JP4139895B2 - Image processing method and image processing program - Google Patents

Description

  The present invention relates to an image processing method and an image processing program, and in particular, an image processing method and an image processing method capable of easily and automatically specifying an image position of a low-contrast analysis object buried in an image with a high noise level. The present invention relates to an image processing program.

  Conventionally, when analyzing the structure of a protein, a method of preparing a sample by crystallizing the protein to be analyzed and analyzing and evaluating the sample by an X-ray crystal structure analysis method and an NMR method has been mainly employed. However, in recent years, a method (single particle structure analysis method) for analyzing a protein structure using a cryogenic transmission electron microscope (Cryo-EM) is being developed (for example, see Non-Patent Document 1).

  This single particle structure analysis method cuts out images of individual spherical protein samples from a TEM image obtained from a particulate protein sample cooled to a cryogenic temperature in a transmission electron microscope (TEM), and extracts these sample images. This is a technique to reduce the noise of the sample image by averaging and to obtain the three-dimensional structure of the particulate protein sample from the obtained averaged image. Against the backdrop of recent advances in image processing technology and computer speedup It has been attracting attention as a powerful and useful analysis method.

W. V. Nicholson and R. M. Glaeser, “Review: Automatic Particle Detection in Electron Microscopy”, Journal of Structural Biology, Vol.133, pp.90-101 (2001).

  When performing image processing using a conventional single particle structure analysis method, the analyst himself manually cuts out each of the protein particle images captured in the electron microscope image, and adds and averages the images. Is required.

  However, because the contrast of TEM images obtained with cryogenic Cryo-EM has to be low and the noise level is also high, identifying the position of protein particles in the image is an option for experienced researchers. Since this is a very difficult task, it is difficult to perform a quick analysis. Furthermore, there is a problem that individual differences in results obtained depending on the skill level and experience of the analyst must increase. This has been one of the major factors hindering the spread of the single particle structure analysis method as a general analysis method.

  The present invention has been made in view of such problems, and an object of the present invention is to easily and automatically specify the image position of an analysis object with low contrast buried in an image with a high noise level. An object is to provide an image processing method and an image processing program that can be performed.

  In order to achieve such an object, the present invention provides an image processing method for specifying a position of an analysis target image in an image, and for extracting a local part image in the image. A first step of arranging a plurality of frames in the image, a second step of averaging an image cut out by the plurality of frames to form an average frame image, and a basis of the average frame image A third step of calculating a first energy value (E1), and selecting one frame from the plurality of frames and changing the position and angle of the selected frame in the image Obtained in the fourth step of rearranging the frames, the fifth step of averaging the images cut out by the rearranged frames to form an average frame image, and the fifth step The sixth step of calculating the second energy value (E2) based on the average frame image obtained is compared with the first and second energy values. When E1 <E2, the fourth step While adopting step frame rearrangement, if E1 ≧ E2, the seventh step for determining whether or not to adopt the fourth step frame rearrangement, and the first to seventh steps, An eighth step of decreasing the temperature parameter T after repeating a predetermined number of times and a ninth step of repeating the first to eighth steps a predetermined number of cycles are provided.

  Preferably, in the seventh step, the determination as to whether or not to adopt the frame rearrangement of the fourth step when E1 ≧ E2 is made by determining whether the first energy value E1 and the second energy value E2 are used. The adoption probability P (ΔE) is obtained from the difference (ΔE) by the following equation and compared with a random number. If the adoption probability P (ΔE) is larger than the random number, the frame rearrangement in the fourth step is performed. On the other hand, when the adoption probability P (ΔE) is equal to or less than the random number, it is executed by adopting the frame arrangement before the frame rearrangement in the fourth step.

Preferably, the first and second energy values are energy values calculated based on the actual image of the image (energy value E _{real of the} actual image) or an image obtained by performing FFT on the actual image. Either one of the energy values in the frequency domain (frequency domain energy value E _pow ) obtained based on the sum of the energy value E _{real of the} real image and the energy value E _pow of the frequency domain (E _real + E _pow ) is there.

Preferably, the energy value E _real of the _real image is calculated by the following equation based on the luminance d (x, y) at each coordinate point of the (x, y) coordinates provided in the average frame image. A luminance average value d _ave is obtained, a value d ′ (x, y) obtained by subtracting the pixel luminance average value d _ave from the average frame image d (x, y) is obtained, and the d ′ (x, y) value is further calculated. Is obtained by substituting into the following equation.

(N and M are the pixel sizes of the x-axis and y-axis of the frame, and H is the luminance value when the value of E _real is 0.5)

Preferably, the energy value E _{pow in the} frequency domain is calculated by the following equation based on the luminance d (x, y) at each coordinate point of the (x, y) coordinates provided in the average frame image. A luminance average value d _ave is obtained, a value d ′ (x, y) obtained by subtracting the pixel luminance average value d _ave from the average frame image d (x, y) is obtained, and the d ′ (x, y) value is further calculated. The amplitude of the spectrum | D ′ (u, v) | is obtained by FFT from the above, and the amplitude of the spectrum | D ′ (u, v) | is multiplied by a circular mask that defines the transmission frequency, and coordinates (u, For each pixel in v), the sum is obtained by the following equation.

(N and M are the pixel sizes of the x and y axes of the frame, r is the radius of the circular mask that defines the transmission frequency)

  Further preferably, the rate of decrease R of the temperature parameter T in the eighth step is given by the following equation.

(T ₀ : initial temperature, T _e : final temperature at which calculation is terminated, C _max : predetermined number of times in the eighth step)

  A second invention is an image processing program for causing a computer to execute image processing for specifying the position of an analysis target image in an image, wherein a plurality of frames for extracting a local part image in the image are obtained. A first step for arranging within the image; a second step for averaging the images cut out by the plurality of frames to form an average frame image; and a first energy based on the average frame image. A third step of calculating a value (E1), and selecting one frame from the plurality of frames, rearranging the frame by changing the position and angle of the selected frame in the image A fourth step, a fifth step of averaging the images cut out by the rearranged frames to form an average frame image, and the fifth step The sixth step of calculating the second energy value (E2) based on the obtained average frame image is compared with the first and second energy values, and if E1 <E2, the fourth step In the case where E1 ≧ E2, the seventh step of determining whether to adopt the frame rearrangement of the fourth step and the first to seventh steps are adopted. Is repeated for a predetermined number of times, and an eighth step for decreasing the temperature parameter T and a ninth step for repeating the first to eighth steps for a predetermined number of cycles are provided.

  Preferably, in the seventh step, the determination as to whether or not to adopt the frame rearrangement of the fourth step when E1 ≧ E2 is made by determining whether the first energy value E1 and the second energy value E2 are used. The adoption probability P (ΔE) is obtained from the difference (ΔE) by the following equation and compared with a random number. If the adoption probability P (ΔE) is larger than the random number, the frame rearrangement in the fourth step is performed. On the other hand, when the adoption probability P (ΔE) is equal to or less than the random number, it is executed by adopting the frame arrangement before the frame rearrangement in the fourth step.

  In the image processing method of the present invention, a large number of virtual frames for extracting a local image are arranged in an image in which a large number of particles to be analyzed are photographed, and each frame is moved while being randomly moved in the TEM image. The addition average of all the images cut out is obtained, and restrictions are imposed on both the position movement and the rotation movement of each frame so that the contrast of the average image becomes high. This restriction is controlled by the temperature parameter T, and the temperature is gradually decreased according to an annealing schedule that defines a procedure for decreasing the temperature parameter T from a high value to a low value. It is possible to provide an image processing method and an image processing program that can easily and automatically specify an image position of an analysis object with a low contrast buried in the image. Further, by averaging the images at the specified positions, the shape of the analysis object can be reproduced with high accuracy.

  Embodiments of the present invention will be described below with reference to the drawings. In the following embodiments, as a suitable example of an image of an analysis object with a low contrast buried in an image having a high noise level, the image was taken in a state where it was buried in noise in a transmission electron microscope image (TEM image). The image processing method and the image processing program of the present invention will be described by taking up a protein particle image having a weak contrast, but the present invention is not limited to such electron microscope image processing. Needless to say, general application such as identification of the position of the vehicle photographed in the photograph is possible.

The image processing method of the present invention is a method for executing self-integration of particle images according to an algorithm based on an annealing method (simulated annealing), which is known as one solution of the combination optimization problem. In the method of the present invention, a large number (for example, several hundreds) of virtual frames for extracting a local image are arranged in one TEM image in which a large number of particles to be analyzed are captured. While these frames are moved randomly in the TEM image, the average of all the images cut out by each frame is obtained, and both the position movement and the rotation movement of each frame are restricted so that the contrast of the average image becomes high. Add. This constraint is controlled by a temperature parameter (T), and an annealing schedule that defines a procedure for reducing the temperature parameter T from a high value to a low value.
When the temperature is gradually decreased according to the schedule), each frame is finally arranged with high accuracy at the particle image position. An image obtained by adding and averaging the images cut out by the frames arranged in this way can reproduce the shape of the particle to be analyzed with high accuracy.

  In the image processing method of the present invention, image processing can be executed only by presetting only the number and size (radius) of frames used for cutting out a local image, and the shape related to the analysis target particles required in the conventional method It is not necessary for special information such as factors. Therefore, since image processing without a template or learning image data is possible, it is possible to achieve complete automation of the processing.

  The procedure of the image processing method of the present invention will be specifically described below.

  FIG. 1 is a flowchart for explaining a simulated annealing algorithm (SA algorithm) when the image processing method of the present invention is executed, and FIG. 2 is an initial setting state when the analysis target is a protein particle. It is each image for demonstrating a TEM image (FIG.2 (a)), the position estimation process by SA algorithm (FIG.2 (b))), and the estimation result of a protein particle image position (FIG.2 (c))).

  In the image processing method of the present invention, as shown in FIG. 2, frames (F1 to F5 in the figure) for cutting out images of local parts are arranged in the TEM image, and the images cut out by these frames are averaged. The position and rotation angle of each frame in the TEM image are changed according to the SA algorithm shown in FIG. Here, the “score” is a “system energy value” calculated by a procedure described later, and serves as an index of the appropriateness of processing.

First, the size of each frame is set to a size in which an image of a single protein particle can enter, and the initial position of each frame is randomly arranged in the TEM image so that the frames do not overlap each other. Note that the initial value of the rotation angle of each frame is 0 °. Also, set the maximum number (Ite _max1 and Ite _max2 ) of counters (change count counter Ite ₁ and non-change count counter Ite ₂ ) of the frame position / angle change / non-change count described later, and the temperature setting the number of repetitions C _max reduction cycle (step S100).

Next, as shown in FIG. 2B, local images are cut out by frames arranged in the TEM image, and these images are averaged to obtain an average frame image. Based on this average frame image, the following In this manner, the initial energy value of the system is calculated (step S101). Here, as the energy value, an energy value calculated based on the real image (energy value E _{real of the} real image) or an energy value in the frequency domain obtained based on the image obtained by FFT of the real image ( Any energy value of the frequency domain energy value E _pow ) may be used, but here, the sum of these energy values (E _real + E _pow ) is defined as the energy value (E) of the system.

The energy value E _real of the real image is calculated according to the following procedure. First, (x, y) coordinates are provided in the average frame image to determine the luminance d (x, y) at each coordinate point. Based on these luminance d (x, y), the following equation (1) is obtained. The pixel luminance average value d _ave is obtained.

Here, N and M are the pixel sizes of the x-axis and y-axis of the frame.

Next, a value d ′ (x, y) obtained by subtracting the pixel luminance average value d _ave from the average frame image d (x, y) is obtained (Expression 2), and this d ′ (x, y) value is obtained as a saturated function. Substituting it into the Michaels-Meaintai function of equation (3), the sum is taken as the energy value E _real of the real image.

  Here, H is a luminance value when the value of the saturation function is 0.5. This handling avoids the inconvenience that the score increases rapidly as the luminance value increases and only the luminance value of only a part of the average frame image increases as the luminance value increases. It becomes possible.

On the other hand, the energy value E _{pow in} the frequency domain is calculated by _obtaining the spectrum amplitude | D ′ (u, v) | by FFT from the value d ′ (x, y) obtained by the above equation (2). Is performed by multiplying the amplitude | D ′ (u, v) | by a circular mask that defines the transmission frequency and taking the sum by the following equation (4) for each pixel at coordinates (u, v) in the frequency domain. Here, a circular mask F (u, v) is a function defined by the following equation (5), the size of the circular mask (radius r) is the center position (u _m, v _m) from a radius r = 6. It was set to 4 (pixel).

Following such initial setting, the change count counter Ite ₁ = 0 and the non-change count counter Ite ₂ = 0 are set in step S102, and one of the frames on the TEM image is randomly selected (step S103). The position and angle of the frame are changed (step S104). Here, the amount of change before and after the change is a normal random number of 7σ for the x-axis and y-axis for the position, and a normal random number of 30σ for the angle.

Based on the calculation described above, the energy value E2 of the average frame image after the position / angle change is calculated to obtain a difference (ΔE = E1−E2) from the energy value E1 before the change (step S105). The energy value is compared with the energy value before the change to determine whether the energy value after the change is higher than the energy value before the change (step S106). Here, when the energy value after the change is higher than the energy value before the change (step S106: Yes), the score is updated to the energy value after the change (step S107), and the position / angle of the frame in step S104 and held adopted changes (step S108), it increases the change counter Ite ₁ 1 (step S109).

On the contrary, when the energy value after the change is equal to or less than the energy value before the change (step S106: No), the adoption probability (transition probability) P from the change amount (ΔE) with the score before the change according to the following equation (6). (ΔE) is obtained (step S110) and compared with random numbers from 0 to 1 (P (ΔE)> (random numbers 0 to 1)) (step S111). When the random number is less than the adoption probability P (ΔE) ( Step S111: Yes) adopts the frame change in step S104, and if the random number is greater than or equal to the adoption probability P (ΔE) (step S111: No), the position / angle of the frame is changed to the place / value before the change. Returning (step S112), the non-change count counter Ite ₂ is incremented by 1 (step S113).

In step S114, it compares the values and values of the non-change counter Ite ₂ changes counter Ite ₁ and each maximum number (Ite _max1 and Ite _max2), in "Ite ₁ <Ite _max1 and Ite ₂ <Ite _max2" if (step S114: Yes) return repeated subsequent steps step S103, "Ite ₁ <Ite _max1 and Ite ₂ <Ite _max2" Otherwise (step S114: No) proceeds to a temperature parameter of the system to step S115 Decrease T

The decrease rate R of the temperature parameter T is given by the following equation (7). Here, T ₀ is an initial temperature, _Te is a final temperature at which the calculation is finished, and C _max is a predetermined number of cycles. That is, the decreasing rate R of the temperature parameter T is set by the following equation (7) according to a predetermined cycle number _Cmax , and the temperature parameter T decreases exponentially for each cycle by the following equation (8).

As a condition for executing this temperature reduction, for example, the number of frame changes Ite ₁ and the number of non-changes Ite ₂ are totaled, and the number of changes Ite ₁ is 20 times the total number of frames, or the number of non-changes Ite _Assume that ₂ is 100 times the total number of frames.

Each time the temperature is decreased, the cycle counter C is incremented by 1 (step S116), and it is determined whether the cycle is equal to or greater than the predetermined number C _max set in step S100 (step S117). (Step S117: Yes) is completed, and if the predetermined number of times is not reached (Step S117: No), the process proceeds to Step S102 and the change count counter Ite ₁ = 0 and the non-change count counter Ite ₂ = 0 are set again. Then, the steps after step S103 are repeated.

  When such a series of frame arrangement operations is completed, all the frames are arranged on the protein particle image (T1 to T5) (FIG. 2 (c)), and the position of the protein particle image to be analyzed exists. The average image obtained by averaging the images cut out by these frames reproduces the protein particle image with high accuracy.

  FIG. 3 is a diagram for explaining a frame arrangement for each number of cycles of temperature reduction when image processing of a model image of protein molecules is executed by an electronic computer capable of executing the processing program of the image processing method of the present invention. is there. In these drawings, in order to facilitate understanding of the position recognition state of the protein particle, the frame in which the particle exists is shown in white, and the frame in which the particle does not exist is shown in black.

  In the cycle number 0 (FIG. 3A), the frames are randomly arranged, and protein particles are not present in most frames. As the number of cycles increases to 120 (FIG. 3 (b)), 150 (FIG. 3 (c)), and 300 (FIG. 3 (d)), the number of circles arranged at the protein particle position gradually increases. In 300, all the frames are arranged at the particle positions.

  FIG. 4 is a diagram for explaining the noise content dependency of the particle position recognition level when noise is added to the original image.

  FIG. 4A is an original image, and FIGS. 4B to 4D are composite images in which noise is included in the original image. When normal random noise with variance σ = 20 is added (FIG. 4B), particles are present in almost all frames. When the noise content is increased and normal random noise with variance σ = 30 is added (FIG. 4C), the probability that the frame is arranged at the particle position decreases to about 80%, and further, normal random with variance σ = 40 is added. When noise is added (FIG. 4C), the probability that the frame is arranged at the particle position decreases to about 50%. That is, the particle position recognition level depends on the noise level included in the image.

  However, while it is almost impossible to visually identify the particle position from an image with a high noise level as shown in FIG. 4D, the image processing method of the present invention has a probability of about 50%. It is possible to automatically specify the particle position.

  FIG. 5 is a diagram for explaining an application example of the image processing method of the present invention to a TEM image of a Na channel that has been subjected to negative stain treatment with a 2% depleted uranium solution. FIG. 5A is an image of the final result obtained by executing the frame arrangement based on the algorithm described above, and almost all the frames are arranged at the particle positions. FIG. 5B shows a frame average image for each cycle of temperature decrease. In the initial image (cycle count = 0), the particle shape cannot be confirmed only by noise, but the frame average of 70 cycles. The particle shape can be confirmed in the image, and as the number of cycles is increased to 120, 150, and 300, a shape close to the original Na channel is gradually generated. FIG. 5C shows changes in temperature and score (system energy value) for each number of cycles. As the temperature decreases exponentially, the score (energy) increases, and the validity of the processing is increased. I can understand how it gets higher.

  FIG. 6 is a diagram for explaining the result of image processing according to the method of the present invention applied to a cryogenic Cryo-EM image of apoferritin protein, and FIG. 6 (a) is a frame based on the algorithm described above. This is an image of the final result of the placement, and almost all frames are placed at the particle positions. FIG. 6B shows a frame average image for each cycle of temperature decrease. In the initial image (cycle count = 0), the shape of particles cannot be confirmed only by noise, but the frame average of cycle number 70 is shown. In the image, a particle shape with a recognizable structure can be confirmed. As the number of cycles is increased to 120, 150, and 300, a shape close to the original apoferritin protein is gradually generated. FIG. 6C shows changes in temperature and score (system energy value) for each number of cycles. As the temperature decreases exponentially, the score increases and the validity of the process increases. Can understand.

  As described above, according to the image processing method of the present invention, even if the analysis target image with low contrast is an image buried in a high noise level, the position of the protein particle in the image is accurately captured and the shape thereof is high. Can be reproduced with accuracy.

  As described above, assuming that the method of the present invention is applied to protein analysis, the contents executed by the image processing method of the present invention simulate the state in which the protein is crystallized on a computer. It is similar to that. Therefore, when protein crystallization is performed, it is similar to protein crystals that have been randomly arranged and accumulated in a regular manner so as to have a more stable structure (minimum energy state of the system). The average image of the images cut out by each frame gradually reproduces the particulate structure from the initial state where it is buried in noise and the shape is unclear.

  As described above, in the image processing method of the present invention, it is not necessary to know the shape of the analysis object existing in a state where it is buried in noise. Shape-shaped particles can be picked up. Further, since the image processing method of the present invention can be applied to an image with a high noise level, even a blurred particle image that cannot be recognized at the visual level can be extracted with high accuracy and simplicity.

  The present invention provides an image processing method and an image processing program that can easily and automatically specify an image position of an analysis object with a low contrast buried in an image with a high noise level.

It is a flowchart for demonstrating the simulated annealing algorithm (SA algorithm) at the time of performing the image processing method of this invention. It is each image for TEM image (a) in the initial setting state in case analysis object is protein particles, a position estimation process (b) by SA algorithm, and a protein particle image position estimation result (c). It is a figure for demonstrating the frame arrangement | positioning for every repetition frequency at the time of performing the image process of the model image of a protein molecule by the computer which can execute the processing program of the image processing method of this invention. It is a figure for demonstrating the noise content dependence of the particle position recognition level at the time of adding noise to an original image. It is a figure explaining the application example of the image processing method of this invention with respect to the TEM image of Na channel which performed Negative stain process by 2% depleted uranium solution. It is a figure for demonstrating the result of having performed the image process by the method of this invention to the cryogenic unstained Cryo-EM image of an apoferritin protein.

Explanation of symbols

F1-F5 frame T1-T5 protein particles

Claims (8)

An image processing method for specifying a position of an analysis target image in an image,
A first step of arranging in the image a plurality of frames for cutting out the local part image in the image;
A second step of averaging an image cut out by the plurality of frames to form an average frame image;
A third step of calculating a first energy value (E1) based on the average frame image;
A fourth step of selecting one frame from the plurality of frames, changing a position and an angle of the selected frame in the image, and rearranging the frame;
A fifth step of averaging the images cut out by the rearranged frames to form an average frame image;
A sixth step of calculating a second energy value (E2) based on the average frame image obtained in the fifth step;
The first and second energy values are compared, and the frame rearrangement of the fourth step is adopted when E1 <E2, while the frame rearrangement of the fourth step is adopted when E1 ≧ E2. A seventh step for determining whether to adopt the arrangement;
An eighth step of decreasing the temperature parameter T after repeating the first to seventh steps a predetermined number of times;
A ninth step of repeating the first to eighth steps a predetermined number of cycles;
An image processing method comprising: In the seventh step, when E1 ≧ E2, whether to adopt the frame rearrangement of the fourth step is determined as follows:
The adoption probability P (ΔE) is obtained from the difference (ΔE) between the first energy value E1 and the second energy value E2 by the following equation and compared with a random number. The adoption probability P (ΔE) is If it is larger than the random number, the frame rearrangement in the fourth step is adopted, while if the adoption probability P (ΔE) is equal to or less than the random number, the frame arrangement before the frame rearrangement in the fourth step is adopted. The image processing method according to claim 1, wherein the image processing method is executed.

The first and second energy values are energy values calculated based on the actual image of the image (energy value E _{real of the} actual image) or a frequency obtained based on an image obtained by performing FFT on the actual image. One of the energy values in the region (energy value E _{pow in the} frequency region) or the sum of the energy value E _{real in the} real image and the energy value E _{pow in} the frequency region (E _real + E _pow ) The image processing method according to claim 1 or 2. The energy value E _real of the real image is
Based on the luminance d (x, y) at each coordinate point of (x, y) coordinates provided in the average frame image, a pixel luminance average value d _ave is obtained by the following equation, and the average frame image d (x , y) is obtained by subtracting the pixel brightness average value d _ave from d ′ (x, y), and substituting the d ′ (x, y) value into the following equation. The image processing method according to claim 3.

(N and M are the pixel sizes of the x-axis and y-axis of the frame, and H is the luminance value when the value of E _real is 0.5) Energy value E _pow of the frequency domain, the provided in the average frame image (x, y) the luminance d at each coordinate point of the coordinate (x, y) pixel luminance average value d _ave by the following equation based on A value d ′ (x, y) obtained by subtracting the pixel luminance average value d _ave from the average frame image d (x, y) is obtained, and the spectrum is obtained by FFT from the d ′ (x, y) value. The amplitude | D '(u, v) | of the spectrum is obtained, and the amplitude | D' (u, v) | of the spectrum is multiplied by a circular mask F (u, v) that defines the transmission frequency to obtain coordinates (u , v), the image processing method according to claim 3, wherein the image processing method is obtained by calculating a sum by the following formula for each pixel in (v):

(N and M are the pixel sizes of the x and y axes of the frame) 6. The image processing method according to claim 1, wherein the rate of decrease R of the temperature parameter T in the eighth step is given by the following equation.

(T ₀ : initial temperature, T _e : final temperature at which calculation is terminated, C _max : predetermined number of times in the eighth step) An image processing program for causing a computer to execute image processing for specifying the position of an analysis target image in an image,
A first step of arranging in the image a plurality of frames for cutting out the local part image in the image;
A second step of averaging an image cut out by the plurality of frames to form an average frame image;
A third step of calculating a first energy value (E1) based on the average frame image;
A fourth step of selecting one frame from the plurality of frames, changing a position and an angle of the selected frame in the image, and rearranging the frame;
A fifth step of averaging the images cut out by the rearranged frames to form an average frame image;
A sixth step of calculating a second energy value (E2) based on the average frame image obtained in the fifth step;
The first and second energy values are compared, and the frame rearrangement of the fourth step is adopted when E1 <E2, while the frame rearrangement of the fourth step is adopted when E1 ≧ E2. A seventh step for determining whether to adopt the arrangement;
An eighth step of decreasing the temperature parameter T after repeating the first to seventh steps a predetermined number of times;
A ninth step of repeating the first to eighth steps a predetermined number of cycles;
An image processing program comprising: In the seventh step, when E1 ≧ E2, whether to adopt the frame rearrangement of the fourth step is determined as follows:
The adoption probability P (ΔE) is obtained from the difference (ΔE) between the first energy value E1 and the second energy value E2 by the following equation and compared with a random number. The adoption probability P (ΔE) is If it is larger than the random number, the frame rearrangement in the fourth step is adopted, while if the adoption probability P (ΔE) is equal to or less than the random number, the frame arrangement before the frame rearrangement in the fourth step is adopted. The image processing program according to claim 7, wherein the image processing program is executed.

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