JP6302219B2 - MTF measuring apparatus and MTF measuring program - Google Patents

Description

  The present invention relates to an MTF measuring apparatus and an MTF measuring program for measuring an MTF representing a spatial frequency characteristic of an imaging system.

  Conventionally, in order to evaluate the quality of an imaging system (digital camera, scanner, etc.), a method using an MTF (Modulation Transfer Function) representing a spatial frequency characteristic as an index is known. This MTF expresses how faithfully the contrast of a subject to be imaged can be reproduced as a spatial frequency characteristic.

As a method for measuring this MTF, a method using an edge image having an inclination described in a chart for MTF measurement (the Slanted-edge method [inclined edge method]; see Patent Documents 1 and 2, Non-Patent Documents 1 and 2) It has been known.
This Slanted-edge method uses an image portion (ROI: Region Of Interest) that is a measurement object obtained by imaging a monochrome pattern in which a boundary inclined by several degrees from a vertical (or horizontal) direction with respect to an image sensor is a straight line. It is used to obtain a horizontal frequency characteristic or a vertical frequency characteristic (MTF).

FIG. 8A shows an ROI image (vertical edge image) obtained by capturing a black and white pattern in which a boundary inclined several degrees from the vertical direction is a straight line, and FIG. 8B shows a boundary inclined several degrees from the horizontal direction. The ROI image (horizontal edge image) which image | photographed the monochrome pattern used as a straight line is shown.
For example, when obtaining the horizontal frequency characteristics as MTF from the ROI image (vertical edge image) in FIG. 8A, first, the Slanted-edge method uses the slope of the edge as shown in FIG. The pixels of the edge image are projected on the horizontal axis (x axis) at the same angle.
The Slanted-edge method generates an edge profile indicating edge characteristics by averaging pixel values of pixels projected on the horizontal axis (x-axis) as shown in FIG. 9B.

The Slanted-edge method obtains a line spread function (LSF) by differentiating an edge profile, and obtains an MTF by Fourier transforming the LSF.
In addition, when calculating | requiring the vertical frequency characteristic as MTF from the ROI image (horizontal edge image) of FIG.8 (b), Slanted-edge method makes the axis | shaft which projects the pixel of an edge image a vertical axis, The MTF is obtained by the same method as that for the ROI image (vertical edge image) in FIG.
Alternatively, in the Slanted-edge method, the captured ROI image (horizontal edge image) in FIG. 8B is rotated by 90 °, and the edge image is displayed in the same manner as the ROI image (vertical edge image) in FIG. Pixels are projected on the horizontal axis (x-axis) to obtain the MTF.

Japanese Patent No. 4092853 Japanese Patent No. 5193113

ISO 12233: 2000, “Photography-Electronic Still-picture Cameras-Resolution Measurements” K.Masaoka, M.Sugawara, Y.Nojiri, “Muitidirectional MTF measurement of digital image acquisition devices using a Siemens star,” Proc.SPIE-IS & T, vol.7537, pp.75370V-1-75370V-8, Jan.2010 .

As described above, the conventional Slanted-edge method obtains the MTF by regarding the edge of the edge image as a straight line.
However, even if the edge is a straight line on the MTF measurement chart, distortion occurs in the edge of the image captured through the imaging system because lens distortion occurs.
For example, when taking an image through a lens like the barrel distortion of the lens shown in FIG. 10A and the pincushion distortion shown in FIG. 10B, the edge is more distorted in the peripheral portion of the captured image.
Therefore, in particular, when it is desired to measure the MTF around the lens, the conventional Slanted-edge method regards the distorted edge as a straight line and obtains the MTF, and thus there is a problem that the MTF cannot be measured correctly. It was.

  In view of such a problem, the present invention has an object to provide an MTF measuring apparatus and an MTF measuring program capable of measuring MTF with high accuracy by estimating edge distortion of a captured edge image. To do.

  In order to solve the above problems, an MTF measuring apparatus according to the present invention is an MTF measuring apparatus that measures an MTF that represents a spatial frequency characteristic of an imaging system, and includes an edge image extracting unit, an edge function approximating unit, and a pixel projecting unit. And a projection pixel value averaging means and an MTF calculation means.

In such a configuration, the MTF measurement apparatus inputs a captured image captured by an imaging system (digital camera) that is a measurement target. This captured image is obtained by capturing an image of a chart having a different contrast at a linear boundary so that the linear boundary is inclined at a predetermined angle with respect to a direction orthogonal to the MTF measurement direction. The predetermined angle is an angle that is determined in advance as an angle at which various phases can be measured by the Slanted-edge method, and is, for example, about 1 ° to several degrees.
Then, the MTF measuring apparatus extracts an edge image including a straight boundary as an edge from the captured image captured by the imaging system by the edge image extraction unit. For example, the edge image extraction means extracts an edge image by designating an extraction region from the outside.

  Then, the MTF measuring apparatus approximates the edge by a non-linear function such as a quadratic function or an exponential function from the pixel value distribution of the edge image extracted by the edge image extracting unit by the edge function approximating unit. Thereby, the MTF measuring apparatus can estimate the shape of the edge even when the edge is distorted.

Further, the MTF measuring apparatus projects the pixels of the edge image onto the one-dimensional coordinate axis along the shape of the nonlinear function approximated by the edge function approximating means by the pixel projecting means. It should be noted that the projected coordinate axes have sub-pixels smaller than the pixels of the edge image as coordinate units. This is because MTF in a sufficiently wide band exceeding the sampling frequency is measured by oversampling.
As a result, the MTF measuring apparatus projects each pixel of the edge image onto the one-dimensional coordinate axis along the edge distortion.

Then, the MTF measuring apparatus uses the projection pixel value averaging unit to subdivide each pixel projected on the coordinate axis by the pixel projection unit in each sub-pixel section divided into 1/4 or 1/8 pixel intervals on the coordinate axis. The pixel values are averaged, and an edge profile is generated by oversampling by 4 times or 8 times.
Thus, the MTF measurement device can generate a more accurate edge profile by generating an edge profile in which pixels are projected along a distorted edge curve.

  Then, the MTF measuring device calculates the MTF by performing Fourier transform after differentiating the edge profile by the MTF calculating means to obtain the line spread function.

  The MTF measurement apparatus according to the present invention is an MTF measurement for causing a computer of the MTF measurement apparatus to function as an edge image extraction unit, an edge function approximation unit, a pixel projection unit, a projection pixel value averaging unit, and an MTF calculation unit. Can be operated programmatically.

The present invention has the following excellent effects.
In the present invention, since the shape of the edge of the edge image captured by the imaging system is estimated by a non-linear function, even when the edge is distorted and the shape cannot be regarded as a straight line, the shape can be estimated by a curve. Furthermore, since the edge profile of the edge image is generated along the shape of the estimated nonlinear function, the MTF can be measured with high accuracy.
Thus, according to the present invention, even when distortion such as barrel distortion and pincushion distortion is generated in the captured image by the lens of the imaging system, the MTF can be accurately measured from the edge image.

It is a block block diagram which shows the structure of the MTF measuring apparatus which concerns on embodiment of this invention. It is the figure which has arrange | positioned the edge image which the MTF measuring apparatus which concerns on embodiment of this invention measures in xy coordinate system. It is a graph for demonstrating the relationship between a normal cumulative distribution function and edge shape distribution, (a) is a graph of a normal cumulative distribution function, (b) is a graph which shows the pixel value distribution of the horizontal direction of an edge image. is there. It is the graph which applied the graph of FIG.3 (b) to the two-dimensional pixel value distribution of an edge image. It is a figure for demonstrating the process which the pixel projection means of the MTF measuring apparatus which concerns on embodiment of this invention projects the pixel of an edge image on a horizontal axis using a nonlinear function. It is a flowchart which shows operation | movement of the MTF measuring apparatus which concerns on embodiment of this invention. It is a chart which shows the pattern which colored different contrast for every radiation | emission area | region. It is an edge image used in the conventional Slanted-edge method, where (a) is an image for obtaining horizontal frequency characteristics as an MTF (vertical edge image), and (b) is an image for obtaining vertical frequency characteristics as an MTF. It is an image (horizontal edge image). It is a figure for demonstrating the production | generation procedure of the edge profile of the conventional Slanted-edge method, Comprising: (a) is the process which projects the pixel of an edge image on a horizontal axis (x-axis) with the inclination of an edge, (b) is It is a figure which shows the process which averages the pixel value of the projected pixel and produces | generates an edge profile. It is a figure for demonstrating the distortion aberration of the lens of an imaging system, (a) shows barrel distortion, (b) shows pincushion distortion.

Embodiments of the present invention will be described below with reference to the drawings.
[Configuration of MTF measuring device]
Initially, with reference to FIG. 1, the structure of the MTF measuring apparatus which concerns on embodiment of this invention is demonstrated. This MTF measuring apparatus 1 measures MTF representing the spatial frequency characteristics of an imaging system. Here, the MTF measuring apparatus 1 includes an image input unit 10, an image storage unit 11, an edge image extraction unit 12, an edge profile generation unit 13, and an MTF calculation unit 14. Here, the MTF measuring device 1 is connected to an imaging system (digital camera, scanner, etc.) 2 to be measured and a display device 3 that provides a user interface for operating the MTF measuring device 1. To do.

  The image input means 10 inputs an image captured through the imaging system 2. Here, from the imaging system 2, a captured image obtained by capturing an MTF measurement chart (for example, a black and white pattern) having a different contrast at a linear boundary for measuring the MTF is input. The image input unit 10 writes and stores the captured image in the image storage unit 11.

  Note that the imaging system 2 captures charts having different contrasts at the linear boundary so that the linear boundary is inclined at a predetermined angle with respect to a direction orthogonal to the measurement direction of the MTF. For example, when measuring the MTF in the vertical direction, the imaging system 2 images the chart so that the linear boundary is inclined at a predetermined angle from the horizontal direction. For example, when measuring the MTF in the horizontal direction, the imaging system 2 images the imaging target so that the straight line boundary is inclined at a predetermined angle from the vertical direction. This predetermined angle is, for example, about 1 ° to several degrees.

  The captured image may be an image obtained by attaching a chart for MTF measurement by tilting a predetermined angle and attaching the chart to the wall surface, or by capturing the chart without tilt by tilting the imaging system 2 by a predetermined angle. It may be a thing. Alternatively, the captured image may be an image obtained by arranging a black and white pattern in which a linear boundary is inclined by a predetermined angle in a chart having no inclination.

  In addition, the operator can set the MTF of the imaging system 2 in an imaging region where the MTF is to be measured, for example, a central portion, a central right (left, upper, lower) portion, a right (left) diagonal upper portion, a right (left) diagonal lower portion, etc. The chart is imaged by the imaging system 2 so that the monochrome pattern is arranged.

  The image storage unit 11 stores an image captured by the imaging system 2 input via the image input unit 10 and is a general storage device such as a hard disk. The image stored in the image storage unit 11 is referred to by the edge image extraction unit 12.

The edge image extraction unit 12 extracts an edge image (ROI image) including a linear boundary of contrast as an edge as an object for measuring the MTF from the image captured by the imaging system 2 stored in the image storage unit 11. Is. Here, the edge image extracted from the captured image is the edge image of the monochrome pattern shown in FIG. That is, for the vertical edge image (FIG. 8A) for obtaining the MTF in the horizontal direction, an image in which a black area is arranged on the left side and a white area is arranged on the right side is used. As for the horizontal edge image (FIG. 8B) for obtaining the MTF in the vertical direction, an image in which a black area is arranged on the lower side and a white area is arranged on the upper side is used.
Here, the edge image extraction unit 12 includes an ROI extraction unit 121 and an ROI rotation unit 122.

The ROI extracting unit (measuring target image extracting unit) 121 designates rectangular information such as the position and size at which the MTF is measured in the captured image, so that the MTF measuring target image (edge image) ( ROI image) is extracted.
The ROI extraction unit 121 displays the captured image stored in the image storage unit 11 on the display device 3. The ROI extraction unit 121 specifies the position and size of the ROI image by inputting a rectangular area designated by the operator via a pointing device such as the touch pen 31.

  Here, the ROI extraction unit 121 outputs the extracted ROI image to the edge profile generation unit 13 when a vertical edge image (see FIG. 8A) having edges in the vertical direction is extracted as the ROI image. When the ROI extraction unit 121 extracts a horizontal edge image (see FIG. 8B) having edges in the horizontal direction as the ROI image, the ROI extraction unit 121 outputs the extracted ROI image to the ROI rotation unit 122.

The determination of whether the ROI image performed by the ROI extraction unit 121 is a vertical edge image or a horizontal edge image may be appropriately designated from the outside. For example, if the image is a vertically long rectangle, the vertical edge image or the horizontally long rectangle is used. If so, it may be determined as a horizontal edge image.
Alternatively, the ROI extraction unit 121 may determine whether the ROI image is a vertical edge image or a horizontal edge image based on the distribution of pixel values in the designated rectangular area.

The ROI rotation means (measurement target image rotation means) 122 rotates the ROI image (horizontal edge image) extracted by the ROI extraction means 121 and converts it into a vertical edge image. The ROI rotation unit 122 outputs the rotated ROI image (vertical edge image) to the edge profile generation unit 13.
When rotating the horizontal edge image, the ROI rotation unit 122 rotates the horizontal edge image so that the monochrome pattern of the rotated image is the same as the monochrome pattern of the vertical edge image extracted by the ROI extraction unit 121. .
That is, here, the ROI rotation means 122 is such that the horizontal edge image in FIG. 8B has the same black and white pattern as the vertical edge image in FIG. 8A (the black area on the left side and the white area on the right side). And turn 90 ° clockwise.

  The edge profile generation unit 13 generates an edge profile indicating the pixel distribution shape of the edge from the ROI image (vertical edge image) extracted by the edge image extraction unit 12. Here, the edge profile generation unit 13 includes an edge function approximation unit 131, a pixel projection unit 132, and a projection pixel value averaging unit 133.

The edge function approximating unit 131 approximates an edge in the ROI image by a nonlinear function such as a quadratic function or an exponential function from the pixel value distribution of the ROI image (edge image) extracted by the edge image extracting unit 12. is there.
That is, the edge function approximating means 131 approximates the edge when the ROI image is arranged in a coordinate system (xy coordinate system) having two horizontal and vertical axes as a nonlinear function. Here, an example using a quadratic function as the nonlinear function will be described.
A quadratic function in the xy coordinate system approximating the edge is represented by the following expression (1). Note that p ₁ , p ₂ , and p ₃ are parameters to be estimated when the function is approximated.

  Here, the normal cumulative distribution function normcdf is defined as the following equation (2). μ represents the average of the distribution, and σ represents the standard deviation of the distribution.

  The edge function approximating means 131 estimates the parameter that the distribution function of the following expression (3) obtained by applying the expression (2) to the two-dimensional distribution approximates the pixel value distribution of the edge image. Specify the quadratic function of equation (1).

Here, p _{1 to} p ₅ are parameters, and p ₁ to p ₃ are the same parameters as in the formula (1).

Here, the meaning of the expression (3) will be described with reference to FIGS.
FIG. 2 shows a state in which ROI images (edge images) are arranged on the xy coordinates so that a black region and a white region are arranged in the positive direction of the x axis.
As shown in FIG. 2, the edge e of the ROI image R may not be regarded as a straight line due to the distortion of the lens, and is approximated by the quadratic function of the equation (1) here.
In this case, p _{1 in the} formula (1) is a coefficient of y, and p ₂ is a coefficient of y ² . In addition, _{p 3} is an x-intercept. By using this y ² term, it becomes possible to approximate a distorted edge.

Here, attention is paid to the distribution of pixel values at y = 0 in the ROI image R. As shown in FIG. 3, this distribution can be approximated using the normal cumulative distribution function normcdf of the equation (2).
When the normal cumulative distribution function f (x) of the equation (2) is graphed, the graph shape of FIG. The normal cumulative distribution function f (x) changes from “0” to “1” as x increases. On the other hand, in order to represent the level change of the pixel value from the left black area to the right white area of the ROI image R, the normal cumulative distribution function f (x) is expressed as p ₄ as shown in FIG. Double. That, _{p 4} shows the level difference between the black and white pixel values of the ROI image R.

Further, the pixel value of the black area of the ROI image R is not a necessarily "0", keep p ₅ adds the level of the pixel values. That, _{p 5,} a pixel value of the black area of the ROI image R.

Here, since only the edge distortion has to be obtained and the standard deviation need not be estimated, the standard deviation σ of the normal cumulative distribution function f (x) is not set to the constant “1” for optimization.
The average μ of the normal cumulative distribution function f (x) can be regarded as an edge that switches from the left black area to the right white area of the ROI image R when the standard deviation σ is a constant “1”. That is, the average μ may be estimated as the x-intercept p ₃ when the edge is approximated by the quadratic function of the equation (1) in which the pixel value in the black and white area is switched.

By expanding the one-dimensional distribution of pixel values at y = 0 in the ROI image R in the y direction, the distribution of two-dimensional pixel values in the ROI image R can be expressed as shown in FIG. .
In other words, the distribution function f (x, y) in the expression (3) is a function that represents the distribution of the two-dimensional pixel values of the ROI image R using a quadratic function.
Returning to FIG. 1, the description of the configuration of the MTF measuring apparatus 1 will be continued.

The parameters p _{1 to} p ₅ of the distribution function f (x, y) in the equation (3) can be estimated by fitting by a general least square method.
That is, the edge function approximating means 131, as shown in the following formula (4), for all the pixels on the (x, y) coordinates constituting the ROI image R, the pixel value v (x, y) of the ROI image R. ) And the value of the distribution function f (x, y) of the equation (3) are specified as parameters p _{1 to} p ₅ that minimize the sum S of squares. Here, N indicates the number of horizontal pixels of the ROI image R, and M indicates the number of vertical pixels of the ROI image R.

Note that the edge function approximating means 131, as shown in the following formula (5), for all pixels on the (x, y) coordinates constituting the ROI image R, the pixel value v (x, y) of the ROI image R. ) And the value of the distribution function f (x, y) of the equation (3) may be specified as parameters p _{1 to} p ₅ that minimize the sum S ′ of absolute values.

Here, for the parameter p ₄ , the level difference between the monochrome pixel values in the ROI image R can be used as an initial value when performing optimization. As for the parameters p _5, the pixel value of the black area of the ROI image R, can be used as an initial value when performing optimization.
For example, in the ROI image R, the edge function approximating unit 131 sets the pixel value that is the largest among the pixel values smaller than the average pixel value as the pixel value of the black region, and is the largest among the pixel values that are larger than the average pixel value. By setting many pixel values as pixel values in the white area, the parameters p ₄ and p ₅ are determined in advance and set as initial values for optimization.

The pixel projecting unit 132 projects the pixels of the ROI image R onto a one-dimensional coordinate axis along the edge curve obtained by approximation by the edge function approximating unit 131. Here, the pixels of the ROI image R are projected onto the horizontal coordinate axis (x-axis) along the slope (curve) of the edge specified by the quadratic function estimated by the edge function approximation means 131.
Note that the coordinate system of the projected axis is a sub-pixel unit smaller than the pixel-based coordinate system of the ROI image R, for example, 1/4 or 1/8 of one pixel.
The pixel projecting unit 132 outputs the coordinate position on the horizontal axis of the sub-pixel on which each pixel of the ROI image R is projected to the projected pixel value averaging unit 133.

Here, with reference to FIG. 5, a method in which the pixel projecting unit 132 performs pixel projection on the horizontal axis using the function represented by the formula (3) will be specifically described.
In FIG. 5, for easy understanding, an edge e specified by a nonlinear function is superimposed on the ROI image R. The white point or black point of each pixel of the ROI image R indicates the pixel position in the coordinate system (xy coordinates) of the ROI image R.

As shown in FIG. 5, the pixel projecting unit 132 arranges the ROI image R on the xy coordinates so that the contrast differs in the x-axis direction, and moves the pixels on the ROI image R along the inclination (distortion) of the edge e. To the horizontal axis (x _sub coordinate) of the subpixel.
For example, the pixel g ₁ on the edge e is projected onto x ₁ of the x _sub coordinate corresponding to y = 0 in the quadratic function of the edge e. Further, the pixel g ₂ that does not exist on the edge e is x _{2 of the} sub-pixel coordinates corresponding to y = 0 in the quadratic function (dotted line in the figure) passing through the pixel g ₂ obtained by sliding the edge e in the horizontal direction. Projected on.

Specifically, the pixel projecting unit 132 corresponds to y = m (0 ≦ m ≦ M−1; M is the number of vertical pixels of the ROI image) when the nonlinear function is a quadratic function of the formula (1). X coordinate x _e (x _e = p ₃ −p ₁ m−p ₂ m ² ) of the edge e to be performed, and x coordinate x _R (0 ≦ x _R ≦ N−1) of the projection source pixel at y = m; N Is the difference Δx from the number of horizontal pixels of the ROI image) by the following equation (6).

As a result, the difference between the x coordinate of the edge e and the projection source pixel at y = m is obtained.
Then, as shown in the following formula (7), the pixel projection unit 132 sets the x coordinate (x = p ₃ ) of the edge e at y = 0 to the x of the edge at y = m obtained by the formula (6). By adding the difference Δx between the coordinates and the x coordinate of the projection source pixel, the value of the x coordinate of y = 0 corresponding to the projection source pixel is calculated.

Here, in order to explain the processing procedure in an easy-to-understand manner, the x-coordinate values are calculated in the order of Equation (6) and Equation (7). However, the pixel projection unit 132 may calculate the x-coordinate value according to the following equation (8) obtained by merging the equations (6) and (7). Thereby, it is possible to omit the p ₃ from the calculation target.

  Here, the pixel is projected onto the coordinate axis (x axis) of y = 0, but this coordinate axis may be anywhere as long as it is a horizontal axis. That is, the pixel projecting unit 132 may project a pixel on a coordinate axis (horizontal axis) specified by an arbitrary predetermined y value.

Thereby, the pixel projecting unit 132 can slide the edge e on the projection source pixel in the horizontal direction and project the projection source pixel on the horizontal axis along the inclination (distortion) of the edge e.
Returning to FIG. 1, the description of the configuration of the MTF measuring apparatus 1 will be continued.

The projection pixel value averaging means 133 averages the pixel values of each pixel projected onto the coordinate axis (horizontal axis) by the pixel projection means 132 in each section divided into sub-pixel intervals on the coordinate axis, and oversamples. To generate an edge file.
Here, the projection pixel value averaging means 133 is a pixel of a pixel to be projected in each sub-pixel section of a 1/4 or 1/8 pixel section on the horizontal axis that is the projection destination specified by the pixel projection means 132. The values are averaged and an edge file is generated by oversampling at 4 times or 8 times. Note that the number of pixels whose pixel values are averaged does not have to be all pixels, and an upper limit may be determined by a predetermined number for each sub-sampling section.
The projection pixel value averaging unit 133 outputs the generated edge profile to the MTF calculation unit 14.
As described above, the edge profile generation unit 13 projects a pixel along a curve of a quadratic function that approximates an edge, so that an edge profile with high accuracy can be generated.

The MTF calculating unit 14 calculates MTF from the edge profile generated by the edge profile generating unit 13.
As a method for calculating the MTF from the edge profile in the MTF calculating unit 14, a known general method may be used. For example, the MTF calculating unit 14 calculates the MTF by a method similar to a general Slanted-edge method. That is, the MTF calculation means 14 performs a Fourier transform after obtaining a line broadening function (LSF) by differentiating the edge profile by sequentially applying a window function.
As a result, the MTF calculating unit 14 can calculate the MTF for each spatial frequency.

  By configuring the MTF measurement device 1 as described above, the shape of the MTF measurement device 1 can be obtained even when the edge is distorted due to the distortion of the lens in the image captured through the imaging system 2. Can be estimated using a quadratic function as shown in the equation (3). The MTF measuring apparatus 1 generates an edge profile along the shape of the edge estimated by a quadratic function so that the edge distribution can be accurately reflected in the edge profile. can do.

  The MTF measuring apparatus 1 can be realized by a general computer having a CPU and a memory (not shown). At this time, the MTF measuring apparatus 1 operates according to the MTF measuring program for causing the computer to function as each of the above-described means.

[Operation of MTF measuring device]
Next, the operation of the MTF measuring apparatus according to the embodiment of the present invention will be described with reference to FIG.

First, the MTF measuring apparatus 1 inputs the captured image of the chart for MTF measurement with different contrast at the linear boundary for measuring the MTF, which is captured by the imaging system 2 by the image input means 10 (step S1). It memorize | stores in the memory | storage means 11 (step S2).
Then, the MTF measurement apparatus 1 extracts an edge image (ROI image) including a straight line boundary of contrast as an edge from the captured image by the edge image extraction unit 12 (ROI extraction unit 121) (step S3).

  When the extracted ROI image is a horizontal edge image (see FIG. 8B) in which edges exist in the horizontal direction, the MTF measuring apparatus 1 extracts the ROI extracted by the ROI rotation unit 122 of the edge image extraction unit 12. The image is rotated into a vertical edge image (not shown as a step).

Then, the MTF measuring apparatus 1 approximates the edge of the ROI image extracted in step S3 by the edge function approximating unit 131 of the edge profile generating unit 13 with a nonlinear function (for example, the equation (1)) (step S4). .
For example, when an edge is approximated by a quadratic function, the edge function approximating unit 131 uses the normal cumulative distribution function (see the above formula (1)) as a two-dimensional distribution, and the distribution function of the above formula (3) is ROI. A parameter that approximates the pixel value distribution of the image is estimated.
As a result, even when the edge is distorted, it can be approximated by a nonlinear function.

Then, the MTF measuring apparatus 1 uses the pixel projection unit 132 of the edge profile generation unit 13 to convert the pixels of the ROI image along the edge inclination (distortion) specified by the nonlinear function approximated in step S4 to the horizontal coordinate axis. Projecting to (x-axis) (step S5).
At this time, the coordinate axis in the horizontal direction is set to a sub-pixel unit (1/4 pixel or 1/8 pixel) finer than the pixel-based coordinate system of the ROI image.

  Then, the MTF measuring apparatus 1 uses the projected pixel value averaging unit 133 of the edge profile generating unit 13 to divide each pixel of the ROI image that is projected into each segment divided into the sub-pixel intervals of the coordinate axis (horizontal axis). Are averaged and oversampled (4 times or 8 times) (step S6). As a result, an edge profile is generated.

  The MTF measuring apparatus 1 calculates the MTF by performing Fourier transform after obtaining the line broadening function (LSF) for the edge profile generated in step S6 by the MTF calculating unit 14 (step S7).

  With the above operation, the MTF measuring apparatus 1 can accurately reflect the edge distribution in the edge profile even when the edge of the edge image is distorted, and can calculate the MTF with high accuracy.

As mentioned above, although embodiment of this invention was described, this invention is not limited to this structure. For example, here, the vertical edge image (see FIG. 8A) is used as a reference, and the horizontal edge image (see FIG. 8B) is rotated by the ROI rotation means 122.
However, when generating an edge profile for a horizontal edge image, the axis for projecting pixels of the edge image may be the vertical axis. That is, when measuring the MTF of the horizontal edge image, the same processing may be performed in each unit of the edge profile generation unit 13 by changing the x axis and the y axis. Thereby, the ROI rotating means 122 can be omitted from the configuration.

Here, as the edge image (ROI image), an image in which a black region on the left side and a white region on the right side are arranged as shown in FIG. 8A is used. However, the black and white arrangement of the edge image may be reversed. In that case, the shape of the pixel distribution of the edge image is the target shape on the vertical axis of x = 0 with respect to the shape of the normal cumulative distribution function shown in FIG.
Therefore, when using an edge image in which a white region is placed on the left side and a black region is placed on the right side, the edge function approximating unit 131 uses a quadratic function to approximate to the above equation (1) with the sign of x and p ₃ and changing the sign equation (9), in the formula (3), changing the code of the code and p ₃ of x, using the distribution function of equation (10) below, may be estimated parameters.

Further, here, the ROI extraction unit 121 extracts a rectangular region in which each side is parallel to the x axis or the y axis as an ROI image (edge image).
However, when the ROI image (edge image) is extracted from the chart CH including the pattern in which different contrasts are arranged for each radiation region as shown in Japanese Patent No. 5193113 as shown in FIG. A rectangular area having sides along the radial direction (for example, R _{1 in} FIG. 7) may be extracted as a rotated area so that the side is horizontal or vertical.

  Here, the MTF calculated by the MTF calculating means 14 is output to the outside. However, the MTF measurement device 1 may further include a graph generation unit that graphs the MTF for each spatial frequency, and the generated graph may be output to the display device 3 for visualization.

DESCRIPTION OF SYMBOLS 1 MTF measuring apparatus 10 Image input means 11 Image storage means 12 Edge image extraction means 121 ROI extraction means (measurement object image extraction means)
122 ROI rotation means (measurement object image rotation means)
DESCRIPTION OF SYMBOLS 13 Edge profile production | generation means 131 Edge function approximation means 132 Pixel projection means 133 Projection pixel value averaging means 14 MTF calculation means 2 Imaging system 3 Display apparatus

Claims (4)

An MTF measuring apparatus for measuring an MTF representing a spatial frequency characteristic of an imaging system,
An edge that includes the linear boundary as an edge from a captured image captured by the imaging system such that a chart having different contrast at the linear boundary is inclined at a predetermined angle with respect to a direction orthogonal to the measurement direction of the MTF. Edge image extraction means for extracting an image;
From the pixel value distribution of the edge image extracted by the edge image extraction means, an edge function approximation means for approximating the edge with a nonlinear function;
Pixel projection means for projecting the pixels of the edge image onto the coordinate axes whose sub-pixels are smaller than the pixels of the edge image along the shape of the nonlinear function approximated by the edge function approximation means;
In each section of the sub-pixel on the coordinate axis , an edge profile indicating the pixel distribution shape of the edge is obtained by averaging the pixel values of the projection source pixels of the edge image projected on the section by the pixel projection unit. A projection pixel value averaging means for generating;
MTF calculating means for calculating the MTF from the edge profile ,
The edge function approximating unit arranges the edge images on the xy coordinates so that the black region and the white region are in the positive direction of the x-axis, and p ₁ , p ₂ , and p ₃ are used as the nonlinear functions. It is a quadratic function as a parameter
, And the level difference of the pixel value between the black area and the white area is parameter p ₄ , and the pixel value of the black area is parameter p ₅ , μ is the average of the distribution and σ is the standard deviation of the distribution Normal cumulative distribution function f (x) = normcdf (x, μ, σ)
The sum of the squares of the pixel-by-pixel differences between the pixel value distribution function f (x, y) of the edge image used as the edge image and the pixel value v (x, y) of the edge image or the absolute value of the pixel-by-pixel difference MTF measuring system the sum of the parameter _{p 1,} p _2, p ₃ with the _smallest, p 4, obtains the _{p 5,} characterized that you approximate the edges by the quadratic function. An MTF measuring apparatus for measuring an MTF representing a spatial frequency characteristic of an imaging system,
An edge that includes the linear boundary as an edge from a captured image captured by the imaging system such that a chart having different contrast at the linear boundary is inclined at a predetermined angle with respect to a direction orthogonal to the measurement direction of the MTF. Edge image extraction means for extracting an image;
From the pixel value distribution of the edge image extracted by the edge image extraction means, an edge function approximation means for approximating the edge with a nonlinear function;
Pixel projection means for projecting the pixels of the edge image onto the coordinate axes whose sub-pixels are smaller than the pixels of the edge image along the shape of the nonlinear function approximated by the edge function approximation means;
In each section of the sub-pixel on the coordinate axis , an edge profile indicating the pixel distribution shape of the edge is obtained by averaging the pixel values of the projection source pixels of the edge image projected on the section by the pixel projection unit. A projection pixel value averaging means for generating;
MTF calculating means for calculating the MTF from the edge profile ,
The edge function approximating unit arranges the edge images on the xy coordinates so that the white region and the black region are in the positive direction of the x axis, and p ₁ , p ₂ , and p ₃ are used as the nonlinear functions. It is a quadratic function as a parameter
, And the level difference of the pixel value between the black area and the white area is parameter p ₄ , and the pixel value of the black area is parameter p ₅ , μ is the average of the distribution and σ is the standard deviation of the distribution Normal cumulative distribution function f (x) = normcdf (x, μ, σ)
The sum of the squares of the pixel-by-pixel differences between the pixel value distribution function f (x, y) of the edge image used as the edge image and the pixel value v (x, y) of the edge image or the absolute value of the pixel-by-pixel difference MTF measuring system the sum of the parameter _{p 1,} p _2, p ₃ with the _smallest, p 4, obtains the _{p 5,} characterized that you approximate the edges by the quadratic function. The pixel projection unit arranges the edge image on the xy coordinate so that the contrast differs in the x-axis direction, and for each pixel of the edge image, the value of the x coordinate of the pixel position and the y coordinate of the pixel position The pixel position (x, y) of the edge image is shifted so that the value of the x coordinate in the predetermined y value of the nonlinear function is shifted by the difference from the value of the x coordinate of the nonlinear function corresponding to MTF measuring system according to claim 1 or claim 2, characterized in that projecting on the position of the coordinate axis specified by the value of a predetermined y. An MTF measurement program for causing a computer to function as the MTF measurement device according to any one of claims 1 to 3 .