embodiment>
In general, nearest neighbor method, linear interpolation method, cubic convolution method, B-spline method and the like are used for data interpolation. These interpolation methods express interpolation pixel image data (interpolation data) by convolution of a weight function specific to each interpolation method and reference pixel data (image data of peripheral pixels referred to obtain interpolation pixel data). can do. The weight function is generally expressed as follows.

ここで、ａ_１、ｂ_１、ｃ_１、ｄ_１、ａ_２、ｂ_２、ｃ_２、ｄ_２は不定係数である。

Here, a ₁ , b ₁ , c ₁ , d ₁ , a ₂ , b ₂ , c ₂ , and d ₂ are indefinite coefficients.

ここで、ｘは補間画素の位置、ｆ_−１、ｆ_０、ｆ_１、ｆ_２は参照画素データ、ｆ（ｘ）は補間データである。このように、補間データは、補間画素位置の３次関数で表わされる。 Interpolated pixel data (interpolated data) is expressed by convolution of a weight function and reference pixel data, and is expressed as follows.

Here, x is the position of the interpolation pixel, f ₋₁ , f ₀ , f ₁ , and f ₂ are reference pixel data, and f (x) is the interpolation data. Thus, the interpolation data is represented by a cubic function of the interpolation pixel position.

このように変形した後も、補間データは補間画素の位置ｘの３次関数で表すことができる。 The above equation is transformed into the following equation.

Even after such modification, the interpolation data can be expressed by a cubic function of the position x of the interpolation pixel.

とおいて式を簡略化すると、補間データｆ（ｘ）は次のように表される。 Further here

When the equation is simplified, the interpolation data f (x) is expressed as follows.

ここで、Ｐ_-1（ｘ）、Ｐ₀（ｘ）、Ｐ₁（ｘ）、Ｐ₂（ｘ）は、各参照画素の重み係数（補間係数）であり、この重み係数の二乗和は次式になる。

Here, P ₋₁ (x), P ₀ (x), P ₁ (x), and P ₂ (x) are the weighting coefficients (interpolation coefficients) of the respective reference pixels. It becomes an expression.

上記した重み係数の二乗和ｋ（ｘ）がｘに対してほぼ一定となる条件が、モアレを発生させない条件として望ましい。

The condition that the sum of squares k (x) of the above weight coefficients is substantially constant with respect to x is desirable as a condition that does not cause moire.

However, since each weighting factor is expressed by a cubic function, the condition that the sum of squares is completely constant is very strict and cannot coexist with other conditions necessary for interpolation. Define the condition of the sum of squares. Each indefinite coefficient (a ₁ , b ₁ , c ₁ , d ₁ , a ₂ , b ₂ , so as to satisfy this limited sum of squares condition and other conditions necessary for interpolation (boundary conditions, etc.) simultaneously. Determine the value of c ₂ , d ₂ ).

<How to set the sum of squares condition>
An example of a method of setting the above-mentioned “restrictive sum of squares conditions” will be shown. In general, when the interpolation point is on the reference pixel data (x = 0, 1), based on the square sum k (0) or k (1) of the weighting coefficient, the reference pixel data of the two nearest points are used. The sum of squares k (0.5) of the weighting coefficients when estimating the interpolation data at the interpolation point located in the middle (x = 0.5) is the most deviated from the reference (difference from when x = 0, 1) Is maximized). Therefore, the sum of squares of weighting factors (k (0.5)) in the case of x = 0.5 and the sum of squares of weighting factors in the case of x = 0 or 1 (k (0), k (1)) Is a “limited sum-of-squares condition”.

<Application example of the above-mentioned "Limited sum of squares conditions" for cubic convolution method>
Also in the cubic convolution method, the square sum k of weighting factors tends to deviate most when x = 0.5. On the other hand, when x = 0 or 1, the difference from the original image data is 0 due to the nature of the cubic convolution method, so that the sum of squares of the weighting coefficients at this time (when x = 0) and x = 0. If the square sum of the weighting coefficient at 5 is matched, moire at the time of minute enlargement / reduction is improved.

From the condition that the sum of squares of the weight coefficients is equal to each other when x = 0 and x = 0.5,
k (0) = k (0.5) (Condition 1)
Are added to the conditions of the cubic convolution method to determine indefinite coefficients (a ₁ , b ₁ , c ₁ , d ₁ , a ₂ , b ₂ , c ₂ , d ₂ ).

When the conditions of the cubic convolution method are applied, one undetermined coefficient remains. Here, if the remaining undetermined coefficient is a = a ₂ , the other solutions are as follows.
_{a 1 = a + 1, b} 1 = - (a + 3), c 1 = 0, d 1 = 1, a 2 = a, b 2 = -5a, c 2 = 8a, d 2 = -4a

これが一般的なキュービックコンボリューションの重み関数であり、未定係数ａは、一般にａ＝−０．５やａ＝−１．０が適用されることが多い。 Applying the above, the weight function is as follows.

This is a weight function of a general cubic convolution, and the undetermined coefficient a is generally often applied with a = −0.5 or a = −1.0.

Here, when the above-described (Condition 1) is applied to obtain the undetermined coefficient, the undetermined coefficient a is as follows.

  FIG. 1 shows a case where the weighting function F1 (a in FIG. 1) in the general cubic convolution method (a = −0.5) and the above (condition 1) regarding the sum of squares are considered (a = −1.46). Is compared with the weighting function F2 of FIG.

FIG. 2 shows the interpolation coefficient values (P ₋₁ (x), P ₀ (x), P ₁ (x), P ₂ (x)) of each original data for each interpolation position in the cubic convolution method. The case where == 0.5 is compared with the case where (condition 1) is applied and a = −1.46 is set. FIG. 3 also shows the case where the sum of squares k (x) of the interpolation coefficients for each interpolation position is set to a = −0.5 in the cubic convolution method and (condition 1), where a = −1. .46 for comparison.

  In the conventional cubic convolution method in which a = −0.5 as shown in FIG. 3A, the square sum value k (x) varies depending on the position x of the interpolation point. When (Condition 1) is applied and a = −1.46 as shown in FIG. 3B, the square sum value k (x) of the interpolation coefficient is substantially constant regardless of the position x of the interpolation point. It has become.

  FIG. 4 shows interpolation data in a case where sine wave image data simulating a screen (halftone dot) image is interpolated at the same magnification (simulating small enlargement / reduction). (A) shows the original image, (b) shows the interpolation data in the vicinity where a = −0.5 and the interpolation position is x = 0, and (c) shows the interpolation when a = −0.5. Interpolation data in the vicinity where the position is x = 0.5, FIG. 6D shows interpolation data in the vicinity where a = −1.46 and the interpolation position is x = 0, and FIG. .46, the interpolation data in the vicinity where the interpolation position is x = 0.5 are shown.

  As can be seen by comparing FIGS. 4B and 4C, when a = −0.5, the amplitude of the interpolation data is different between the interpolation position x = 0 and X = 0.5. to differ greatly. On the other hand, when optimization is performed so that the sum of squares is constant with a = −1.46, the interpolation position is x = 0 ((d) in the figure) and x = 0.5 ( (E)) shows almost no change (difference) in the amplitude of the interpolation data.

  As described above, by optimizing the sum of squares of the weighting coefficients using the “limited square sum condition” (the above condition 1), it is possible to obtain an effect of making the moire almost inconspicuous in the screen image. Therefore, in the minute enlargement / reduction processing of a document with a screen image, moire is suppressed by using the cubic convolution method that optimizes the sum of squares of the weighting coefficients using the “restricted sum of squares conditions”. As a result, a great improvement in image quality is achieved.

<Application example of the above-mentioned “restricted sum of squares conditions” for other interpolation methods>
The method of optimizing the sum of squares of the weighting coefficients using the “limited sum of squares condition” is not limited to the cubic convolution method, and can be applied to other functions such as a B-spline method. Further, the present invention is not limited to a cubic function, and a function of a fourth order or higher can also be applied. Furthermore, the present invention can be applied to the case where the number of reference pixels is 5 pixels or more or 3 pixels. However, in the cubic convolution method, indefinite coefficients remained in nature, but in the B-spline method, indefinite coefficients do not remain, and the weight function is uniquely determined. The sum of squares cannot be optimized by applying

ここで、通常は補間データｆ（ｘ）を以下のように求める。 As described above, the interpolation data is expressed by convolution of the weight function and the reference pixel data, and the weight function Ψ (x) of the B-spline method is expressed as follows.

Here, usually, the interpolation data f (x) is obtained as follows.

ここで、ｆ_−１，ｆ_０，ｆ_１，ｆ_２は参照画素データであるが、以下のように、参照画素データを置き換えて補間データを求める。

Here, f ₋₁ , f ₀ , f ₁ , and f ₂ are reference pixel data, but interpolation data is obtained by replacing the reference pixel data as follows.

である。

It is.

  This is because, by adding the influence of the surrounding reference pixel data to the reference pixel data to be secondarily convolved, the degree of freedom is given to the calculation of the interpolation data. Is applied.

By making A ₁ and B ₀ 1 and other indefinite coefficients (A ₀ , B ₁ , C ₀ , C ₁ , D ₀ , D ₁ ) close to 0, interpolation close to the normal B-spline method is performed. become.

  The image quality effect is characterized in that the original image is not stored in the B-spline method, but the smoothing action of the image is larger than that in the cubic convolution method, and ringing hardly occurs. Therefore, by performing the optimization of the sum of squares by applying the “restricted sum of squares conditions” according to the present invention, the sharpness is lower than the original image, but moire and ringing can be prevented, and minute enlargement / Good image quality can be obtained even when reduction is performed.

In the present invention, an effect of suppressing moire is obtained by making the sum of squares of interpolation coefficients constant, and a weighting coefficient is obtained using a higher-order function as a weighting function, such as a cubic convolution method or a B-spline method. since, the implementation in hardware circuit not include complicated operations such as square root facilitates the calculation to determine the weighting coefficients. As a result, even a device that requires high-speed image processing, such as a multi-function peripheral, can realize minute zooming with reduced moire.

  Next, a description will be given of a multifunction machine 10 that is an example of an image processing apparatus that performs a minute enlargement / reduction process of an image by applying the data interpolation method according to the present invention.

  FIG. 5 is a block diagram showing the overall configuration of the multifunction machine 10. The multifunction machine 10 has a copy function, a facsimile function, a printer function, and the like that optically read a document, print a duplicate image on a recording sheet, and output the same. Further, regarding reading of a document, a so-called “double-sided one-pass reading” function of simultaneously reading both front and back sides is provided.

  The multifunction machine 10 includes a central processing unit (CPU) 11 that performs overall control of the operation of the multifunction machine 10, and an operation unit 13, a network interface (I / F) unit 14, and a FAX control unit 15 are connected to the CPU 11 through a system bus 12. , An external memory I / F unit 16, a RAM (Random Access Memory) 17, a ROM (Read Only Memory) 18, an HDD (Hard Disk Drive) 19, etc. Further, a scanner unit 21 and a printer unit 22 are connected. Various circuits for processing image data are arranged between the two.

  The ROM 18 stores programs and various fixed data, and the CPU 11 controls the operation of the multifunction machine 10 by executing the programs stored in the ROM 18. The RAM 17 is used as a work memory that temporarily stores various data when the CPU 11 executes a program.

The operation unit 13 includes a liquid crystal display having a touch panel on the surface and various operation switches, and performs a function of performing various guidance displays and status displays to the user and receiving various operations from the user. The network I / F unit 14 is a LAN (Local Area).
(Network) and various networks such as the Internet, and functions to communicate with external devices. The FAX control unit 15 is connected to a public line and performs various controls (for example, protocol control, compression / decompression, etc.) related to image transmission / reception by facsimile communication.

  The HDD 19 is a large-capacity nonvolatile storage device that holds image data and other data. It fulfills its function and is composed of a storage device such as a semiconductor memory or a hard disk device.

  The scanner unit 21 is a device that optically reads a document in color, feeds the document placed on the document table one sheet at a time, and transports two image sensor units (on the front and back sides of the document being transported). The first image sensor 23 for reading the front surface and the second image sensor 24 for reading the back surface are equipped with a so-called “double-sided one-pass reading” function.

  The first image sensor I / F unit 25 controls the reading operation by the first image sensor 23 for surface reading and takes in the image data output from the first image sensor 23. The first minute enlargement / reduction processing unit 26 performs enlargement processing or reduction processing at a minute magnification on the image captured by the first image sensor I / F unit 25.

  Similarly, the second image sensor I / F unit 27 controls the reading operation by the second image sensor 24 for reading the back surface and takes in the image data output from the second image sensor 24. The second minute enlargement / reduction processing unit 28 performs enlargement processing or reduction processing at a minute magnification on the image captured by the second image sensor I / F unit 27.

  The reading system image processing unit 29 takes in the image data output from the first minute enlargement / reduction processing unit 26 and the second minute enlargement / reduction processing unit 28, and performs color management, noise reduction, This is a circuit that performs image processing such as digitization.

  The output of the reading system image processing unit 29 is input to the compression / decompression / memory control unit 31. The compression / decompression / memory control unit 31 is connected to the system bus 12 and the writing system image processing unit 33, and a DRAM (Dynamic Random Access Memory) 32 is connected to the subordinate. The compression / decompression / memory control unit 31 has a function of compressing and decompressing image data, a function of controlling reading / writing of data to / from the DRAM 32, an HDD 19 and a RAM 17, the network I / F unit 14 and the like via the bus 12. And the like, a function of outputting image data to the writing system image processing unit 33, and the like.

  The writing system image processing unit 33 performs image processing such as cell averaging, resolution conversion, printer γ conversion, micro scaling, and screen processing on the image data input from the compression / decompression / memory control unit 31. This is a circuit for outputting to the printer unit 22.

  The printer unit 22 prints an image on recording paper according to the image data input from the writing system image processing unit 33. Here, the printer unit 22 includes a recording paper conveyance device, a photosensitive drum, a charging device, a laser unit, a developing device, a transfer separation device, a cleaning device, and a fixing device. It is configured as a so-called laser printer that forms an image by a process.

  The image data output from the first image sensor 23 for reading the front surface and the second image sensor 24 for reading the back surface passes through the first image sensor I / F unit 25 and the second image sensor I / F unit 27, and the first, The images are input to the second minute enlargement / reduction processing units 26, 28, and are subjected to minute scaling processing by the first and second minute enlargement / reduction processing units 26, 28, whereby the front and back images have the same magnification. It is adjusted so that.

  Thereafter, the image processing unit 29 performs necessary image processing, and then the data is sent to the compression / decompression / memory control unit 31. The compression / decompression / memory control unit 31 compresses the image data, stores it in the HDD 19, transfers it to the outside via the network, and outputs from the scanner unit 21 or from the outside through the network I / F unit 14. A process of outputting the image data to the writing system image processing unit 33 is performed. The output image data is output to the printer unit 22 via the writing system image processing unit 33 and the printer I / F unit 34, and the printer unit 22 prints the corresponding image on a recording sheet and outputs it.

  FIG. 6 shows a schematic configuration of the first minute enlargement / reduction processing unit 26. The second minute enlargement / reduction processing unit 28 has the same configuration as the first minute enlargement / reduction processing unit 26, and the description thereof is omitted. The first minute enlargement / reduction processing unit 26 selects an interpolation method (selection of an interpolation method such as cubic convolution and B-spline method, selection of an indefinite coefficient parameter setting value of the cubic convolution method, etc.) and a magnification. Setting is possible.

  The first minute enlargement / reduction processing unit 26 includes a line FIFO (First-In First-Out) 41 that temporarily stores input image data, and a three-stage flip-flop cascaded to the output of the FIFO memory 41. (F / F) circuits 42 to 44, an interpolation control unit 45, and an interpolation calculation unit 46.

  Information indicating the scaling factor is set in the interpolation control unit 45 from the CPU 11, and the interpolation control unit 45 calculates each interpolation position (x) according to the set scaling factor, and also stores the line where the input image data is stored. Control of data input / output timing with respect to the FIFO 41 and data latch timing with respect to the data delay flip-flop circuits 42 to 44 (image output timing varies depending on the magnification) is performed.

  Furthermore, the interpolation control unit 45 includes a weight function selection unit 45a that selects a weight function according to the set magnification. For example, when the scaling factor is a minute scaling factor (for example, between 0.95 and 1.05), selection information for instructing the interpolation calculation unit 46 to use the first weight function is used as the other scaling factor. Then, the weight function selection information 52 instructing the use of the second weight function is output.

Interpolation position information 51 indicating the interpolation position (x) and weight function selection information 52 are input from the interpolation control section 45 to the interpolation calculation section 46, and interpolation method selection information 53 is input from the CPU 11. The output of the line FIFO 41 is the reference pixel data (f ₋₁ ), and the output of the data delay flip-flop circuit 42 delayed by one clock is the reference pixel data (f ₀ ). The data delay is further delayed by one clock. The output of the flip-flop circuit 43 is input as reference pixel data (f ₁ ), and the output of the data delay flip-flop circuit 44 delayed by one clock is input to the interpolation calculation unit 46 as reference pixel data (f ₂ ). Is done.

  The interpolation calculation unit 46 selects an interpolation method (cubic convolution method, B-spline method, etc.) used for data interpolation processing according to the input interpolation method selection information 53. Further, the weight function is selected according to the input interpolation method selection information 53. For example, when the interpolation method is a cubic convolution method, the first weight function is a = −0.5 (see FIG. 2A), and the second weight function is a = −1. 46 (see FIG. 2B) is adopted. That is, a weighting function with a = −1.46 is used so that the sum of squares of the interpolation coefficient is constant at the time of minute scaling, and in the case of scaling factors other than minute scaling, a general cubic convolution method is used. Interpolation processing is performed using a weight function with a = −0.5.

The interpolation calculation unit 46 is input from the line FIFO 41 and the flip-flop circuits 42 to 44 using the interpolation method according to the input interpolation method selection information 53 and the weight function selection information 52 and the weight function used in the interpolation method. Interpolation data of the interpolation position (x) indicated by the interpolation position information 51 is calculated from each reference pixel data (f ₋₁ , f ₀ , f ₁ , f ₂ ) and output.

  For example, a difference in magnification between the first image sensor 23 and the second image sensor 24 of the scanner unit 21 is examined in advance, and the first and second images are corrected so that the front and back images have the same magnification. By setting the variable magnification in the minute enlargement / reduction processing unit 26 and / or the second minute enlargement / reduction processing unit 28, an image having no magnification difference between the front and back surfaces can be output.

  The embodiment of the present invention has been described with reference to the drawings. However, the specific configuration is not limited to that shown in the embodiment, and there are changes and additions within the scope of the present invention. Are also included in the present invention.

  For example, in the embodiment, the interpolation point matches the position of the latest reference data so that the square sum k (x) of the weighting coefficient for each reference data becomes substantially constant regardless of the position x of the interpolation data. The sum of squares k (0) of the weighting coefficients when (x = 0) and the sum of the squares of the weighting coefficients k (0.5) between the two most recent reference data (x = 0.5) However, the condition added to make the square sum k (x) of the weighting coefficient for each reference data almost constant regardless of the position (x) of the interpolation data is It is not limited.

  For example, the sum of squares k (x) of the weighting factors of each reference data is the sum of the squares of weighting factors k (0) when the position of the interpolation point matches the position of the nearest reference data, and the two most recent references. The coefficient of the weighting function is set on condition that the sum of squares of the weighting coefficient (for example, k (0.25), k (0.5), k (0.75)) at a plurality of locations between the data matches. You may decide. As described above, by increasing the number of coincidence points, it is possible to further reduce the variation of the square sum k (x) of the weighting coefficient and optimize it to a constant value.

Also, the value of a (indefinite coefficient) of the weight function is determined on condition that the variance of the square sum k (x) of the weight coefficient when the position of the interpolation point is the variable (x) is minimized. You may do it. That is, when the ke the mean value of the sum of the squares of the weighting factor for the position of the interpolation point (the estimated position of the data), the difference between the average value ke the square sum k of the weighting factors at each position of the interpolation point (x) ( The value of a (indefinite coefficient) of the weight function is determined so that the sum of the squares of (deviation) is minimized. For example, the value of a may be changed variously, and a that minimizes the variance may be derived and set.

  The weight function a (indefinite coefficient) is provided on the condition that the difference between the maximum value and the minimum value of the square sum k (x) of the weight coefficient when the position of the interpolation point is a variable (x) is minimized. ) Value may be determined. For example, the difference between the maximum value and the minimum value of k (x) when the position x of the interpolation point is changed in the range from 0 to 1 is obtained for various values of a, and the difference a becomes the minimum The value of may be adopted.

  Further, the data interpolation method of the present invention is not limited to the case of applying to one dimension (for example, the horizontal direction). When it is necessary to perform interpolation in multi-dimensional directions (such as when enlarging or reducing image data in both the vertical and horizontal directions), the interpolation coefficients in each direction are calculated linearly in the same way as general interpolation methods. What is necessary is just to combine.

  The data interpolation method of the present invention is not limited to the multifunction machine 10 shown in the embodiment, and can be applied to various devices that interpolate data.

A weighting function F1 in a general cubic convolution method (a = −0.5) and a weighting function F2 in a case where a condition for making the value of the sum of squares of the weighting function constant is considered (a = −1.46) It is explanatory drawing which compares and shows. When the interpolation coefficient values (P ₋₁ (x), P ₀ (x), P ₁ (x), P ₂ (x)) for each interpolation position are set to a = −0.5 in the cubic convolution method It is explanatory drawing shown in comparison about the case where a = -1.46. FIG. 5 is an explanatory diagram showing a comparison between a case where a value of the square sum of interpolation coefficients k (x) for each interpolation position is set to a = −0.5 and a = −1.46 in the cubic convolution method. is there. Interpolation data obtained by interpolating sine wave image data simulating a screen (halftone dot) image with the same magnification (simulating micro enlargement / reduction) is compared between the conventional interpolation method and the data interpolation method of the present invention. It is explanatory drawing shown. 1 is a block diagram illustrating an overall configuration of a multifunction peripheral according to an embodiment of the present invention. FIG. 2 is a block diagram illustrating a schematic configuration of a minute enlargement / reduction processing unit included in the multifunction peripheral according to the embodiment of the present invention. It is explanatory drawing which shows an example of the positional relationship of original image data, the data after expansion / reduction ratio, and interpolation data. It is explanatory drawing which illustrated the positional relationship between the position of several reference image data, and an interpolation point. It is explanatory drawing which shows the difference in smoothness between the case where an interpolation point exists in the position which corresponds with original data, and the case where it is located in the middle of original data. It is explanatory drawing which shows that the area | region of smoothing effect | action small and the area | region of smoothing effect | action large appear continuously when carrying out micro scaling.

Explanation of symbols

10 ... Machine 11 ... CPU
DESCRIPTION OF SYMBOLS 12 ... System bus 13 ... Operation part 14 ... Network I / F part 15 ... FAX control part 16 ... External memory I / F part 17 ... RAM
18 ... ROM
19 ... HDD
DESCRIPTION OF SYMBOLS 21 ... Scanner part 22 ... Printer part 23 ... 1st image sensor 24 ... 2nd image sensor 25 ... 1st image sensor I / F part 26 ... 1st minute enlargement / reduction processing part 27 ... 2nd image sensor I / F Unit 28 ... Second minute enlargement / reduction processing unit 29 ... Reading system image processing unit 31 ... Compression / decompression / memory control unit 32 ... DRAM
33 ... Writing system image processing unit 34 ... Printer I / F unit 41 ... Line FIFO
42-44 ... flip-flop circuit 45 ... interpolation control unit 45a ... weight function selection unit 46 ... interpolation calculation unit 51 ... interpolation position information 52 ... weight function selection information 53 ... interpolation method selection information

Claims (14)

Data definitive in each of a plurality of positions arranged at equal intervals in a specific direction with the reference data, a data interpolation method to estimate the data of the interpolation points at an arbitrary position in the specific direction from the value of these reference data,
The value of the data of the interpolation point is represented by a product sum of each reference data and a weight coefficient for the reference data,
The weighting coefficient of each reference data is represented by a high-order function of the position of the interpolation point , and the sum of squares of the weighting coefficient for the reference data is set to be substantially constant regardless of the position of the interpolation point. A data interpolation method characterized by being performed. The high-order function, the the sum of squares of the weighting factors for each reference data, intermediate the two reference data is the most recent position of the interpolation point and if the position of the interpolation point coincides with the position of the most recent reference data 2. The data interpolation method according to claim 1, wherein the data interpolation method is set so as to coincide with the case of the data. The high-order function, the the sum of squares of the weighting factors for each reference data, between two reference data position is nearest the interpolation point and if the position of the interpolation point coincides with the position of the most recent reference data 2. The data interpolation method according to claim 1, wherein the data interpolation method is set so as to coincide with a case in a plurality of predetermined locations. In the higher-order function , when the position of the interpolation point is changed between the two most recent reference data, the sum of squares of the weighting coefficient at the position of each interpolation point and the weighting coefficient at the position of each interpolation point The data interpolation method according to claim 1, wherein the sum of squares of the difference from the mean value of the sum of squares is set to be minimum. The difference between the maximum value and the minimum value in the sum of squares of the weighting coefficient at the position of each interpolation point when the position of the interpolation point is changed between the two most recent reference data in the higher-order function is The data interpolation method according to claim 1, wherein the data interpolation method is set to be minimized. The data interpolation method according to claim 1, wherein the data of the interpolation point is expressed by convolution of the reference data and a weighting function represented by the higher-order function. The data interpolation method according to claim 1, wherein the data of the interpolation point is obtained by a cubic convolution method. The indefinite coefficients of the cubic convolution method, the is the sum of the squares of the weighting factors for each reference data, the reference position of the interpolation point and if the position of the interpolation point coincides with the position of the most recent reference data last two The data interpolation method according to claim 7, wherein the data interpolation method is set so as to coincide with a case where the data is in the middle. The indefinite coefficients of the cubic convolution method, the at the position of each interpolation point and the square sum of the weighting factors at the position of each interpolation point in the case of changing the position of the interpolation point between the last two reference data The data interpolation method according to claim 7, wherein the sum of squares of the difference from the mean value of the sum of squares of the weighting coefficients is set to be minimum. When the indefinite coefficient of the cubic convolution method is changed , the maximum value and the minimum value in the sum of squares of the weighting coefficient at the position of each interpolation point when the position of the interpolation point is changed between the two nearest reference data, The data interpolation method according to claim 7, wherein the difference is set to be a minimum. 11. The data interpolation method according to claim 1, wherein the data interpolation method according to any one of claims 1 to 10 is used only for a scaling process in a case where a scaling ratio is in a very small area centered at 1.0. An image scaling method, wherein the data interpolation method according to any one of claims 1 to 11 is applied to each of horizontal scaling and vertical scaling of an image. An image processing apparatus that uses data at a plurality of positions arranged at equal intervals in a specific direction as reference data and generates data of interpolation points at arbitrary positions in the specific direction from the values of the reference data, and performs image enlargement / reduction Because
An interpolation point position deriving unit that obtains the position of the interpolation point according to the specified magnification;
A weighting factor for each of the plurality of reference data to be referred to when generating the data of the interpolation point is derived by a high-order function using the position of the interpolation point as a variable, and the derivation for each of the reference data and each reference data. An interpolation calculation unit for calculating a product sum with the weighting factor as data of the interpolation point;
An enlargement / reduction processing unit having
The higher-order function is set so that the sum of squares of the weighting factors for each reference data is substantially constant regardless of the position of the interpolation point.
An image processing apparatus. And a second image sensor for reading a first image sensor for reading the surface of the original optically backside of the document optically,
The image on the front side of the document obtained by reading with the first image sensor and the image on the back side of the document obtained by reading with the second image sensor are enlarged or reduced by the enlargement / reduction processing unit, and The image processing apparatus according to claim 13, wherein the images on the front and back surfaces are made equal.

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