JP2007128355A - Image processing device, computer, and image forming device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image processing device for generating image data which enables a person who has an insufficient focus adjusting capability to perceive an image indicated by original image data. <P>SOLUTION: The PC (image processing device) 1 provides a memory section 2b for storing an inverse matrix of the Teplitz matrix organized by a point spread function of indicating the focus adjusting capability of eyes of the human being, and a deformed image data generating section 2e for generating deformed image data by calculating a product of the input image data and the inverse matrix of the Teplitz matrix stored in the memory section 2b. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention includes an image processing device that transforms image data so that the image data can be perceived normally for a human who has insufficient eye focus adjustment, a computer including the image processing device, and the image processing device. The present invention relates to an image forming apparatus.

When the human eye has insufficient focus adjustment power, the image looks degraded (blurred). Patent Document 1 discloses an apparatus that simulates how an image is perceived by a human who has insufficient eye focus adjustment.
JP 2000-338857 A

  However, there has been no device that generates image data that can be perceived normally by a person with insufficient eye focus adjustment power without degrading the image indicated by the original image data.

  The present invention has been made in view of the above problems, and an image processing apparatus, a computer, and a computer capable of generating image data capable of perceiving an image represented by original image data by a person who lacks the focus adjustment power of the eye An object of the present invention is to provide an image forming apparatus.

  The image processing apparatus according to claim 1 is an image processing apparatus that generates deformed image data obtained by transforming image data so that the image data is normally perceived by a human having insufficient eye focus adjustment power. Calculating a product of storage means for storing an inverse matrix of a Toeplitz matrix comprising a point spread function indicating the focus adjustment power of the human eye, and input image data and an inverse matrix of the Toeplitz matrix stored in the storage means. And a modified image data generating means for generating the modified image data.

  According to the above configuration, the storage means stores the inverse matrix of the Toeplitz matrix consisting of a point spread function indicating a lack of focus adjustment power of the human eye, and the deformed image data generation means stores the input image data and the storage means. By calculating the product of the stored Toeplitz matrix and the inverse matrix, deformed image data is generated.

  Accordingly, since the product of the input image data and the inverse matrix of the Toeplitz matrix composed of a point spread function indicating the lack of focus adjustment power of the human eye is calculated, deformed image data is generated, that is, the human eye. Since the input image data is preliminarily multiplied by the one that cancels out the focus adjustment power of the eye, when the user who lacks the eye focus adjustment power views the image indicated by the deformed image data, the lack of the eye focus adjustment power is canceled out. The image indicated by the input image data (original image data) can be perceived without deterioration.

  The image processing apparatus according to claim 2 is the image processing apparatus according to claim 1, wherein the image processing apparatus includes a receiving unit that receives a selection of one of a plurality of visual characteristics, and the storage unit further includes: The plurality of visual characteristics are stored in association with the inverse matrix of the Toeplitz matrix corresponding to each visual characteristic, and the deformed image data generation means is the visual characteristic whose selection is received by the input image data and the reception means The modified image data is generated by calculating the product of the Toeplitz matrix associated with the inverse matrix of the Toeplitz matrix.

  According to the above configuration, the storage means stores the plurality of visual characteristics and the inverse matrix of the Toeplitz matrix corresponding to each visual characteristic, and the reception means selects one of the plurality of visual characteristics. Then, the deformed image data generating means generates the deformed image data by calculating the product of the input image data and the inverse matrix of the Toeplitz matrix associated with the visual characteristics for which the selection has been received.

  Therefore, the user can select visual characteristics (for example, visual acuity 0.1 for presbyopia, visual acuity 0.2 for myopic eyes, etc.), and the inverse of the Toeplitz matrix associated with the visual characteristics for which the selection has been accepted. Since the deformed image data is generated using the matrix, it is possible to generate the deformed image data according to the visual characteristics of the user.

  The image processing apparatus according to claim 3 is an image processing apparatus that generates deformed image data obtained by deforming image data so that the image data is normally perceived by a human having insufficient eye focus adjustment power. Storage means for storing a Toeplitz matrix composed of a point spread function indicating the focus adjustment power of the human eye, discrete sine transform means for discrete sine transform each of the input image data and the Toeplitz matrix stored in the storage means, and First calculation means for calculating an inverse matrix of the Toeplitz matrix subjected to discrete sine transform by the discrete sine transform means, input image data subjected to discrete sine transform by the discrete sine transform means, and the first calculation means. A second calculating means for calculating a product with an inverse matrix, and inversely transforming the product calculated by the second calculating means by discrete sine Is characterized by and a discrete sine inverse transform means for generating said deformed image data.

  According to the above configuration, the Toeplitz matrix composed of a point spread function indicating a lack of focus adjustment power of the human eye is stored in the storage unit, and is stored in the input image data and the storage unit by the discrete sine transform unit. The Toeplitz matrix is discretely sine, the inverse of the Toeplitz matrix subjected to the discrete sine transform is calculated by the first calculation means, and the input image data subjected to the discrete sine transform and the discrete sine transform are calculated by the second calculation means. The product of the Toeplitz matrix and the inverse matrix is calculated. Then, the discrete sine inverse transform means generates the transformed image data by inversely transforming the product of the input image data subjected to the discrete sine transform and the inverse matrix of the Toeplitz matrix subjected to the discrete sine transform.

  Therefore, since the deformed image data is generated using the discrete sine transformation (DST) and the inverse discrete sine transformation (IDST), it is possible to generate highly accurate deformed image data. it can. That is, when deformed image data is generated by using Fourier transform and inverse Fourier transform, complex numbers are generated in each pixel constituting the deformed image data. Since the deformed image data is generated using the transform and the inverse discrete sine transform, the accuracy of the deformed image data is improved without generating a complex number in each pixel constituting the deformed image data. In addition, when the inverse matrix of the Toeplitz matrix is calculated, the Toeplitz matrix is approximated to a diagonal matrix by a similar (equivalent, equivalent) transformation in order to shorten the calculation processing time. In addition, using the discrete sine transform and the inverse discrete sine transform to diagonalize the Toeplitz matrix improves the accuracy of the approximation, thereby improving the accuracy of the deformed image data. As a result, when a user with insufficient eye focus adjustment power views the image indicated by the deformed image data, the image indicated by the input image data (original image data) can be perceived. In addition, when deformed image data is generated using Fourier transform and inverse Fourier transform, when a person with insufficient eye focus adjustment power sees the image indicated by the deformed image data, the periphery of the image deteriorates. Although it is perceived, deformed image data is generated using discrete sine transform and inverse discrete sine transform. Therefore, when a user with insufficient eye focus adjustment power sees the image indicated by the deformed image data, the deformed image is displayed. The periphery of the image indicated by the data is not deteriorated and perceived.

  The image processing apparatus according to claim 4 is the image processing apparatus according to claim 3, wherein the image processing apparatus includes a reception unit that receives one of a plurality of visual characteristics, and the storage unit further includes: The plurality of visual characteristics are stored in association with a Toeplitz matrix corresponding to each visual characteristic, and the discrete sine transform unit is associated with the input image data and the visual characteristic selected by the receiving unit. Each Toeplitz matrix is characterized by discrete sine transform.

  According to the above configuration, the storage means stores a plurality of visual characteristics and the Toeplitz matrix corresponding to each visual characteristic in association with each other, and the accepting means accepts one selection of the plurality of visual characteristics. The Toeplitz matrix associated with the input image data and the visual characteristic for which the selection has been received is discretely transformed by the discrete sine transform unit, and the inverse matrix of the Toeplitz matrix that has been subjected to the discrete sine transform is obtained by the first calculation unit. The product of the input image data subjected to discrete sine transform and the inverse matrix of the Toeplitz matrix subjected to discrete sine transform is calculated by the second calculation means. Then, the discrete sine inverse transform means generates the transformed image data by inversely transforming the product of the input image data subjected to the discrete sine transform and the inverse matrix of the Toeplitz matrix subjected to the discrete sine transform.

  Therefore, the user can select visual characteristics (for example, visual acuity 0.1 for presbyopia, visual acuity 0.2 for myopic eyes, etc.) and use the Toeplitz matrix associated with the visual characteristics for which the selection is accepted. Since the deformed image data is generated, the deformed image data corresponding to the visual characteristics of the user can be generated.

  According to a fifth aspect of the present invention, there is provided a computer comprising the image processing apparatus according to any one of the first to fourth aspects, and display output means for displaying and outputting the deformed image data.

  According to the above configuration, the generated deformed image data is displayed and output by the display output means.

  Therefore, since the generated deformed image data is displayed and output instead of the input image data, a clear image can be visually recognized with the naked eye even for presbyopia and myopia.

  An image forming apparatus according to a sixth aspect includes the image processing apparatus according to any one of the first to fourth aspects, and a print output unit that prints out the modified image data.

  According to the above configuration, the generated deformed image data is printed out by the print output unit.

  Therefore, since the generated deformed image data is printed out instead of the input image data, a clear image can be visually recognized with the naked eye even for presbyopia and myopic eyes.

  According to the image processing apparatus of the first aspect, the product of the input image data and the inverse matrix of the Toeplitz matrix composed of the point spread function indicating the lack of focus adjustment power of the human eye is calculated, whereby the deformed image data is When the user who has insufficient eye focus adjustment power sees the image indicated by the deformed image data because it is generated, that is, the input image data is preliminarily multiplied by the one that cancels the focus adjustment power of the human eye Insufficient focus adjustment power of the eye is offset, and the image indicated by the input image data (original image data) can be perceived without deterioration.

  According to the image processing apparatus of the second aspect, the user can select visual characteristics (for example, visual acuity 0.1 for presbyopia, visual acuity 0.2 for myopic eyes, etc.), and the selection is accepted. Since the deformed image data is generated using the inverse matrix of the Toeplitz matrix associated with the characteristics, the deformed image data according to the visual characteristics of the user can be generated.

  According to the image processing apparatus of the third aspect, since the deformed image data is generated by using the discrete sine transform and the discrete sine inverse transform, it is possible to generate the deformed image data with high accuracy. That is, when deformed image data is generated using Fourier transform and inverse Fourier transform, a complex number is generated in each pixel constituting the deformed image data. Since the deformed image data is generated by using the discrete sine inverse transform, the accuracy of the deformed image data is improved without generating a complex number in each pixel constituting the deformed image data. As a result, when a user with insufficient eye focus adjustment power views the image indicated by the deformed image data, the image indicated by the input image data (original image data) can be perceived. In addition, when deformed image data is generated using Fourier transform and inverse Fourier transform, when a person with insufficient eye focus adjustment power sees the image indicated by the deformed image data, the periphery of the image deteriorates. Although it is perceived, deformed image data is generated using discrete sine transform and inverse discrete sine transform. Therefore, when a user with insufficient eye focus adjustment power sees the image indicated by the deformed image data, the deformed image is displayed. The periphery of the image indicated by the data is not deteriorated and perceived.

  According to the image processing apparatus of the fourth aspect, the user can select visual characteristics (for example, visual acuity 0.1 for presbyopia, visual acuity 0.2 for myopic eyes, etc.), and the selection is accepted. Since the deformed image data is generated using the Toeplitz matrix associated with the characteristics, the deformed image data according to the visual characteristics of the user can be generated.

  According to the computer of the fifth aspect, since the generated deformed image data is displayed and output instead of the input image data, a clear image can be visually recognized with the naked eye even for presbyopia, myopia and the like.

  According to the image forming apparatus of the sixth aspect, since the generated deformed image data is printed out instead of the input image data, a clear image can be visually recognized with the naked eye even for presbyopia, myopia and the like. it can.

  The image processing apparatus of the present invention will be described below with reference to the drawings. In the present embodiment, an embodiment in which the image processing apparatus of the present invention is embodied in a personal computer (hereinafter referred to as “PC”) which is an example of a computer will be described. FIG. 1 is a block diagram illustrating a configuration example of a PC (image processing apparatus, computer) 1 according to an embodiment of the present invention. As illustrated, the PC 1 includes a control unit (CPU: Central Processing Unit) 2, a ROM (Read Only Memory) 3, a RAM (Random Access Memory) 4, an operation unit 5, a display unit 6, an auxiliary storage device (HDD: Hard). Disk Drive) 7 and LAN I / F (Local Network Interface) 8, and the units 2 to 8 are communicably connected by a bus 9. The image processing apparatus of the present invention includes a control unit 2, a ROM 3, a RAM 4, an operation unit 5, and a display unit 6 in the PC 1. In addition, a scanner 10 and a printer 11 are connected to the PC 1.

  The control unit 2 executes various processes according to a control program stored in the ROM 3, and functions as an input image data receiving unit 2a (see FIG. 2) described later. The RAM 4 functions as a main memory, work area, and the like of the control unit 2 and stores various setting information and the like.

  Here, the operation unit 5 includes a keyboard, a mouse, and the like, and receives inputs such as instructions and settings for the PC 1. The display unit 6 (corresponding to display output means) is a liquid crystal display or a CRT display, and displays various screen information. Specifically, the display unit 6 displays the operation state of the PC 1, various setting screens, and the like. The auxiliary storage device 7 is a storage device that incorporates a storage medium having a large-capacity memory area. The auxiliary storage device 7 incorporates various application software such as document creation software and graphic software, and stores image data created using the document creation software and graphic software. Yes.

  The LAN I / F 8 is an interface that connects a LAN (Local Network Interface) 9 and the PC 1 so as to communicate with each other. A scanner 10 and a printer 11 are connected to the LAN 9, and the PC 1, the scanner 10, and the printer 11 are communicably connected via the LAN 9. The scanner 10 reads an image of a document to generate image data, and outputs the generated image data to the PC 1. Here, the scanner 10 reads a monochrome image of a document, generates two-dimensional monochrome image data, and outputs it to the PC 1. Although not shown, the scanner 10 includes an image sensor such as a CCD (Charge Coupled Device), a flat bed scanner (FBS) having an optical system such as a light source, an automatic document feeder (ADF), and the like. The document supply mechanism is provided. The printer 11 prints out image data. Specifically, the image indicated by the image data output from the PC 1 is printed on a sheet. As a printing method in the printer 11, for example, an electrophotographic method can be used.

  Next, the functional configuration of the control unit 2 will be described. As shown in FIG. 2, the control unit 2 functionally includes an input image data receiving unit 2a, a storage unit 2b, a receiving unit 2c, a reading unit 2d, a modified image data generating unit 2e, and a modified image data output unit 2f. ing.

  The input image data receiving unit 2a receives image data input from the scanner 10 (hereinafter referred to as “input image data”), and outputs the received input image data to the modified image data generating unit 2e.

なお、ｈ_k,lは、点広がり関数を示しており、図３に示すように、点広がり関数ｈ_k,lは、前記任意の画素ｕ（ｉ，ｊ）を中心とする（２Ｋ＋１）×（２Ｌ＋１）（Ｋ、Ｌはともに自然数）の領域に含まれる変形画像データの各画素に対する重み（係数）を示すものである。焦点調節力が不足している人間ほど、前記任意の画素ｕ（ｉ，ｊ）が多くの周辺画素の影響を受けて知覚されるため、Ｋ、Ｌの値が大きくなる。ここで、点広がり関数は、三角関数、正規関数、２次関数等であり、関数の全ての値の和が「１」となるものである。記憶部２ｂには、例えば、上記のような様々な点広がり関数からなるテプリッツ行列の逆行列が格納されている。 The storage unit 2b (corresponding to the storage means) stores a plurality of visual characteristics in association with an inverse matrix of a Toeplitz Matrix composed of a point spread function corresponding to each visual characteristic. For example, as visual characteristics, visual acuity 0.3 for presbyopia, visual acuity 0.4 for presbyopia, visual acuity 0.3 for myopic eyes, visual acuity 0.4 for myopic eyes, and the like are stored. An inverse matrix of the Toeplitz matrix is associated with such visual characteristics and stored in the storage unit 2b. Here, if an arbitrary pixel of the deformed image data generated by the deformed image data generation unit 2e is u (i, j), the arbitrary pixel u (i, j) has insufficient eye focus adjustment power. Is perceived as an arbitrary pixel z (i, j) of the input image data of the following equation (1).

Note that h _{k, l} represents a point spread function, and as shown in FIG. 3, the point spread function h _{k, l} is (2K + 1) × centered on the arbitrary pixel u (i, j). This indicates the weight (coefficient) for each pixel of the modified image data included in the region of (2L + 1) (K and L are both natural numbers). As a person with insufficient focus adjustment power, the arbitrary pixel u (i, j) is perceived by the influence of many peripheral pixels, and thus the values of K and L are increased. Here, the point spread function is a trigonometric function, a normal function, a quadratic function, or the like, and the sum of all values of the function is “1”. The storage unit 2b stores, for example, an inverse matrix of a Toeplitz matrix composed of various point spread functions as described above.

  The accepting unit 2c (corresponding to accepting means) accepts one of the plurality of visual characteristics via the operation unit 5. For example, the reception unit 2 c displays information on a plurality of visual characteristics on the display unit 6, and when any one of the information on the visual characteristics is selected by the user via the operation unit 5. , Accepting selection of its visual characteristics. The reading unit 2d reads from the storage unit 2b the inverse matrix of the Toeplitz matrix associated with the visual characteristic whose selection is received by the receiving unit 2c, and outputs the read inverse matrix of the Toeplitz matrix to the modified image data generation unit 2e. To do.

  The deformed image data generating unit 2e (corresponding to the deformed image data generating means) generates deformed image data obtained by deforming the image data so that the image data can be perceived normally by a person who has insufficient eye focus adjustment. To do.

また、数２は、次式数３のように表現できる。

ここで、ｉ−ｋに対して、

とすると、数３は、次式数５のようになる。

このとき、１次元の点広がり関数（ｈ_k，ｇ_l）に対する逆フィルタの設計問題を解けば、ｕ（ｉ，ｊ）を求めることができる。 Hereinafter, the principle of generating the deformed image data will be described. For the input / output data {z (i, j), u (i, j)} of Equation 1, the point spread function h _{k, l} = h _k × _gl . This is because the visual characteristics are symmetrical. At this time, Formula 1 becomes Formula 2 below

Equation 2 can be expressed as the following Equation 3.

Here, for i-k,

Then, Equation 3 becomes Equation 5 below.

At this time, u (i, j) can be obtained by solving the inverse filter design problem for the one-dimensional point spread function (h _k , g _l ).

となり、

と表現できる。なお、１次元の点広がり関数からなるテプリッツ行列は、以下の数８に示すＨである。

ここで、数７において、両辺にテプリッツ行列Ｈの逆行列Ｈ^−１を乗じると、

となり、

が求められる。 In Equation 5, if j columns are fixed (j = 1, 2,..., N)

And

Can be expressed as A Toeplitz matrix composed of a one-dimensional point spread function is H shown in the following equation (8).

Here, in Equation 7, when both sides are multiplied by the inverse matrix H ⁻¹ of the Toeplitz matrix H,

And

Is required.

なお、１次元の点広がり関数からなるテプリッツ行列は、次式数１１に示すＧである。

ここで、ｉ−ｋ＝１，２，…，Ｍとし、数１０の両辺にテプリッツ行列Ｇの逆行列Ｇ^-1を乗じると、

となり、

が求められる。 Further, when i−k is fixed in Equation 4, it can be expressed as the following Equation 10.

A Toeplitz matrix composed of a one-dimensional point spread function is G shown in the following equation (11).

Here, if i−k = 1, 2,..., M, and multiplying both sides of Equation 10 by the inverse matrix G ⁻¹ of the Toeplitz matrix G,

And

Is required.

  Deformed image data can be generated based on the principle described above. That is, the modified image data generation unit 2e calculates the product of the input image data received by the input image data reception unit 2a and the inverse matrix of the Toeplitz matrix stored in the storage unit 2b, thereby generating the modified image data. Is generated. Hereinafter, the process for generating the deformed image data is also referred to as “deformation process”.

Note that the storage unit 2b stores inverse matrices of two Toeplitz matrices corresponding to H ⁻¹ and G ⁻¹ in association with visual characteristics. Further, in the present embodiment, the case where the point spread function h _{k, l} is h _k × g _l has been described. However, when the visual characteristic has vertical and horizontal symmetry, h _{k, l} = h _k × It may be h _l . Further, when generating the deformed image data, the deformed image data is generated for each predetermined area (for example, every 512 × 512 pixels). Since the peripheral pixels are regarded as “0”, the pixel values in the predetermined area are preliminarily determined. An average value is obtained, the average value is subtracted from each pixel value included in the predetermined area, and deformed image data is generated using the pixel value from which the average value has been subtracted. Then, an average value is added to each pixel constituting the generated deformed image data.

  Further, here, a case has been described in which deformation image data is generated by performing deformation processing on input image data from the scanner 10, but deformation image data is generated by performing deformation processing on image data stored in the auxiliary storage device 7. May be generated. In addition, the image data displayed on the display unit 6 (for example, image data of characters displayed on the display unit 6 when a document is created using document creation software) is subjected to a deformation process to generate the deformed image data. The generated image may be displayed on the display unit 6 by the generated deformed image data.

  The deformed image data output unit 2 f outputs the deformed image data generated by the deformed image data generation unit 2 e to the printer 11. On the other hand, the printer 11 prints out the deformed image data input from the deformed image data output unit 2f. Although the case where the deformed image data is output to the printer 11 and the deformed image data is printed out by the printer 11 has been described here, the image indicated by the deformed image data may be displayed on the display unit 6. Thereby, even if it is presbyopia, myopia, etc., a clear image can be visually recognized with a naked eye.

  Hereinafter, an operation performed in the PC 1 when input image data from the scanner 10 is received will be described based on a flowchart shown in FIG. First, the input image data receiving unit 2a determines whether or not input image data from the scanner 10 has been received (S1). If it is determined that the input image data from the scanner 10 is not received (S1: NO), a standby state is entered. Conversely, when it is determined that the input image data from the scanner 10 has been received (S1: YES), the reading unit 2d uses an inverse matrix of the Toeplitz matrix associated with the visual characteristics whose selection is received by the receiving unit 2c. The data is read from the storage unit 2b and output to the modified image data generation unit 2e (S2).

  Next, the deformed image data generation unit 2e generates deformed image data from the input image data and the inverse matrix of the Toeplitz matrix (S3). That is, by calculating the product of the input image data accepted by the input image data accepting unit 2a and the inverse matrix of the Toeplitz matrix associated with the visual characteristic accepted by the accepting unit 2c, the modified image data Is generated. Then, the deformed image data output unit 2f outputs the deformed image data generated by the deformed image data generation unit 2e to the printer 11 (S4). The printer 11 prints out the deformed image data input from the deformed image data output unit 2f.

  As described above, in the PC 1, the deformed image data is generated by calculating the product of the input image data and the inverse matrix of the Toeplitz matrix composed of the point spread function indicating the lack of focus adjustment power of the human eye. That is, since the input image data is preliminarily multiplied by the input image data to cancel out the focus adjustment power of the human eye, when the user who has insufficient eye focus adjustment power views the image indicated by the deformed image data, the focus of the eye The lack of adjustment power is offset and the image indicated by the input image data (original image data) can be perceived without deterioration.

  In addition, the user can select visual characteristics (for example, visual acuity 0.1 for presbyopia, visual acuity 0.2 for myopic eyes, etc.), and the inverse of the Toeplitz matrix associated with the visual characteristics for which the selection has been accepted. Since the deformed image data is generated using the matrix, it is possible to generate the deformed image data according to the visual characteristics of the user.

  Next, another embodiment of generating deformed image data will be described. In another embodiment, the storage unit 2b stores a plurality of visual characteristics and a Toeplitz matrix composed of a point spread function corresponding to each visual characteristic, and the reading unit 2d is selected by the receiving unit 2c. Is read from the storage unit 2b, and the read Toeplitz matrix is output to the modified image data generation unit 2e. Hereinafter, the principle of generating modified image data in other embodiments will be described.

ただし、

であり、点広がり関数ｈ_k,lに対称性ｈ_k,l＝ｈ_-k,lを仮定する。このとき、テプリッツ行列Ｈ_T,lは次式数１５のように分解できる。

ただし、行列Ｑ＝[ｑ_i,j]は３重対角行列であり、

すなわち、

である。また、Ｈ_H,lはハンケル行列（Hankel matrix）、すなわち、

ここで、Ｈ_lをＱの多項式として、

と表現することができる。なお、上記数２０、数２１における[（Ｋ−ｋ）／２]は、（Ｋ−ｋ）／２以下の最大の整数を示す。 First, when Expression 1 is expressed as a vector matrix, it can be expressed as the following Expression 13 using the Toeplitz matrix H _{T, l} .

However,

And symmetries h _{k, l} = h _{−k, l} are assumed for the point spread function h _{k, l} . At this time, the Toeplitz matrix H _{T, l} can be decomposed as in the following equation (15).

Where the matrix Q = [q _{i, j} ] is a tridiagonal matrix,

That is,

It is. H _{H, l} is a Hankel matrix, that is,

Where H _l is a polynomial in Q,

It can be expressed as In addition, [(K−k) / 2] in the above Equations 20 and 21 represents the maximum integer of (K−k) / 2 or less.

ここで、離散サイン変換行列Ｓを数２２の両辺に左から掛けると、次式数２３の関係式となる。

すなわち、

となる。ただし、

である。なお、Ｉは単位行列を示す。ここで、行列Ｑは、サイン変換行列Ｓを用いて対角化できることが知られており、

となる。したがって、ＳＨ_lＳは以下のように、対角行列（diagonal matrix）となる。なお、数２６、数２８において、ｄｉａｇ[]は、[]内の要素を対角成分にもつ対角行列を表す。

すなわち、ＳＳ＝Ｉ（単位行列）であるので、

したがって、数２４は、次式数３０のように、近似的に各行が分離できる。

すなわち、各ｉ行目について

が成立する。数３１の逆問題、すなわち、ｙ_i,jからｘ_i,jを求めることによりｕ（ｉ，ｊ）は離散サイン逆変換を利用して求めることができる。また、

は、反復計算によって求められる。この

は、フーリエ変換、及びフーリエ逆変換を用いる場合に比べて、離散サイン変換、及び離散サイン逆変換を用いた方が値が小さくなるため、ｕ（ｉ，ｊ）の精度が向上する。 On the other hand, the decomposition associated with the discrete Fourier transform appears by approximating the Toeplitz matrix H _{T, l} with a circulant matrix. Here, using the above decomposition, Equation 13 can be expressed as Equation 22 below.

Here, when the discrete sine transform matrix S is multiplied on both sides of the equation 22 from the left, the following equation 23 is obtained.

That is,

It becomes. However,

It is. I represents a unit matrix. Here, it is known that the matrix Q can be diagonalized using the sine transform matrix S,

It becomes. Therefore, SH ₁ S becomes a diagonal matrix as follows. In Equations 26 and 28, diag [] represents a diagonal matrix having the elements in [] as diagonal components.

That is, since SS = I (unit matrix),

Therefore, in Equation 24, each row can be approximately separated as shown in Equation 30 below.

That is, for each i-th row

Is established. By obtaining x _{i, j} from the inverse problem of Equation 31, ie, y _{i, j ,} u (i, j) can be obtained using discrete sine inverse transformation. Also,

Is obtained by iterative calculation. this

Since the value is smaller when the discrete sine transform and the inverse discrete sine transform are used than when the Fourier transform and the inverse Fourier transform are used, the accuracy of u (i, j) is improved.

  Deformed image data can be generated based on the principle described above. In other words, the modified image data generation unit 2e (corresponding to the discrete sine transform unit, the first calculation unit, the second calculation unit, and the discrete sine inverse transform unit) receives the input image data received by the input image data reception unit 2a. And discrete sine transform of the Toeplitz matrix associated with the visual characteristic whose selection is accepted by the accepting unit 2c, calculating an inverse matrix of the Toeplitz matrix subjected to the discrete sine transform, and input image data subjected to the discrete sine transform, A product of the discrete sine-transformed point spread function and the inverse function is calculated, and the transformed image data is generated by performing inverse discrete sine transform on the calculated product.

  As described above, in another embodiment, the deformed image data is generated using the discrete sine transform and the inverse discrete sine transform, and thus it is possible to generate highly accurate deformed image data. That is, when deformed image data is generated using Fourier transform and inverse Fourier transform, a complex number is generated in each pixel constituting the deformed image data. Since the deformed image data is generated by using the discrete sine inverse transform, the accuracy of the deformed image data is improved without generating a complex number in each pixel constituting the deformed image data. Further, when the inverse matrix of the Toeplitz matrix is calculated, the Toeplitz matrix is approximated to a diagonal matrix by the similarity transformation, but as the similarity transformation matrix, the discrete sine transformation, and the Fourier transformation and the inverse Fourier transformation are used. When the Toeplitz matrix is diagonalized using the inverse discrete sine transform, the accuracy of the approximation is improved, so that the accuracy of the deformed image data is improved. As a result, when a user with insufficient eye focus adjustment power views the image indicated by the deformed image data, the image indicated by the input image data (original image data) can be perceived. In addition, when deformed image data is generated using Fourier transform and inverse Fourier transform, when a person with insufficient eye focus adjustment power sees the image indicated by the deformed image data, the periphery of the image deteriorates. Although it is perceived, deformed image data is generated using discrete sine transform and inverse discrete sine transform. Therefore, when a user with insufficient eye focus adjustment power sees the image indicated by the deformed image data, the deformed image is displayed. The periphery of the image indicated by the data is not deteriorated and perceived. In another embodiment, modified image data can be generated even when the point spread function is asymmetric. In other embodiments, even when the number of pixels constituting the image data is large, the deformed image data can be generated with a small amount of calculation.

  Although the case where the input image data is monochrome image data has been described in the present embodiment, the input image data may be color image data. In this case, the deformed image data may be generated for each color component (R component, G component, B component) of the RGB color system color image data input from the scanner 10.

  In this embodiment, the case where the input image data is still image data has been described. However, the input image data may be moving image data including a plurality of still image data. For example, in a digital television device, still image data (frames) are continuously received, and the received still image data (frames) are temporarily stored in a buffer. Deformation processing is performed for each stored still image data (frame) to generate deformation image data. Then, the image indicated by the generated deformed image data may be continuously displayed on the monitor. Thereby, even if it is presbyopia, myopia, etc., a clear image can be visually recognized with a naked eye. Also in a DVD (Digital Versatile Disk) player, deformation processing can be performed for each still image data (frame) read from the DVD and stored in the buffer.

  In the present embodiment, an embodiment in which the image processing apparatus of the present invention is embodied in the PC 1 has been described. However, the present invention is not limited to a personal computer, and may be a workstation or the like as long as it is a computer. Further, the image processing apparatus of the present invention can be embodied in an image forming apparatus that prints out image data. In addition, a copying machine that reads an image of a document to generate image data, prints and outputs the generated image data, a facsimile machine that reads an image of the document to generate image data, and transmits the generated image data by facsimile, and a copying machine Further, the present invention can be embodied in an apparatus that handles image data, such as a multifunction machine of a facsimile apparatus. For example, when embodied in a copying machine, it is possible to produce a large amount of printed matter that allows a clear image to be visually recognized with the naked eye.

1 is a block diagram illustrating an example of a PC (image processing apparatus, computer) according to an embodiment of the present invention. It is the block diagram which showed an example of the function structure of the control part. It is a figure for demonstrating a point spread function. 6 is a flowchart illustrating an operation performed in a PC when input image data from a scanner is received.

Explanation of symbols

1 PC (image processing device, computer)
2 Control unit 2b Storage unit (storage unit)
2c Reception part (reception means)
2e Modified image data generation unit (modified image data generation means, discrete sine conversion means, first calculation means, second calculation means, discrete sine inverse conversion means)
3 ROM
4 RAM
5 Operation section 6 Display section (display output means)
10 Scanner 11 Printer

Claims (6)

An image processing apparatus that generates deformed image data obtained by transforming image data so that the image data is normally perceived for a human who has insufficient eye focus adjustment power,
Calculating a product of storage means for storing an inverse matrix of a Toeplitz matrix comprising a point spread function indicating the focus adjustment power of the human eye, and input image data and an inverse matrix of the Toeplitz matrix stored in the storage means. An image processing apparatus comprising: modified image data generation means for generating the modified image data. The image processing apparatus includes an accepting unit that accepts one of a plurality of visual characteristics.
The storage means further stores the plurality of visual characteristics in association with inverse matrices of Toeplitz matrices corresponding to the visual characteristics,
The deformed image data generation unit generates the deformed image data by calculating a product of the input image data and an inverse matrix of a Toeplitz matrix associated with the visual characteristic selected by the receiving unit. The image processing apparatus according to claim 1. An image processing apparatus that generates deformed image data obtained by transforming image data so that the image data is normally perceived for a human who has insufficient eye focus adjustment power,
Storage means for storing a Toeplitz matrix composed of a point spread function indicating the focus adjustment power of the human eye, discrete image conversion means for discrete sine transform each of the input image data and the Toeplitz matrix stored in the storage means, and First calculation means for calculating an inverse matrix of the Toeplitz matrix subjected to discrete sine transform by the discrete sine transform means, input image data subjected to discrete sine transform by the discrete sine transform means, and the first calculation means. Second calculating means for calculating a product with an inverse matrix; and discrete sine inverse converting means for generating the modified image data by performing inverse discrete sine transformation on the product calculated by the second calculating means. An image processing apparatus comprising: The image processing apparatus includes an accepting unit that accepts one of a plurality of visual characteristics.
The storage means further stores the plurality of visual characteristics in association with a Toeplitz matrix corresponding to each visual characteristic,
4. The image processing apparatus according to claim 3, wherein the discrete sine transform unit performs discrete sine transform on the input image data and the Toeplitz matrix associated with the visual characteristics selected by the receiving unit.   5. A computer comprising: the image processing apparatus according to claim 1; and display output means for displaying and outputting the deformed image data.   An image forming apparatus comprising: the image processing apparatus according to claim 1; and a print output unit that prints out the deformed image data.

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