JP2014203162A - Inclination angle estimation device, mtf measuring apparatus, inclination angle estimation program and mtf measurement program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an inclination angle estimation device which estimates an inclination angle of a knife edge with high accuracy.SOLUTION: An inclination angle estimation device 1 comprises: Fourier transform means 121 for performing two-dimensional discrete Fourier transform of a knife edge image; spatial frequency component detection means 122 which, for every one space frequency component fx, detects the other spatial frequency component fy for giving the maximum amplitude by using data on a spatial frequency area; and angle estimation means 13 for calculating an angle θ to fit to a formula (1) which is an equation of a straight line for a detected set of (fx,Fy(fx)), and estimates that an extension direction of the knife edge image is an angle to be formed with a direction of the other spatial frequency. Here, the formula (1) shows 0=fx×cosθ+Fy(fx)×sinθ, and Fy(fx) shows the other spatial frequency component fy to give the maximum amplitude in one spatial frequency component fx.

Description

  The present invention relates to a tilt angle estimation device that estimates the tilt angle of a figure, an MTF measurement device that measures MTF of an imaging means using the tilt angle estimated by the tilt angle estimation device, and a program that implements these devices. .

An MTF (Modulation Transfer Function) representing an amplitude transfer characteristic with respect to a spatial frequency has been used as a representative index for evaluating the quality of an imaging system such as a scanner, a digital camera, and an imaging lens. As an MTF measurement method, there is a Slanted-edge method (hereinafter referred to as an “edge method” as appropriate), which is a method using a knife edge image obtained by imaging an MTF measurement chart including a figure having a side inclined from horizontal or vertical. (For example, refer nonpatent literature 1 and patent literature 1).
In this edge method, the inclination angle of the knife edge image is used in the MTF calculation process.

  Further, Hough transform is known as a method for automatically detecting a figure such as a straight line for a general image (for example, see Non-Patent Document 2). Specifically, a contour extraction process of a figure is performed on a captured image, and a straight line is detected by applying a Hough transform to pixels constituting the extracted contour. Here, the inclination angle (gradient) of the straight line can be obtained as a detection result of the straight line by the Hough transform.

Japanese Patent No. 4092853

ISO 12233: 2000, ”Photography-Electronic still-picture cameras-Resolution measurements.” Duda, R.O. and Hart, P.E, “Use of the Hough Transformation to Detect Lines and Curves in Pictures”, Comm. ACM, Vol. 15, pp. 11-15, Jan, 1972

  Conventionally, in the estimation of the inclination angle by the method using the Hough transform or the method of fitting by the linear regression method or the like, the contour extraction processing of the figure is performed as the initial stage of the processing as described above. Since this processing is strongly influenced by noise factors in the image, the conventional method sometimes cannot estimate the inclination angle of the knife edge image with high accuracy.

In the MTF measurement by the edge method, the estimation accuracy of the inclination angle of the edge image greatly affects the measurement accuracy. Here, an example will be described with reference to FIGS.
FIG. 10 is a diagram showing the result of simulating the influence of the deviation of the estimated value of the knife edge inclination angle on the MTF measurement value in the MTF measurement by the conventional edge method, and (a) shows the true inclination angle. In the case of 1 degree, (b) shows the case where the true inclination angle is 5 degrees. In FIG. 10, the horizontal axis represents the spatial frequency, the vertical axis represents the MTF value, and the spatial frequency = 0.5 is the Nyquist frequency.

  10 (a) and 10 (b), the MTF characteristic indicated by the thick solid line shows the true MTF characteristic when the deviation (ie, error) of the tilt angle is “0”. On the other hand, the MTF characteristics when the error deviates by ± 0.1 degrees (dashed line and alternate long and short dash line) and ± 0.5 degrees (thin broken line and alternate long and two short dashes line) are significantly different from the true MTF characteristic. It can be seen that even an error of only ± 0.1 degrees greatly affects the MTF measurement value.

FIG. 11 is a diagram showing the result of simulating the influence of the knife edge inclination angle estimation error on the MTF measurement value at the Nyquist frequency in the conventional MTF measurement by the edge method. In FIG. 11, the horizontal axis indicates a deviation that is an estimation error, and the vertical axis indicates an MTF value. Further, a solid line indicates a case where the true inclination angle is 5 degrees, and a broken line indicates a case where the true inclination angle is 1 degree.
As shown in FIG. 11, when the deviation is “0”, the MTF value is about “0.9”, and it can be seen that the MTF value rapidly decreases as the absolute value of the deviation increases. Note that the MTF value when the deviation is “0” is smaller than “1” because the aperture opening has a finite value.
Thus, in order to accurately measure the MTF by the edge method, it is necessary to estimate the inclination angle of the knife edge with high accuracy.

The present invention has been made in view of such a problem, and an object of the present invention is to provide an inclination angle estimation apparatus and program for estimating the inclination angle of a knife edge with high accuracy.
Another object of the present invention is to provide an MTF measuring apparatus that performs MTF measurement by the Slanted-edge method using the inclination angle of the knife edge estimated by the above-described inclination angle estimating apparatus, and a program therefor. .

  In order to solve the above-described problem, an inclination angle estimation apparatus according to the present invention is an inclination angle estimation apparatus that estimates an inclination angle of the knife edge with respect to a knife edge image, and includes a Fourier transform unit and spatial frequency component detection. Means and angle estimation means.

According to such a configuration, the tilt angle estimation device converts the knife edge image into data in the spatial frequency domain by performing a two-dimensional discrete Fourier transform on the Fourier transform means. In addition, the inclination angle estimation device detects the other spatial frequency component fy giving the maximum amplitude for each spatial frequency component fx in the spatial frequency domain data by the spatial frequency component detection means. Then, the inclination angle estimation device calculates an angle θ that fits the equation (1), which is a linear equation, for the set of (fx, fy) detected by the spatial frequency component detection unit by the angle estimation unit. , It is estimated that the extending direction of the knife edge is an angle formed with the direction of the other spatial frequency. That is, the inclination angle of the knife edge is estimated as an angle formed with the y-axis direction that is the direction of the other spatial frequency.
0 = fx · cos θ + Fy (fx) · sin θ (1)
However, in Formula (1), Fy (fx) indicates the other spatial frequency component fy that gives the maximum amplitude in the one spatial frequency component fx, and θ is 0 degree or more and less than 180 degrees in Formula (1). The straight line represented is an angle formed with the one spatial frequency axis.

In addition, the tilt angle estimation apparatus according to the present invention may further include image preparation means.
According to such a configuration, the tilt angle estimation device generates a point-symmetric image of the knife edge image by the image preparation unit, and generates one side of the knife edge image and the point-symmetric image corresponding to the one side. A combined knife edge image is generated by combining the knife edge image and the point-symmetric image so that the sides are in contact with each other. Then, the tilt angle estimation device converts the synthesized knife edge image into the data of the spatial frequency domain by performing the two-dimensional discrete Fourier transform on the synthetic knife edge image instead of the knife edge image by the Fourier transform unit.
As a result, when two-dimensional discrete Fourier transform is performed, artifacts due to mixing of edge components at both ends of the knife edge image can be avoided.

In the tilt angle estimation apparatus according to the present invention, the angle estimation means may estimate that θ that minimizes the value J of the evaluation formula shown in Formula (2) is the tilt angle of the knife edge. preferable.
J = Σ | fx · cos θ + Fy (fy) · sin θ | ^p (2)
However, in Formula (2), (SIGMA) shows that the sum of the right type is calculated about several spatial frequency component fx, and p shows a positive real number.
According to such a configuration, the tilt angle estimation apparatus can accurately estimate the tilt angle by the angle estimation means.

In the tilt angle estimation apparatus according to the present invention, p is preferably less than 2 in the formula (2).
According to such a configuration, the tilt angle estimation device can estimate the tilt angle robustly against a change in noise level by the angle estimation means.

  The MTF measurement apparatus according to the present invention includes an image extraction unit, a tilt angle estimation unit, an edge spread function calculation unit, and an MTF calculation unit, and the tilt angle estimation unit according to the present invention is used as the tilt angle estimation unit. The device was configured.

According to this configuration, the MTF measurement device extracts the knife edge image from the image of the knife edge chart imaged by the imaging unit by the image extraction unit. Further, the MTF measuring apparatus estimates the inclination angle of the knife edge for the knife edge image by the inclination angle estimation means. In addition, the MTF measuring apparatus projects each pixel in the direction of the estimated inclination angle by the edge extension function calculation means, and calculates an edge spread function that is a distribution of image values relating to a dimension orthogonal to the inclination of the knife edge. To do. Then, the MTF measuring device calculates the MTF by differentiating the edge spread function by MTF calculating means and further performing discrete Fourier transform.
As a result, the MTF measuring apparatus can calculate the MTF with high accuracy using the inclination angle of the knife edge estimated with high accuracy by the inclination angle estimation means.

  In addition, the tilt angle estimation device and the MTF measurement device according to the present invention cause a computer including hardware resources such as a CPU (Central Processing Unit) and storage means (for example, a memory and a hard disk) to operate cooperatively as the above-described means. Therefore, it can be realized by an inclination angle estimation program and an MTF measurement program, respectively. This program may be distributed through a communication line, or may be distributed by writing in a recording medium such as an optical disk, a magnetic disk, or a flash memory.

According to the present invention, since the tilt angle is estimated by performing fitting in the spatial frequency domain on the knife edge image, the tilt angle can be estimated robustly and with high accuracy even for an image on which noise is superimposed.
Further, according to the present invention, since the MTF measurement by the Slanted-edge method is performed using the inclination angle of the knife edge that is robust and estimated with high accuracy, the MTF can be calculated with high accuracy.

It is a block diagram which shows the structure of the inclination-angle estimation apparatus which concerns on 1st Embodiment of this invention. The example of the image used in the inclination-angle estimation apparatus which concerns on 1st Embodiment of this invention is shown, (a) shows a mode that a knife edge image is extracted from a captured image and the image for inclination-angle estimation is adjusted, (b) Shows the prepared knife edge image, (c) shows the power spectrum of the knife edge image of (b), and (d) shows the detection points. It is a flowchart which shows operation | movement of the inclination-angle estimation apparatus which concerns on 1st Embodiment of this invention. It is a figure which shows the result of having estimated the inclination angle by the invention method and the conventional method about the knife edge image of various inclination angles on which noise was superimposed. It is a figure which shows the result of having estimated the inclination angle by the invention method and the conventional method about the knife edge image superimposed by changing a noise level, (a) is an inclination angle of 1 degree, (b) is an inclination angle of 5 Is the case of degrees. It is a figure which shows the relationship between the p value of the evaluation formula for evaluating the estimated value of an inclination angle, and an estimation error in the inclination angle estimation apparatus which concerns on 1st Embodiment of this invention. It is a block diagram which shows the structure of the MTF measuring apparatus which concerns on 2nd Embodiment of this invention. It is a figure for demonstrating the calculation process of the edge spread function in the MTF measuring apparatus which concerns on 2nd Embodiment of this invention. It is a flowchart which shows operation | movement of the MTF measuring apparatus which concerns on 2nd Embodiment of this invention. It is a figure which shows the result of having simulated the influence which the estimation error of a knife edge inclination angle has on the MTF measurement value in the MTF measurement method by the conventional Slanted-edge method, (a) (B) shows the case where the true inclination angle is 5 degrees. It is a figure which shows the result of having simulated the influence which the estimation error of a knife edge inclination angle has on the MTF measurement value in a Nyquist frequency in the MTF measurement method by the conventional Slanted-edge method.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings as appropriate.
<First Embodiment>
[Configuration of tilt angle estimation device]
First, the configuration of the tilt angle estimation apparatus according to the first embodiment will be described with reference to FIGS. 1 and 2.
The tilt angle estimation device 1 according to the first embodiment converts a knife edge image input from an external imaging means or the like into spatial frequency domain data by two-dimensional discrete Fourier transform processing, and performs robust fitting in the spatial frequency domain. Thus, the inclination angle of the knife edge is estimated. The fitting in the spatial frequency domain will be sequentially described together with the configuration of each part.
As shown in FIG. 1, the tilt angle estimation apparatus 1 according to this embodiment includes an image preparation unit 11, a frequency spectrum calculation unit 12, and an angle estimation unit 13.

  The image preparation means 11 inputs the knife edge image G2 and prepares an image G4 for estimating the tilt angle. For this purpose, the image preparation unit 11 includes an image conversion unit 111, an image composition unit 112, and an image storage unit 113.

As shown in FIG. 2A, the image conversion unit 111 inputs a knife edge image G2 extracted from an image G1 captured by an imaging unit such as an external camera, and the input knife edge image G2 is converted into a knife. Using the midpoint of one side along the extending direction of the edge (the point indicated by x on the right side of the knife edge image G2 in FIGS. 2 (a) and 2 (b)) as the center point of point symmetry movement, An image (point-symmetric image) G3 subjected to symmetrical movement conversion is generated. The image conversion unit 111 outputs the generated image G3 to the image composition unit 112.
In the present embodiment, the image G3 is generated with the center point of point-symmetrical movement as the midpoint of the right side of the knife edge image G2. However, the present invention is not limited to this, and any point can be point-symmetrically moved. The image G3 can be generated as the center point of the.

The image synthesizing unit 112 inputs the knife edge image G2 from the outside and the image G3 from the image converting unit 111, and synthesizes the image G2 and the image G3 so that the right side of the image G2 and the left side of the image G3 are in contact with each other. As a result, an image (synthetic knife edge image) G4 that is point-symmetric with respect to the image center indicated by x in FIGS. 2A and 2B is generated. The image composition unit 112 stores the generated image G4 in the image storage unit 113.
In this embodiment, the knife edge image G2 and the image G3 that is a point-symmetric image thereof are combined so that the right side of the knife edge image G2 and the corresponding side of the image G3 are in contact with each other, but the present invention is not limited to this. Instead, the other edge of the knife edge image G2 and the edge of the image G3 corresponding to the other edge may be combined.

Here, when the knife edge image is subjected to two-dimensional discrete Fourier transform by combining the knife edge image G2 having only the knife edge extending in one direction and the image G3 subjected to the point-symmetrical movement conversion, at both ends of the image. Artifacts due to mixing of edge components in the vertical direction or horizontal direction can be avoided, and the estimation accuracy of the tilt angle can be improved.
When the captured image G1 shown in FIG. 2A is an image obtained by capturing a barcode chart with continuous parallel knife edges, an image region as shown in FIG. 2B is extracted and used. be able to. For this reason, when an image as shown in FIG. 2B is input as the knife edge image G2, a composition process with an image moved point-symmetrically is unnecessary.

  The image storage means 113 stores the image G4 input from the image composition means 112. The image G4 stored in the image storage unit 113 is referred to by the frequency spectrum calculation unit 12.

The frequency spectrum calculation means 12 receives an image G4 in which knife edges are synthesized symmetrically from the image storage means 113 of the image preparation means 11 and converts them into spatial frequency domain data to contribute to the construction of the knife edge image. The frequency component is detected, and the detected spatial frequency component is output to the angle estimation means 13.
For this purpose, the frequency spectrum calculation unit 12 includes a Fourier transform unit 121 and a spatial frequency component detection unit 122.

The Fourier transform unit 121 receives the image G4 from the image storage unit 113, and converts the input image G4 into spatial frequency domain data by two-dimensional discrete Fourier transform processing. In FIG. 2C, G5 indicates the power spectrum of this two-dimensional discrete Fourier transform, indicating the magnitude of the power in the contrast of the image (brighter is greater in power). In FIG. 2C, the intersection (origin) of the two orthogonal spatial frequency axes fx and fy indicates a direct current component.
The Fourier transform unit 121 outputs data obtained by Fourier transforming the image G4 to the spatial frequency component detection unit 122.

The spatial frequency component detection unit 122 receives a knife edge image obtained by converting the image G4 from the Fourier transform unit 121 into data in the spatial frequency domain by Fourier transform, and the other has the maximum amplitude for each spatial frequency component fx. The spatial frequency component fy is detected.
Here, in the spatial frequency component fx, Fy (fx) is defined as a function indicating fy giving the maximum amplitude. When the number of components of the spatial frequency component fx is N, N points (fx, Fy (fx)) are detected. The spatial frequency component detection unit 122 outputs the detected N points (fx, Fy (fx)) to the angle estimation unit 13.
In FIG. 2D, these detection points are indicated by “●”.

As shown in FIG. 2B, in the image G4, the angle (knife edge inclination angle) formed by the y-axis that is the coordinate axis in the real space region and the extending direction of the knife edge is defined as θ.
In this way, when an image including only one knife edge extending from the end of one side of the image to the end of the opposite side is converted into spatial frequency domain data, as shown in FIG. The spatial frequency component in the direction perpendicular to the extending direction of the knife edge has a large amplitude. Accordingly, the N detection points (fx, Fy (fx)) described above are plotted on a straight line whose angle formed with the fx axis, which is the coordinate axis in the spatial frequency domain, as shown in FIG. 2D. .
In FIG. 2D, detection points plotted at positions deviating from the straight line are spatial frequency components that are affected by noise or the like.

Here, the straight line on which (fx, Fy (fx)) is plotted is expressed by Expression (1).
ρ = fx · cos θ + Fy (fx) · sin θ (1)
However, in equation (1), ρ represents the distance from the origin in the spatial frequency domain to the straight line represented by equation (1), and θ is a straight line represented by equation (1) that is 0 degree or more and less than 180 degrees. An angle formed with the one spatial frequency axis. Further, in the case of a knife edge image in which the edge extends linearly, ρ = 0, and Equation (1) is a straight line passing through the origin.

In the present embodiment, the spatial frequency component fy in the y-axis direction that gives the maximum amplitude is detected for each spatial frequency component fx in the x-axis direction. However, by replacing fx and fy, For each spatial frequency component fy, fx giving the maximum amplitude may be detected.
When a knife edge image G2 having an inclination angle close to the horizontal direction is used, the image G2 is converted into an image rotated 90 degrees clockwise or counterclockwise, and further combined with an image G3 subjected to point-symmetric movement conversion. You may make it use. Accordingly, the subsequent processing can be performed in the same procedure as when the knife edge image G2 having an inclination angle close to the vertical direction is used.

The angle estimation means 13 inputs N detection points (fx, Fy (fx)) from the spatial frequency component detection means 122 of the frequency spectrum calculation means 12 and calculates a straight line that best fits the set of these input detection points. By calculating, it is estimated that the calculated gradient of the straight line is a knife edge inclination angle, that is, an angle formed by the extending direction of the knife edge with the y-axis direction.
The method for calculating the straight line to be fitted is not particularly limited, but will be described below with a specific example. In this example, as shown in FIG. 1, the angle estimation means 13 includes an evaluation value calculation means 131, an inclination angle estimated value update means 132, and an inclination angle estimated value storage means 133.

The evaluation value calculation means 131 receives N detection points (fx, Fy (fx)) from the frequency spectrum calculation means 12, and uses the value of the evaluation expression shown in the expression (2) for these input detection points. A certain evaluation value J is calculated. Note that the evaluation value calculation unit 131 uses the estimated value of the tilt angle stored in the tilt angle estimated value storage unit 133 as the value of θ in Equation (2).
J = Σ | fx · cos θ + Fy (fx) · sin θ | ^p (2)
However, in Formula (2), (SIGMA) shows calculating the sum about several spatial frequency component fx, and p shows a positive real number.

That is, the evaluation value calculation unit 131 calculates an evaluation value for evaluating the degree to which a set of detection points (fx, Fy (fx)) fits to the equation (1) by the equation (2).
The evaluation value calculation unit 131 outputs the calculated evaluation value J to the tilt angle estimated value update unit 132.

  Note that when calculating the evaluation value J using Equation (2), the detection points (fx, Fy (fx)) for all the spatial frequency components fx may be used, but below a predetermined spatial frequency. The detection points for the spatial frequency component fx may be used. By excluding high-frequency components that are easily affected by noise from the calculation of the evaluation value J, the tilt angle can be estimated more stably with stable accuracy.

In Expression (2), the p value is not limited as long as it is a positive real number. For example, when p = 2, Expression (2) performs fitting based on the least square distance. . In addition, by setting p <2, for example, p = 1 and p = 1/2, it is possible to perform robust fitting while suppressing the contribution of outliers in the detection points (fx, Fy (fx)). . Further, the property of noise superimposed on the knife edge image G2 may be examined in advance, and an optimal p value may be selected as appropriate according to the property of noise.
Details of the relationship between the p value and the inclination angle estimation accuracy will be described later.

The inclination angle estimated value updating unit 132 inputs the evaluation value J from the evaluation value calculating unit 131 and determines whether the evaluation value J is a minimum value with respect to θ. When the evaluation value J is not the minimum value with respect to θ, the tilt angle estimated value θ is sequentially updated so as to minimize the evaluation value J, and the updated tilt angle estimated value θ is stored as the tilt angle estimated value. Store in the means 133.
Note that, for example, a simplex method can be used to calculate the update value of the estimated tilt angle value. Further, the update may be performed by adding or subtracting a difference amount (for example, 0.001 degree) smaller than the required accuracy. Further, whether or not the evaluation value is the minimum value can be determined to be the minimum value when the amount of change from the previous evaluation value J is smaller than a predetermined threshold value.
When the tilt angle estimated value updating unit 132 determines that the evaluation value J is the minimum value, the tilt angle estimating device 1 is stored in the tilt angle estimated value storage unit 133 at that time. The estimated angle value is output as an estimated value of the inclination angle of the knife edge image.

  In this example, in the formula (2) for calculating the evaluation value J, the formula (1) that is the formula in the absolute value symbol on the right side is ideally “0”. Therefore, the evaluation value J that is the sum of the p-th power is ideally “0”. Therefore, as a method for determining whether or not the evaluation value J is minimum with respect to θ, it can be determined whether or not the evaluation value J is sufficiently small. Whether or not it is sufficiently small can be determined to be sufficiently small (that is, sufficiently small) when the amount of change from the previous evaluation value J is smaller than a predetermined threshold as described above, It is also possible to determine whether the evaluation value J is smaller than a certain value instead of the amount of change.

The tilt angle estimated value storage unit 133 receives the tilt angle estimated value from the tilt angle estimated value update unit 132 and stores the tilt angle estimated value in place of the stored tilt angle estimated value.
The estimated tilt angle value stored in the tilt angle estimated value storage unit 133 is referred to by the evaluation value calculating unit 131. As an initial value before the tilt angle estimated value is first updated by the tilt angle estimated value updating unit 132, an approximate value of the tilt angle of the knife edge image is input via an input unit (not shown) such as a keyboard. You may make it set.

Note that the estimated value of the tilt angle of the knife edge image output by the tilt angle estimation device 1 is, for example, the knife edge when performing MTF measurement using the edge method in the MTF measurement device 100 (see FIG. 6) described later. It is used as the inclination angle. Further, the estimated value of the tilt angle is not limited to the use in MTF measurement. For example, in the image recognition process, by estimating the tilt angle for each edge of an image including various figures, The shape of the figure can be recognized with high accuracy.
Also, for an image obtained by imaging an index such as a figure with a known inclination angle, such as vertical or horizontal, the method of the present invention is applied to estimate the inclination angle of the index with respect to the image coordinates, and the deviation from the known inclination angle By calculating, the inclination of the imaging system can be detected. Then, the tilt of the imaging system can be corrected using the detected tilt of the imaging system.

[Operation of tilt angle estimation device]
Next, with reference to FIG. 3 (refer to FIGS. 1 and 2 as appropriate), the operation of the tilt angle estimation apparatus 1 according to the present embodiment will be described.
As shown in FIG. 3, the tilt angle estimation device 1 first prepares an image G4 for tilt angle estimation from the knife edge image G2 input from the outside by the image preparation means 11 (step S11). In this step S11, more specifically, the tilt angle estimation device 1 first generates an image G3 obtained by performing point-symmetric movement conversion on the knife edge image G2 by the image conversion unit 111. Next, the tilt angle estimation device 1 combines the image G2 and the image G3 by the image combining unit 112, generates an image G4 in which the center of the image is a point-symmetric center, and stores the image G4 in the image storage unit 113.

Next, the tilt angle estimation device 1 performs two-dimensional discrete Fourier transform on the image G4 by the Fourier transform unit 121 of the frequency spectrum calculation unit 12 to convert it into spatial frequency domain data (step S12).
Then, the inclination angle estimation device 1 calculates Fy (fx) for each spatial frequency component fx of the knife edge image converted into the spatial frequency domain data by the spatial frequency component detection unit 122 of the frequency spectrum calculation unit 12. That is, the other spatial frequency component fy giving the maximum amplitude is detected (step S13).

  Next, the inclination angle estimation device 1 calculates the evaluation value J using the expression (2) by the evaluation value calculation unit 131 of the angle estimation unit 13 (step S14). At this time, the estimated value stored in the estimated tilt angle storage unit 133 is used as the estimated tilt angle θ in the equation (2).

Next, the tilt angle estimation device 1 determines whether or not the evaluation value J calculated in step S14 is sufficiently small by the tilt angle estimated value update unit 132 of the angle estimation unit 13 (step S15).
If it is sufficiently small (Yes in step S15), the tilt angle estimation device 1 ends the process. At this time, the estimated value stored in the tilt angle estimated value storage unit 133 is the final estimated value of the tilt angle of the knife edge image.

On the other hand, if the angle is not sufficiently small (No in step S15), the inclination angle estimation device 1 changes the estimated value of the inclination angle so that the evaluation value J is minimized by the inclination angle estimation value update unit 132. (Step S16), the updated estimated value is stored in the tilt angle estimated value storage means 133 (step S17), and the process returns to step S14.
By the above procedure, the inclination angle estimation device 1 estimates the inclination angle of the knife edge.

[simulation]
Next, an inclination angle estimation method according to the present invention (hereinafter referred to as “invention method” as appropriate) and a conventional method for calculating a linear gradient using a linear regression method on pixels extracted from a knife edge image in real space. A simulation result in which the inclination angle of the knife edge is estimated for the knife edge image on which noise is superimposed will be described.

(First experiment)
First, as a first experiment, a noise-free knife edge image having a true inclination angle of 1 to 20 degrees is generated by computer graphics, and further, an inclination angle is used using an image on which -10 dB of Gaussian white noise is superimposed. An estimation simulation was performed. In the invention method, the p value in the formula (2) was set to “0.5”.

FIG. 4 shows the simulation result of the first experiment. In FIG. 4, the horizontal axis indicates the true inclination angle, and the vertical axis indicates the estimated inclination angle value. In addition, the result of the invention method is indicated by “◯”, the result of the conventional method is indicated by “×”, and the reliability of estimation is indicated by an error bar.
As shown in FIG. 4, even when noise is superimposed on the image, it can be seen that the inventive method can estimate the tilt angle with higher accuracy than the conventional method. Further, it can be seen that the estimated value according to the conventional method can be estimated with high accuracy and high reliability by the invention method even for an inclination angle of 5 degrees or more, which has a large deviation from the true inclination angle.

(Second experiment)
Next, as a second experiment, a noiseless knife edge image having true inclination angles of 1 degree and 5 degrees is generated by computer graphics, and “−13.0103 dB”, “−10 dB”, and “−6. An inclination angle estimation simulation was performed using an image on which Gaussian white noise of “0206 dB” was superimposed, and the influence of the noise level on the error of the inclination angle estimation value was evaluated. In the invention method, the p value in the formula (2) was set to “0.5”.

FIG. 5 shows the simulation result of the second experiment. In FIG. 5, the upper stage shows a case where the inclination angle is 1 degree, and the lower stage shows a case where the inclination angle is 5 degrees. The noise levels are “−13.0103 dB”, “−10 dB” and “−6.0206 dB” in order from the left side. Show the case. The vertical axis indicates the absolute value of the error in the estimated tilt angle.
As shown in FIG. 5, it can be seen that the inventive method can robustly estimate the tilt angle against changes in the noise level as compared with the conventional method.

(Third experiment)
Next, as a third experiment, a noiseless knife edge image having a true inclination angle of 5 degrees is generated by computer graphics, and “−13.0 dB”, “−10.0 dB”, and “−6.99 dB” are generated. Using the image on which Gaussian white noise was superimposed, an inclination angle estimation simulation was performed by changing the p value in the invention method from 0.1 to 5, and the influence of the p value on the error of the estimated inclination angle was evaluated.

FIG. 6 shows the simulation result of the third experiment. In FIG. 6, the horizontal axis indicates the p value, and the vertical axis indicates the estimation error. The case where the noise level is “−13.0 dB” is indicated by “◯”, the case where “−10.0 dB” is indicated by “□”, and the case where “−6.99 dB” is indicated by “Δ”. Further, in this order, the results of the conventional method for the corresponding noise level images are indicated by “●”, “■” and “▲” at the right end of FIG.
As shown in FIG. 6, when the p value is 2 or less, it can be seen that the tilt angle can be estimated more accurately than in the conventional method. In particular, it can be seen that by setting the p-value to less than 2, more preferably 1 or less, the inclination angle can be estimated robustly and with high accuracy against changes in the noise level.

Second Embodiment
Next, as a second embodiment of the present invention, an MTF measurement device using the tilt angle estimation device 1 according to the first embodiment will be described.
First, the configuration of the MTF measuring apparatus according to the second embodiment will be described with reference to FIG. 7 (refer to FIGS. 1 and 2 as appropriate).

  As shown in FIG. 7, the MTF measurement apparatus 100 according to the second embodiment includes an image storage unit 101, an ROI acquisition unit 102, an image extraction unit 103, an inclination angle estimation unit 104, an ESF calculation unit 105, And an MTF calculating means 106.

  Further, the MTF measuring apparatus 100 inputs an image including a knife edge image from an imaging unit 110 such as a camera or a scanner that captures an MTF measurement chart, and via an input interface 120 with an input device such as a keyboard and a mouse. Thus, information indicating a region for extracting the knife edge image from the input image is input. The MTF measuring apparatus 100 outputs the calculated MTF data to an external display device, storage device, or the like via the output interface 130.

  Note that the MTF measurement apparatus 100 according to the present embodiment uses the inclination angle estimation apparatus 1 according to the first embodiment as the inclination angle estimation means 104 to estimate the inclination angle of the knife edge image in the Slanted-edge method with high accuracy. The MTF is measured by the Slanted-edge method using the estimated value of the tilt angle.

The image storage unit 101 stores an MTF measurement chart image G1 (see FIG. 2A) captured by the imaging unit 110 such as a camera or a scanner. The image G1 stored in the image storage unit 101 is referred to by the ROI acquisition unit 102 and the image extraction unit 103.
As the MTF measurement chart, for example, “Resolution test chart” described in Non-Patent Document 1 can be used, but the MTF measurement chart is not limited to this. For example, as shown in FIG. 2A, a chart having a black solid rectangular figure G1k arranged to be inclined on a white background G1w can be used.

  When measuring the MTF in the horizontal direction (x-axis direction), it is preferable to arrange the chart so that the extending direction of the knife edge is slightly inclined (for example, about 1 to 5 degrees) than the vertical direction. . When measuring the MTF in the vertical direction (y-axis direction), it is preferable to arrange the chart so that the extending direction of the knife edge is slightly inclined from the horizontal. Furthermore, when measuring the MTF in another direction, it is preferable to arrange the chart so that the extending direction of the knife edge is slightly inclined than the direction perpendicular to the other direction.

ROI (Region of interest) acquisition means 102 is means for acquiring information indicating a region of a knife edge image used for MTF measurement from an image G1 input from the outside. Here, the ROI acquisition unit 102 receives information indicating the region of the knife edge image designated by the operator (for example, the coordinate values of the pixels in the upper right corner and the lower left corner of the rectangular region in the image G1) via the input interface 120. get.
The ROI acquisition unit 102 outputs information indicating the acquired knife edge image area to the image extraction unit 103.

  For example, the image area can be specified by using an image display device (not shown) for displaying the image G1 and an input device (not shown) such as a mouse. Specifically, a rectangular frame that can be moved using a mouse while displaying an image G1 captured as shown in FIG. 2A on the image display device (a rectangular frame indicated by a broken line in FIG. 2A). And click the mouse button when a rectangular frame is displayed at the desired position. The ROI acquisition unit 102 can acquire the area information of the image G1 corresponding to the area where the rectangular frame is displayed at this time via the input interface 120.

  The image extraction unit 103 inputs the image G1 captured by the imaging unit 110 from the image storage unit 101 and information indicating the knife edge image region from the ROI acquisition unit 102, and indicates the knife edge image region from the image 4. An image of the area designated by the information is extracted as a knife edge image G2. The image extraction unit 103 outputs the extracted knife edge image G2 to the tilt angle estimation unit 104 and the ESF calculation unit 105.

As shown in FIGS. 2A and 2B, the region to be extracted as the knife edge image G2 is such that the straight line indicating the extending direction of the knife edge intersects two opposite sides of the rectangular region. select. In the example shown in FIGS. 2A and 2B, the straight line indicating the extending direction of the knife edge intersects the upper and lower sides of the rectangular area indicating the image G2. That is, the image G2 includes only a knife edge in one direction. By using the image G2 including only one knife edge in one direction, the inclination angle of the knife edge can be accurately estimated.
The examples shown in FIGS. 2A and 2B are images for measuring the MTF in the horizontal direction (x-axis direction).

The inclination angle estimation means 104 uses the inclination angle estimation apparatus 1 according to the first embodiment shown in FIG. Then, the inclination angle estimation means 104 receives the knife edge image G2 from the image extraction means 103, estimates the inclination angle of the knife edge image G2, and outputs the estimated value of the inclination angle to the ESF calculation means 105.
The configuration of the tilt angle estimating means 104 is the same as that of the tilt angle estimating device 1 shown in FIG.

An ESF (Edge Spread Function) calculating means (edge spreading function calculating means) 105 calculates the knife edge image G2 from the image extracting means 103 and the knife edge inclination angle in the knife edge image G2 from the inclination angle estimating means 104. Enter each estimate. The ESF calculation means 105 calculates an ESF that is a profile in the direction perpendicular to the direction inclined by the angle θ from the knife edge stretching direction in the knife edge image G2, that is, the profile in the x-axis direction, as a sub-pixel pitch smaller than the original pixel pitch. Is calculated by
The ESF calculation unit 105 outputs the calculated ESF to the MTF calculation unit 106.

Here, a method for calculating the ESF at the sub-pixel pitch will be described with reference to FIG.
In the lower part of FIG. 8, the hatched area on the right side of the edge position corresponds to the area where the solid figure of the test chart is imaged, and the left area where no hatching is applied is the area where the white background is imaged. Applicable. The knife edge extending direction is inclined by an angle θ with respect to the y-axis indicating the vertical direction.

Here, since the knife edge is a straight line, the projected image of each pixel arranged in the y-axis direction on the axis perpendicular to the knife edge extending direction is composed of sub-pixels having a pitch (sin θ) times the original pixel pitch. It becomes a one-dimensional image.
The upper diagram in FIG. 8 shows an ESF that is a one-dimensional image composed of sub-pixel pitches with the vertical axis as the pixel value.

Since the x-axis is inclined by an angle θ from the axis perpendicular to the knife edge extending direction, a projection image of this one-dimensional image on the x-axis is considered. Then, the ESF shown in the upper part of FIG. 8 can be regarded as an ESF in the x-axis direction sampled by sub-pixels having a pitch (tan θ) times the original pixel pitch.
As described above, an ESF having a resolution exceeding the sampling frequency defined by the original pixel pitch can be calculated by super-resolution processing using an inclined knife edge image.
This makes it possible to measure MTF robustly and with high accuracy.

Returning to FIG. 7, the description of the configuration of the MTF measuring apparatus 100 will be continued.
The MTF calculation means 106 receives the ESF from the ESF calculation means 105 and calculates the MTF for the direction (in this example, the x-axis direction) corresponding to the arrangement direction of the knife edge graphic.
Calculation of MTF using ESF can be performed by a known method using differentiation and Fourier transform.

  Specifically, first, an LSF (Line Spread Function) is calculated by differentiating an ESF that is a one-dimensional image. Next, the MTF for each spatial frequency component in the x-axis direction can be calculated by performing one-dimensional discrete Fourier transform on the LSF and calculating its power spectrum.

  In the present embodiment, the super-resolution processing is performed to calculate the ESF, and the super-resolution ESF is differentiated to calculate the super-resolution LSF. However, the present invention is not limited to this. As in the technique described in Non-Patent Document 1, a plurality of ESFs are calculated at the original pixel pitch, and a plurality of LSFs are calculated by differentiating each of the calculated ESFs. The super resolution LSF may be calculated from the LSF. Also in this case, the calculation of the MTF using the LSF is the same as the procedure described above, and the description thereof is omitted.

[Operation of MTF measuring device]
Next, the operation of the MTF measuring apparatus 100 according to the present embodiment will be described with reference to FIG. 9 (refer to FIGS. 2 and 7 as appropriate).
First, the MTF measuring apparatus 100 stores the image G1 obtained by imaging the MTF measurement chart input from the imaging unit 110 by the image storage unit 101 (step S21).
Next, the MTF measuring apparatus 100 acquires information indicating the knife edge image region used for the MTF measurement from the image G1 stored in Step S21 by the ROI acquisition unit 102 (Step S22).
Next, the MTF measuring apparatus 100 uses the information indicating the knife edge image area acquired in step S22 by the image extraction unit 103 to obtain an image of the area indicated by the information from the image G1 stored in step S21. Extracted as a knife edge image G2 (step S23).

Next, the MTF measuring apparatus 100 estimates the inclination angle of the knife edge using the knife edge image G2 extracted in step S23 by the inclination angle estimation means 104 (step S24). The knife edge inclination angle estimation process is the same as the inclination angle estimation performed by the inclination angle estimation apparatus 1 according to the first embodiment shown in FIG.
Next, the MTF measuring apparatus 100 uses the ESF calculation means 105 to calculate the ESF by super-resolution processing for the knife edge image G2 extracted in step S23, using the estimated inclination angle of the knife edge estimated in step S24. (Step S25).

The MTF measuring apparatus 100 differentiates the ESF calculated in step S25 by the MTF calculating means 106 to calculate LSF, and further calculates the power spectrum by performing one-dimensional discrete Fourier transform on the LSF, thereby obtaining the spatial frequency. The MTF for each component is calculated (step S26).
Through the above procedure, the MTF measuring apparatus 100 can measure the MTF with high accuracy.

  As described above, the tilt angle estimation device and the MTF measurement device according to the embodiment of the present invention have been specifically described by the mode for carrying out the invention, but the gist of the present invention is not limited to these descriptions. It should be construed broadly based on the claims. Needless to say, various changes and modifications based on these descriptions are also included in the spirit of the present invention.

DESCRIPTION OF SYMBOLS 1 Inclination angle estimation apparatus 11 Image preparation means 111 Image conversion means 112 Image composition means 113 Image storage means 12 Frequency spectrum calculation means 121 Fourier transform means 122 Spatial frequency component detection means 13 Angle estimation means 131 Evaluation value calculation means 132 Inclination angle estimation value Update means 133 Inclination angle estimated value storage means 100 MTF measuring device 101 Image storage means 102 ROI acquisition means 103 Image extraction means 104 Inclination angle estimation means 105 ESF calculation means (edge spread function calculation means)
106 MTF calculation means 110 Imaging means 120 Input interface 130 Output interface

Claims (7)

For a knife edge image, an inclination angle estimation device for estimating the inclination angle of the knife edge,
Fourier transform means for transforming the knife edge image into spatial frequency domain data by two-dimensional discrete Fourier transform;
Spatial frequency component detection means for detecting the other spatial frequency component fy giving the maximum amplitude for each spatial frequency component fx for the spatial frequency domain data;
For the set of (fx, fy) detected by the spatial frequency component detecting means, an angle θ that fits the equation (1) that is a linear equation is calculated, and the extension direction of the knife edge is the other spatial frequency. Angle estimation means for estimating the angle formed with the direction of
An inclination angle estimation device comprising:
0 = fx · cos θ + Fy (fx) · sin θ (1)
However, in Formula (1), Fy (fx) indicates the other spatial frequency component fy that gives the maximum amplitude in the one spatial frequency component fx, and θ is 0 degree or more and less than 180 degrees in Formula (1). The straight line represented is an angle formed with the one spatial frequency axis. Generating a point symmetric image of the knife edge image, and the knife edge image and the point symmetric image so that one side of the knife edge image and a side of the point symmetric image corresponding to the one side are in contact with each other. Further comprising image preparation means for generating a combined knife edge image obtained by combining
2. The tilt angle estimation according to claim 1, wherein the Fourier transform unit transforms the synthesized knife edge image into data in a spatial frequency domain by performing a two-dimensional discrete Fourier transform instead of the knife edge image. apparatus. 3. The angle estimation unit estimates θ that minimizes the value J of the evaluation formula represented by Expression (2) as an inclination angle of the knife edge. 4. Tilt angle estimation device.
J = Σ | fx · cos θ + Fy (fy) · sin θ | ^p (2)
However, in Formula (2), (SIGMA) shows that the sum of the right type is calculated about several spatial frequency component fx, and p shows a positive real number.   In the said Formula (2), p is less than 2, The inclination-angle estimation apparatus of Claim 3 characterized by the above-mentioned. Image extracting means for extracting a knife edge image from the image of the knife edge chart imaged by the imaging means;
For the knife edge image, an inclination angle estimating means for estimating the inclination angle of the knife edge;
An edge spread function calculating means for projecting each pixel in the direction of the estimated inclination angle and calculating an edge spread function that is a distribution of image values relating to a dimension orthogonal to the inclination of the knife edge;
MTF calculating means for calculating an MTF (Modulation Transfer Function) by differentiating the edge spread function and further performing discrete Fourier transform,
5. An MTF measurement apparatus using the inclination angle estimation apparatus according to claim 1 as the inclination angle estimation means.   An inclination angle estimation program for causing a computer to function as the inclination angle estimation apparatus according to any one of claims 1 to 4.   An MTF measurement program for causing a computer to function as the MTF measurement device according to claim 5.