JP2016038708A - Image processing apparatus and image processing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an image processing apparatus or the like, configured to perform processing in accordance with various input images.SOLUTION: An image processing apparatus 1 includes: a filter generation section 12 which determines a first transfer function using an amplification factor ρ and a spatial frequency f, as variables, whose values increase as the spatial frequency increases in a spatial frequency band from DC to a spatial frequency f0, and a second transfer function continuous from the first transfer function and using the spatial frequency f, as a variable, whose value decreases as the spatial frequency increases in a spatial frequency band equal to or higher than the spatial frequency f0, to generate an image filter based on the first transfer function and the second transfer function; and a filter processing section 14 which applies the image filter to an input image to obtain an output image.SELECTED DRAWING: Figure 1

Description

  The present invention relates to an image processing apparatus and an image processing method.

  2. Description of the Related Art Conventionally, a technique for performing image processing for edge (outline) enhancement and blurring (noise reduction) using an image filter such as a Laplacian filter, a Gaussian filter, or a box filter is known (for example, Patent Document 1).

JP 2009-79949 A

  In the conventional method, since the parameters of the image filter are fixed in many cases, it is difficult to specify the spatial frequency band to be emphasized or the spatial frequency band to be attenuated, or to adjust the degree of enhancement or attenuation. An image filter with parameters adjusted for an input image was used.

  For example, in a scanning electron microscope image (SEM image), there are various S / N ratios and image sharpnesses depending on imaging conditions such as irradiation current amount, observation magnification, focus adjustment, number of times of image integration, and amplifier gain of detection signals. Since it can be a situation, it is difficult to achieve sufficient image quality improvement by simply applying a combination of uniform pre-built filters.

  The present invention has been made in view of the above problems, and according to some aspects of the present invention, an image processing apparatus capable of processing corresponding to various input images, and An image processing method can be provided.

  (1) The image processing apparatus according to the present invention has a first variable having an amplification factor ρ and a spatial frequency f such that values increase with an increase in the spatial frequency in a spatial frequency band from direct current to the spatial frequency f0. The transfer function is a variable having the spatial frequency f as a variable, which is continuous with the first transfer function at the spatial frequency f0 and whose value decreases as the spatial frequency increases in the spatial frequency band equal to or higher than the spatial frequency f0. And a filter generation unit that generates an image filter based on the first transfer function and the second transfer function, and a filter that obtains an output image by applying the image filter to an input image And a processing unit.

  In addition, the image processing method according to the present invention provides the first transmission using the amplification factor ρ and the spatial frequency f as variables so that the value increases as the spatial frequency increases in the spatial frequency band from direct current to the spatial frequency f0. A second function having a spatial frequency f as a variable that is continuous with the first transfer function at the spatial frequency f0 and decreases with an increase in the spatial frequency in the spatial frequency band equal to or higher than the spatial frequency f0. A filter generation step of generating an image filter based on the first transfer function and the second transfer function, and a filter process for obtaining an output image by applying the image filter to an input image Process.

According to the present invention, an image filter that enhances the spatial frequency band from direct current to the spatial frequency f0 according to the amplification factor ρ and attenuates the spatial frequency band above the spatial frequency f0 is applied to the input image appropriately. It is possible to obtain an output image in which edge enhancement is performed and noise is moderately reduced, and an optimum image filter corresponding to various input images can be obtained simply by setting the spatial frequency f0 and the amplification factor ρ to appropriate values. Can be generated.

  (2) In the image processing apparatus and the image processing method according to the present invention, the spatial frequency f0 may be a maximum spatial frequency including a signal component in the input image.

  According to the present invention, it is possible to generate an optimum image filter corresponding to various input images.

  (3) In the image processing device according to the present invention, the filter generation unit obtains a test statistic by testing the degree of fit to the Rayleigh distribution for the amplitude component of the spatial frequency band equal to or higher than the spatial frequency f in the input image, The change amount of the test statistic associated with the change in the spatial frequency f may be examined from the high frequency side, and the value of the spatial frequency f when the change amount exceeds a predetermined threshold may be determined as the spatial frequency f0.

  Further, in the image processing method according to the present invention, in the filter generation step, a test statistic is obtained by testing a fitness to a Rayleigh distribution for an amplitude component in a spatial frequency band equal to or higher than a spatial frequency f in the input image, The change amount of the test statistic associated with the change in the spatial frequency f may be examined from the high frequency side, and the value of the spatial frequency f when the change amount exceeds a predetermined threshold may be determined as the spatial frequency f0.

  According to the present invention, the optimum spatial frequency f0 corresponding to various input images can be automatically set.

  (4) In the image processing apparatus according to the present invention, the filter generation unit converts the determined spatial frequency f0 and a plurality of candidate values of the amplification factor ρ into the first transfer function and the second transfer function. To generate a plurality of the image filters, sequentially apply the generated plurality of image filters to the input image to generate an output image, and the number of saturated pixels in the generated output image has a predetermined threshold value. The maximum candidate value that does not exceed may be determined as the amplification factor ρ.

  In the image processing method according to the present invention, in the filter generation step, the determined spatial frequency f0 and a plurality of candidate values of the amplification factor ρ are used as the first transfer function and the second transfer function. Apply to generate a plurality of the image filters, sequentially apply the generated plurality of image filters to the input image to generate an output image, and the number of saturated pixels in the generated output image exceeds a predetermined threshold The largest candidate value that does not exist may be determined as the amplification factor ρ.

  According to the present invention, it is possible to automatically set an optimum amplification factor ρ corresponding to various input images.

  (5) In the image processing apparatus according to the present invention, the filter generation unit designates one point on a rectangular area in which a first axis indicates a spatial frequency and a second axis orthogonal to the first axis indicates an amplitude ratio. The spatial frequency f0 and the amplification factor ρ may be determined based on operation information.

  In the image processing method according to the present invention, in the filter generation step, an operation for designating one point on a rectangular area in which the first axis indicates a spatial frequency and the second axis orthogonal to the first axis indicates an amplitude ratio. The spatial frequency f0 and the amplification factor ρ may be determined based on the information.

According to the present invention, the spatial frequency band from DC to the spatial frequency f0 is amplified by an intuitive operation of designating one point on a rectangular area where the first axis indicates the spatial frequency and the second axis indicates the amplitude rate. Rate ρ
Accordingly, it is possible to provide a user with a means for creating an image filter that enhances and attenuates a spatial frequency band equal to or higher than the spatial frequency f0.

It is a figure which shows an example of the functional block diagram of the image processing apparatus which concerns on this embodiment. It is a figure which shows the frequency characteristic of the image filter produced | generated by this embodiment. It is a flowchart which shows the flow of a process at the time of determining automatically the spatial frequency f0 and amplification factor (rho) according to an input image. It is a graph which shows the test statistic calculated by changing the spatial frequency f. It is a graph which shows the saturation pixel number in each output image produced | generated by changing the candidate value of amplification factor (rho). 6A is an input image, FIG. 6B is an output image generated when the gain ρ is set to a value indicated by “A” in FIG. 5, and FIG. FIG. 6D shows an output image generated when the amplification factor ρ is set to a value indicated by “B” in FIG. 5, and FIG. 6D shows a case where the amplification rate ρ is set to a value indicated by “C” in FIG. It is the generated output image. It is a figure which shows an example of the user interface displayed on a display part when performing manual adjustment. It is a figure which shows the other example of the user interface displayed on a display part when performing manual adjustment. It is a figure for demonstrating a modification.

  DESCRIPTION OF EMBODIMENTS Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the drawings. The embodiments described below do not unduly limit the contents of the present invention described in the claims. Also, not all of the configurations described below are essential constituent requirements of the present invention.

1. Configuration FIG. 1 shows an example of a functional block diagram of an image processing apparatus according to the present embodiment. Note that the image processing apparatus according to the present embodiment may have a configuration in which some of the components (each unit) in FIG. 1 are omitted.

  The image processing apparatus 1 according to the present embodiment is an apparatus that performs image processing for improving the image quality of an input image using an image (SEM image) captured by a scanning electron microscope (SEM) as an input image. The image processing apparatus 1 includes a processing unit 10, an operation unit 20, a display unit 30, and a storage unit 40.

  The operation unit 20 is for a user to input operation information, and outputs the input operation information to the processing unit 10. The function of the operation unit 20 can be realized by hardware such as a keyboard, a mouse, a button, and a touch panel.

  The display unit 30 displays an image (output image) generated by the processing unit 10, and its function can be realized by an LCD, a CRT, or the like.

  The storage unit 40 stores a program and various data for causing the computer to function as each unit of the processing unit 10 and functions as a work area of the processing unit 10, and the function can be realized by a hard disk, a RAM, or the like.

  The processing unit 10 (computer) generates an image filter and performs image processing to apply the generated image filter to the input image. The functions of the processing unit 10 can be realized by hardware such as various processors (CPU, DSP, etc.) and programs. The processing unit 10 includes a filter generation unit 12 and a filter processing unit 14.

  The filter generation unit 12 enhances (amplifies) the spatial frequency band from direct current to the spatial frequency f0 according to the amplification factor ρ, and generates an image filter that attenuates the spatial frequency band equal to or higher than the spatial frequency f0. For example, the filter generation unit 12 has a first transfer function with the gain ρ and the spatial frequency f as variables, the values of which increase as the spatial frequency increases in the spatial frequency band from direct current to the spatial frequency f0. A second transfer function having the spatial frequency f as a variable is obtained, which is continuous with the first transfer function at the spatial frequency f0 and decreases in the spatial frequency band of the spatial frequency f0 or higher with a decrease in the spatial frequency. And generating an image filter based on the first transfer function and the second transfer function.

  The filter processing unit 14 generates an output image by applying the image filter generated by the filter generation unit 12 to the input image to be processed. For example, the filter processing unit 14 multiplies the result of Fourier transform of the input image by the image filter (frequency characteristics) generated by the filter generation unit 12, and generates an output image by performing inverse Fourier transform on the result. . Further, the filter processing unit 14 generates a filter kernel by performing inverse Fourier transform on the image filter generated by the filter generation unit 12, and generates an output image by applying the generated filter kernel to the input image (convolution operation). May be. The output image generated by the filter processing unit 14 is stored in the storage unit 40 and displayed on the display unit 30.

  Here, the filter generation unit 12 determines the spatial frequency f0 and the amplification factor ρ based on the input image, and applies the determined spatial frequency f0 and the amplification factor ρ to the first transfer function and the second transfer function. A filter may be generated (automatic adjustment). In this case, the filter generation unit 12 obtains a test statistic by testing the degree of fit to the Rayleigh distribution for the amplitude component in the spatial frequency band equal to or higher than the spatial frequency f in the input image, and the test statistic accompanying the change in the spatial frequency f. May be determined from the high frequency side, and the value of the spatial frequency f when the amount of change exceeds a predetermined threshold may be determined as the spatial frequency f0. The filter generation unit 12 generates and generates a plurality of image filters by applying the determined spatial frequency f0 and a plurality of candidate values of the amplification factor ρ to the first transfer function and the second transfer function. A plurality of image filters may be sequentially applied to the input image to generate an output image, and the maximum candidate value in which the number of saturated pixels does not exceed a predetermined threshold in the generated output image may be determined as the amplification factor ρ.

  Further, the filter generation unit 12 determines the spatial frequency f0 and the amplification factor ρ based on the operation information from the operation unit 20, and uses the determined spatial frequency f0 and the amplification factor ρ as the first transfer function and the second transfer function. May be applied to generate an image filter (manual adjustment). In this case, the processing unit 10 causes the display unit 30 to display a rectangular region in which the first axis indicates the spatial frequency and the second axis orthogonal to the first axis indicates the amplitude rate, and the filter generation unit 12 includes the display unit 30. The spatial frequency f0 and the amplification factor ρ may be determined based on the operation information (coordinate information of the designated position) that designates one point in the rectangular area displayed in FIG.

2. Next, the method of this embodiment will be described with reference to the drawings.

2-1. Overview FIG. 2 is a diagram illustrating frequency characteristics of an image filter generated in the present embodiment. In the figure, the horizontal axis represents the spatial frequency f, and the vertical axis represents the amplification factor (amplification gain, unit: dB).

The image filter of the present embodiment has a transfer function h _ρ (f) (first transfer function) whose value increases as the spatial frequency f increases in the spatial frequency band from direct current to f0 (cutoff frequency), and f0 It consists of a transfer function g (f) (second transfer function) that is continuous with the transfer function h _ρ (f) and whose value decreases with an increase in the spatial frequency f in the spatial frequency band of f0 or more. Here, in the transfer function h _ρ (f) and the transfer function g (f), the amplification factor when the spatial frequency f is f0 is ρ. F0 is the maximum frequency including the signal component in the frequency space of the input image, and is preferably the maximum spatial frequency in which the signal component is dominant over the noise component in the frequency space of the input image.

The transfer function h _ρ (f) and the transfer function g (f) are functions that are linear on the log-log graph. The reason why the transfer function h _ρ (f) and the transfer function g (f) are designed on the log-log graph is to consider Weber-Fechner's law. The transfer function h _ρ (f) and the transfer function g (f) are expressed as follows: However, in the transfer function g (f), the amplification factor is multiplied by d (d <1) every time the spatial frequency f is increased 10 times.

The transfer function h _ρ (f) has an effect of enhancing the edge of the input image, and the transfer function g (f) has an effect of reducing shot noise of the input image. That is, by applying the image filter of this embodiment to an input image, an output image in which edge enhancement is performed and shot noise is reduced can be obtained. In addition, by setting the spatial frequency f0 and the amplification factor ρ to appropriate values according to the input image, it is possible to generate optimal image filters corresponding to various input images.

The image filter may be designed so that the transfer function h _ρ (f) and the transfer function g (f) are smoothly connected, or the transfer function h _ρ (f) and the transfer function g (f) The image filter may be designed so that the shape is a monotone curve or a smooth S-curve.

2-2. Next, a method for automatically adjusting the image quality of an input image will be described. In this method, the two parameters of the image filter, the spatial frequency f0 and the amplification factor ρ, are automatically determined according to the input image.

  Consider a case where a gray-scale digital image captured by a charged particle beam (for example, an electron beam) having a beam diameter of d (d> 1) pixels is processed as an input image.

When an input image cut out to a size of N × N pixels fast Fourier transform, the frequency space of the input image (the Fourier space, the reciprocal space), the spatial frequency _{f0 (≡N / 2d ≦ √ (} f x 2 + f y 2) , f _x, f _y are the x direction, in the region of the high-frequency side of the y direction of the frequency), does not include the amplitude component from the imaging target (signal component), the amplitude component (noise component of all shot noise or random noise from ) The distribution of the real component and the imaginary component in the complex plane of the wave constituting such a noise component is considered to follow a Gaussian distribution with the same standard deviation.

  On the other hand, in the region on the lower frequency side than the spatial frequency f0, the periodicity of the object to be imaged is reflected, and a reciprocal lattice point with high intensity exists. It is considered that the distribution of the real component and the imaginary component in the complex plane of the wave constituting such a signal component does not necessarily follow the Gaussian distribution.

On the complex plane, when the real component Re and the imaginary component Im follow a Gaussian distribution with the same standard deviation centered on the origin, the distribution of the absolute value (amplitude value) √ (Re ² + Im ² ) of the complex number is the Rayleigh distribution. be called. Therefore, in the present embodiment, in the frequency space of the input image, whether or not the absolute value of the complex number follows the Rayleigh distribution in a region where the spatial frequency is f or higher is sequentially verified by changing f from the high frequency side toward the low frequency side. Then, f when the test result changes from pass to fail is determined as the spatial frequency f0. Thereby, the maximum spatial frequency f0 including the signal component in the frequency space of the input image can be accurately determined.

  FIG. 3 is a flowchart showing the flow of processing when the spatial frequency f0 and the amplification factor ρ are automatically determined according to the input image.

  First, the filter generation unit 12 performs a fast Fourier transform on the entire region or a partially extracted region of the input image (step S10). Next, the filter generation unit 12 sets 0 to the spatial frequency f (radial distance from the origin (wave number = 0)) (step S12), and the spatial frequency f is obtained from the result of fast Fourier transform of the input image. Using the amplitude values of all the angles as samples, basic statistics of average, variance, skewness, and kurtosis are obtained, and the degree of fit to the Rayleigh distribution is tested to calculate a test statistic Test (step S14). . Here, the Gaussian distribution test method Jack-Bella test is applied to the Rayleigh distribution test, and the test statistic Test is obtained by the following equation.

Here, V indicates variance / average, S indicates skewness, and K indicates kurtosis. V0, S0, and K0 are constants taken by V, S, and K, respectively, if the sample is a complete Rayleigh distribution.

The test statistic calculated in step S14 is stored in the storage unit 40 in association with the spatial frequency f at that time. Next, the filter generation unit 12 determines whether or not the spatial frequency f has reached a predetermined maximum spatial frequency f _max (for example, a Nyquist frequency) (step S16), and has not reached the maximum spatial frequency f _max In (N of step S16), the spatial frequency f is increased by Δf (Δf <f _max ) (step S18), and the process proceeds to step S14. Hereinafter, until the spatial frequency f reaches the maximum spatial frequency _{f max,} it repeats the processing of steps S14 to S18.

  FIG. 4 is a graph showing a test statistic calculated by changing the spatial frequency f (a test statistic obtained by testing the fitness to the Rayleigh distribution). FIG. 4 also shows the power spectrum of the input image. In the figure, the horizontal axis represents the spatial frequency f, and the vertical axis in the figure represents the test statistic (the amplitude intensity for the power spectrum).

When the spatial frequency f reaches the maximum spatial frequency f _max (Y in step S16), the filter generation unit 12 determines the spatial frequency f based on the test statistic for each spatial frequency f stored in the storage unit 40. The amount of change in the test statistic when the value is changed from the high frequency side to the low frequency side is calculated from the high frequency side (step S20), and when the change amount exceeds a predetermined threshold (the test result is passed) The value of the spatial frequency f at the time of changing from (to) to reject is determined as f0 (step S22).

Next, the filter generation unit 12 sets a predetermined minimum value ρ _min (minimum value among a plurality of candidate values) to the amplification factor ρ (step S24), and the spatial frequency f0 and the amplification factor ρ determined in step S22. _Are applied to the transfer function h _ρ (f) and the transfer function g (f) to generate an image filter (step S26), and the generated image filter is applied to the input image to generate an output image (step S28). Then, the saturation pixel number (the number of pixels saturated in white or black) in the generated output image is calculated (step S30). The calculated number of saturated pixels is stored in the storage unit 40 in association with the amplification factor ρ at that time.

Next, the filter generation unit 12 determines whether or not the amplification factor ρ has reached a predetermined maximum value ρ _max (step S32). When the gain ρ has not reached the maximum value ρ _max (N in step S32). The amplification factor ρ is increased by Δρ (Δρ <ρ _max −ρ _min ) (step S34), and the process proceeds to step S26. Hereinafter, until the amplification factor [rho reaches the maximum value [rho _max, repeats the processing of steps S26～S34.

  FIG. 5 is a graph showing the number of saturated pixels in each output image generated by changing the candidate value of the amplification factor ρ. In the figure, the horizontal axis indicates the amplification factor, and in the figure, the vertical axis indicates the number of black pixels or white pixels. 6A is an input image (SEM image), and FIG. 6B is an output image generated when the gain ρ is set to a value indicated by “A” in FIG. (C) is an output image generated when the amplification factor ρ is set to a value indicated by “B” in FIG. 5. In the output image shown in FIG. 6B, the amplification factor ρ is too low, so that the contour is unclear. In the output image shown in FIG. 6C, the amplification factor ρ is too high, so There are many images.

When the amplification factor ρ reaches the maximum value ρ _max (Y in step S32), the filter generation unit 12 determines that the saturation pixel number is based on the saturation pixel number for each amplification factor ρ stored in the storage unit 40. The maximum amplification factor ρ that does not exceed the predetermined threshold is determined as a final value of the amplification factor ρ (step S36).

  In the example shown in FIG. 5, the value indicated by “C” in the figure is determined as the maximum value (the determined value of the amplification factor ρ) that does not exceed the predetermined threshold value. FIG. 6D is an output image (final output image when the amplification factor ρ is determined) generated when the amplification factor ρ is set to a value indicated by “C” in FIG. 5. Comparing the input image shown in FIG. 6 (A) with the output image shown in FIG. 6 (D), the output image shown in FIG. 6 (D) shows that edge enhancement is moderately performed and noise is moderately reduced. I understand.

  As described above, according to the automatic adjustment method of the present embodiment, an optimal image filter can be generated by automatically setting the optimal spatial frequency f0 and amplification factor ρ corresponding to various input images, An output image in which edge enhancement is appropriately performed and noise is appropriately reduced can be obtained.

2-3. Manual Adjustment Method Next, a method for manually adjusting the image quality of an input image will be described. In this method, the spatial frequency f0 and the amplification factor ρ, which are two parameters of the image filter, are determined based on operation information input by the user.

  FIG. 7 is a diagram illustrating an example of a user interface displayed on the display unit 30 when manual adjustment is performed.

In the user interface shown in FIG. 7, the horizontal axis (first axis) represents the spatial frequency, and the vertical axis (second
(Axis) includes a log-log graph (an example of a rectangular area) indicating the amplification factor. Note that a log-log graph in which the vertical axis indicates amplitude intensity may be used. When the user performs an operation for specifying a position (one point) on the logarithmic graph (an operation for touching one point on the touch panel or an operation for specifying a position using a mouse), the side of the specified position is displayed. The spatial frequency corresponding to the coordinate of the axis is set as f0, and the amplification factor corresponding to the coordinate of the vertical axis at the designated position is set as ρ. That is, the user can simultaneously specify the spatial frequency f0 and the amplification factor ρ (two parameters of the image filter) by an intuitive operation of specifying one point on the log-log graph.

As shown in FIG. 7, the logarithmic graph includes a transfer function (transfer function h _ρ (f) and image filter frequency consisting of transfer function g (f) based on the determined spatial frequency f 0 and amplification factor ρ. Characteristic) is displayed. Therefore, the user can confirm the frequency characteristics of the image filter based on the designated spatial frequency f0 and amplification factor ρ while designating the spatial frequency f0 and amplification factor ρ. Further, the power spectrum of the input image and the power spectrum of the output image may be displayed on the log-log graph. In this way, the user changes the power spectrum of the input image as a result of applying the image filter based on the designated spatial frequency f0 and amplification factor ρ while designating the spatial frequency f0 and amplification factor ρ. Can be confirmed.

  When a general user is targeted, as shown in FIG. 8, for example, the horizontal axis indicates the degree of noise reduction (“soft”, “sharp”), and the vertical axis indicates the magnitude of amplification factor (“strong”). , “Weak”) is displayed on the display unit 30, the spatial frequency f0 is determined based on the horizontal axis coordinates of the position on the rectangular area RA designated by the user, and the vertical axis of the designated position The amplification factor ρ may be determined based on the coordinates. In this way, the user can specify the spatial frequency f0 and the amplification factor ρ with a more intuitive and easy-to-understand interface.

3. Modifications The present invention is not limited to the above-described embodiment, and various modifications can be made. The present invention includes configurations that are substantially the same as the configurations described in the embodiments (for example, configurations that have the same functions, methods, and results, or configurations that have the same objects and effects). In addition, the invention includes a configuration in which a non-essential part of the configuration described in the embodiment is replaced. In addition, the present invention includes a configuration that exhibits the same operational effects as the configuration described in the embodiment or a configuration that can achieve the same object. Further, the invention includes a configuration in which a known technique is added to the configuration described in the embodiment.

  For example, in the above embodiment, the spatial frequency f0 (cut-off frequency) is determined by obtaining a test statistic obtained by testing the fitness of the Rayleigh distribution for the amplitude component in the spatial frequency band equal to or higher than the spatial frequency f in the input image. Although the case has been described, the method for obtaining the spatial frequency f0 is not limited to this.

  For example, a power spectrum is obtained by multiplying the entire area or a partial area of the input image by a window function, and the average value function V (f of the spectrum intensity of all directional components with respect to the frequency f from DC to the maximum frequency (Nyquist frequency). ) And the spatial frequency f0 may be estimated from the obtained average value function V (f). In this case, the frequency corresponding to the intersection of the average value function V (f) and the constant value Vc = Vmin + 0.1 × (Vmax−Vmin) may be estimated as the spatial frequency f0. Here, Vmin and Vmax are the minimum value and the maximum value of the average value function V (f), respectively. Also, two linear components when the average value function V (f) is drawn on the log-log graph using the Hough transform are extracted, and the frequency corresponding to the intersection of the two extracted straight lines is estimated as the spatial frequency f0. May be.

Then, from the obtained average value function V (f), a scaling index is obtained by fitting a region between the DC component and the spatial frequency f0 with a power function by the least square method, and the obtained spatial frequency f0 and the obtained scaling. The frequency characteristics of the image filter may be designed based on the index. Here, in the design of the frequency characteristics of the image filter, a preset value may be used as the scaling index of the power function representing the characteristics in the low frequency region lower than the spatial frequency f0, or the image filter may be configured using a plurality of values. It may be configured such that one value is selected from a plurality of values based on, for example, the maximum information entropy as a reference.

  If it is determined that the estimated spatial frequency f0 is in the vicinity of the Nyquist frequency, and the frequency characteristic attenuation rate is substantially kept below the spatial frequency f0 between the spatial frequency f0 and the Nyquist frequency, the estimated frequency is up to the Nyquist frequency. The S / N ratio is estimated to be sufficiently high. Therefore, in such a case, the spatial frequency f0 may be regarded as being equal to the Nyquist frequency.

  For example, in the case of a scanning electron microscope, the frequency characteristics of noise may vary depending on the direction of the image, such as the influence of charging appearing in the scanning direction of the electron beam. In such a case, the average value function V (f) of the spectrum intensity may be obtained by excluding a specific direction component.

  An image filter is generated by the method of the above-described modification, and the generated image filter is applied to the input image to obtain an output image. FIG. 9A is a diagram showing frequency characteristics of an input image, FIG. 9B is an input image (1280 × 948 pixels, 256-step gray scale SEM image), and FIG. FIG. 9D is a diagram illustrating the frequency characteristics of the image filter actually generated, and FIG. 9E is a diagram illustrating the actually generated frequency characteristics of the image filter. FIG. 9F is a diagram illustrating the frequency characteristics (portion indicated by a solid line) of the output image, and FIG. 9G is the output image. In this example, the spatial frequency f0 is determined to be about 80 (unit: wave number), and the scaling index of the power function is determined to be 0.26. When the input image shown in FIG. 9B is compared with the output image shown in FIG. 9G, the output image shown in FIG. 9G is moderately edge-enhanced and moderately reduced in noise. I understand.

1 image processing apparatus, 10 processing unit, 12 filter generation unit, 14 filter processing unit, 20
Operation unit, 30 display unit, 40 storage unit

Claims (6)

A first transfer function having a variable amplification factor ρ and spatial frequency f such that the value increases as the spatial frequency increases in a spatial frequency band from direct current to spatial frequency f0; And a second transfer function having a spatial frequency f as a variable such that the value decreases as the spatial frequency increases in a spatial frequency band equal to or higher than the spatial frequency f0. A filter generation unit for generating an image filter based on the transfer function and the second transfer function;
And a filter processing unit that applies the image filter to an input image to obtain an output image. In claim 1,
The image processing apparatus, wherein the spatial frequency f0 is a maximum spatial frequency including a signal component in the input image. In claim 1 or 2,
The filter generation unit
A test statistic is obtained by testing the degree of fit to the Rayleigh distribution for amplitude components in the spatial frequency band equal to or higher than the spatial frequency f in the input image, and the amount of change in the test statistic accompanying the change in the spatial frequency f is determined from the high frequency side. An image processing apparatus that examines and determines the value of the spatial frequency f when the amount of change exceeds a predetermined threshold as the spatial frequency f0. In claim 3,
The filter generation unit
Applying the determined spatial frequency f0 and a plurality of candidate values of the amplification factor ρ to the first transfer function and the second transfer function to generate a plurality of the image filters, Image processing in which an image filter is sequentially applied to the input image to generate an output image, and the maximum candidate value that does not exceed a predetermined threshold in the generated output image is determined as the amplification factor ρ. apparatus. In claim 1,
The filter generation unit
The spatial frequency f0 and the amplification factor ρ are determined based on operation information specifying one point on a rectangular area where the first axis indicates the spatial frequency and the second axis orthogonal to the first axis indicates the amplitude rate. , Image processing device. A first transfer function having a variable amplification factor ρ and spatial frequency f such that the value increases as the spatial frequency increases in a spatial frequency band from direct current to spatial frequency f0; And a second transfer function having a spatial frequency f as a variable such that the value decreases as the spatial frequency increases in a spatial frequency band equal to or higher than the spatial frequency f0. A filter generation step of generating an image filter based on the transfer function and the second transfer function;
A filter processing step of obtaining an output image by applying the image filter to the input image.