JP2006350576A - Image processor, image processing method and image processing program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image processor for detecting a region under consideration according to the number of regions under consideration included in image data when detecting a region under consideration such as a hand region or a foot region included in the image data. <P>SOLUTION: This image processor is configured to acquire the map of score values where score values relating to such a level that each of unit regions included in image data is included in a region under consideration are associated with the positions of the unit regions in the image data, and to make a detection start point determining part 24 determine a plurality of detection start points, and to make a candidate region detection part 25 detect the candidate regions of a plurality of regions under consideration associated with the respective detection start points based on the map of the score values, and to make a hand region specification part 26 decide whether or not the candidate region is a region under consideration based on a relation between the mean value of the score values associated with the unit regions included in each candidate region and a predetermined threshold. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an image processing apparatus, an image processing method, and an image processing program for detecting an area including a portion related to a person's hand or foot included in image data.

  Detecting a part related to a person's hand or foot from image data is a very important technique for recognizing the posture and state of the person. As a method for detecting hands and feet, for example, there is a method of acquiring skin color information of the person's skin as a color distribution by some method and demarcating an image region including the hands and feet using the color distribution. For example, in order to detect a hand region by the above technique, based on the acquired skin color distribution, a score value related to the degree included in the hand region is calculated for each pixel included in the image data, and the position of each pixel is calculated. A map of score values associated with the score values is generated. Then, a hand region is detected using this score value map. When a hand region is detected using a score value map, a detection start point is first set on the score value map based on a predetermined condition. Then, using the detection start point as a base point, an area where pixels around the periphery having high score values gather is detected and determined as a hand area (see, for example, Patent Document 1).

When detecting an area using the above method, the number of hand areas and foot areas to be included in the image data is designated in advance. Accordingly, the intended number of regions can be obtained by determining the number of detection start points according to the number of designated regions and determining the region based on each of the detection start points.
Japanese Patent Laying-Open No. 2005-078257

  However, according to the technique of the conventional example, when the number of hand regions and foot regions included in the image data cannot be known in advance, the correct number of hand regions and foot regions cannot be detected.

  The present invention has been made in view of the above circumstances, and one of its purposes is to preliminarily store image data when detecting a region of interest including a part related to a person's hand or foot included in the image data. To provide an image processing device, an image processing method, and an image processing program capable of detecting an attention area according to the number of attention areas included in image data even when the number of attention areas included cannot be known. is there.

  An image processing apparatus according to the present invention for solving the above-described problem is focused on image data generated by imaging at least a part of a person, including a part related to the person's hand or foot from the image data. An image processing apparatus for detecting an area, wherein for each unit area included in the image data, a score value relating to a degree that the unit area is included in the attention area is associated with a position in the image data of the unit area. Map acquisition means for acquiring a map of the score values obtained, detection start point determination means for determining a plurality of detection start points based on a predetermined condition, and each detection start point based on the map of score values Candidate area detecting means for detecting candidate areas that are candidates for a plurality of attention areas respectively associated with each of the candidate areas, and each candidate area is included in the candidate area Characterized in that on the basis of the relationship between the average value with a predetermined threshold value of the score values associated with the unit areas including a determining area specifying means whether the candidate region is a region of interest.

  Here, the area specifying unit is configured such that, for the two candidate areas in descending order of the average value of the score values, the candidate area is an attention area based on a ratio of the average values of the score values related to the two candidate areas. It may be determined whether or not there is.

  Further, the detection start point determination means may determine the detection start point such that a plurality of the detection start points are separated by a predetermined distance or more on the score value map.

  In addition, the image processing method according to the present invention is directed to image data generated by imaging at least a part of a person using a computer, including a part relating to the hand or foot of the person from the image data. An image processing method for detecting an area, wherein for each unit area included in the image data, a score value relating to a degree that the unit area is included in the attention area is associated with a position in the image data of the unit area. Obtaining a map of score values obtained, determining a plurality of detection start points based on a predetermined condition, and corresponding to each detection start point based on the map of score values Detecting candidate areas that are candidates for a plurality of attention areas, and associating each candidate area with a unit area included in the candidate area The candidate region is characterized in that it comprises a, determining whether a region of interest based on the relationship between the average value with a predetermined threshold value of the score values.

  In addition, the image processing program according to the present invention, for image data generated by imaging at least a part of a person in a computer, includes a region of interest including a part related to the person's hand or foot from the image data. In the image processing program to be detected, for each of the unit areas included in the image data, a score value related to the degree to which the unit area is included in the attention area is associated with the position of the unit area in the image data. Obtaining a score value map; determining a plurality of detection start points based on a predetermined condition; and a plurality of detection points corresponding to the detection start points based on the score value map. Detecting a candidate area that is a candidate for the attention area; and for each candidate area, a unit area included in the candidate area Determining whether the candidate region is a region of interest based on the relationship between the average value and a predetermined threshold of response correlated obtained score value, the characterized in that for causing the computer to execute.

  According to the present invention, when detecting a region of interest including a portion related to a person's hand or foot included in the image data, even when the number of hands or feet included in the image data cannot be known in advance, The attention area can be detected according to the number of attention areas included in the image data, and the detection accuracy can be improved.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

  As shown in FIG. 1, the image processing apparatus 10 according to the embodiment of the present invention includes a control unit 11, a storage unit 12, an operation unit 13, a display unit 14, and an imaging unit 15.

  Here, the control part 11 is comprised, for example with CPU etc., and operate | moves according to the program stored in the memory | storage part 12. FIG. The storage unit 12 includes a memory element such as a RAM and a ROM and / or a disk device. The storage unit 12 stores a program executed by the control unit 11. The storage unit 12 also operates as a work memory for the control unit 11. The contents of the processing executed by the control unit 11 in the present embodiment will be described in detail later.

  The operation unit 13 is a keyboard, a mouse, or the like, receives a user's instruction operation, and outputs the content of the instruction operation to the control unit 11. The display unit 14 is a display or the like, and displays information according to an instruction from the control unit 11.

  The imaging unit 15 is a digital still camera, a video camera, or the like, and outputs image data obtained by capturing an image to the control unit 11. Note that the imaging unit 15 is not always necessary. In this case, the image data to be processed according to the present embodiment may be stored in the storage unit 12 in advance, or may be received from another device via a network by a communication unit (not shown).

  In the following, a face area including a portion related to the person's face is first extracted from the image data generated by imaging the person, and the person's color information of the person included in the face area is extracted. An example of processing executed by the image processing apparatus 10 when detecting a hand region including a portion related to the hand will be described. In addition, embodiment of this invention is not restricted to the above-mentioned form, For example, it is good also as detecting a foot area | region instead of a hand area | region. Further, the present invention can be applied to a case where a plurality of image areas (attention areas) including at least a part of the target object are detected from image data based on property information of the target object. For example, not only a person but also a plurality of regions included in image data, such as animals and robots, can be applied to various objects that can be detected using appearance property information. In this case, depending on the appearance of the target object or the data format of the image to be captured, information on other appearance properties such as pixel density information may be used instead of color information.

  As shown in FIG. 2, the image processing apparatus 10 functionally includes a face area extraction unit 21, a color histogram generation unit 22, a map generation unit 23, a detection start point determination unit 24, a candidate area detection unit 25, and a hand area. The identification unit 26 is included. These functions are stored as programs in the storage unit 12 of the image processing apparatus 10 and executed by the control unit 11.

  The face area extraction unit 21 extracts, from the image data obtained by the imaging unit 15 or the like, an image area that includes a portion related to a person's face used as sample data. When the imaging unit 15 is a video camera or the like, moving image data is obtained. In this case, the face area extracting unit 21 performs processing on still image data of each frame included in the moving image data. .

  The method for extracting the face area is not particularly limited, and any technique can be used. For example, the face area extraction unit 21 may extract a face area using statistical data regarding a face shape pattern acquired in advance by learning. Further, the face area extracting unit 21 may specify not only the position of the face but also the direction and size of the face.

  The color histogram generation unit 22 generates a color histogram representing the color distribution of pixels included in the image region extracted by the face region extraction unit 21. The generated color histogram represents the skin color information unique to the person obtained from the face color information of the person represented in the target image data.

Specifically, the color histogram generation unit 22 first converts the color values of the pixels included in the face area into values in an appropriate color space as necessary. For example, each pixel included in the original image data has 256 gradation values from 0 to 255 for each of the three primary colors red, green, and blue (hereinafter, represented by R, G, and B, respectively) It is assumed that the color of a pixel is represented by a combination of these three values. In this case, the color histogram generation unit 22 may generate a three-dimensional histogram using the values of R, G, and B as they are without performing conversion to another color space, or one of the three values. A lower-dimensional histogram may be generated using only the value of the part. In particular, when capturing the characteristics of a person's skin color, it is desirable to convert the color represented by the R, G, and B values into values in a normalized rg space or HSV space. Here, the values are converted into values in the normalized rg space. Each value of the r component and the g component on the normalized rg space is calculated by the following calculation formula.
r = R / (R + G + B)
g = G / (R + G + B)
From this calculation formula, the color histogram generation unit 22 obtains a value (r, g) in the normalized rg space from the value of (R, G, B) for each pixel. Here, r and g each take a value from 0 to 1.

  Further, the color histogram generation unit 22 determines in which bin of the color histogram the value in the color space converted as necessary for each pixel included in the face region. Here, an appropriate predetermined value is used as the number of bins in the histogram. For example, assuming that the number of bins is 50 for each of the r component and the g component, the generated color histogram is a two-dimensional histogram having 50 × 50 bins. Since r and g each take a value from 0 to 1, when the bin width is uniform, each bin width is 1/50.

  In this way, the color histogram generation unit 22 generates a color distribution in a predetermined color space as a color histogram for the pixels included in the image region extracted by the face region extraction unit 21. This color histogram has, for each bin, the number of pixels having the color of the component corresponding to that bin as the frequency. Further, the frequency may be a value obtained by dividing the number of pixels having the component color corresponding to the bin by the number of pixels to be investigated. In this case, the frequency of each bin is expressed as a ratio with respect to all the pixels included in the image area, and becomes 1 when the frequencies of all bins are summed.

  The map generation unit 23 generates a score value map (activation map) using the color histogram data generated by the color histogram generation unit 22. Here, the score value map relates to the position information on the pixel data of each pixel included in the image data to be processed and the degree to which the pixel is included in the hand region to be detected. This is data in which score values are associated with each other. The score value is a value obtained by calculating the degree of inclusion of each pixel included in the image data in the attention area (in this embodiment, the hand area) by a predetermined method. For example, the score value can be calculated based on the likelihood representing the probability that the pixel is included in the hand region. In the present embodiment, the score value is calculated mainly based on information regarding the degree of possibility that the color of the pixel is the skin color of a person captured in the image data.

  As a method for calculating the score value, a method such as a back projection method or a correlation method can be used. Specifically, for example, the following is performed. That is, first, the color value of the pixel for which the score value is calculated is converted into a value in the color space used by the color histogram generation unit 22 as necessary. Then, in the color histogram obtained by the color histogram generation unit 22, the frequency value of the bin corresponding to the color information of the pixel after conversion is set as the skin color score value of the pixel.

  Here, since the face area extracted by the face area extracting unit 21 is excluded from the target from which the hand area detecting unit 25 detects the hand area, the score value need not be calculated. In this case, by setting the score value of the pixel included in the image area to 0, it can be excluded from the object detected by the hand area detection unit 25.

  Further, when calculating the score value, the positional relationship with the face area may be taken into consideration. That is, from the information on the position and size of the face area and the orientation of the face, even if the pixel at a position where the possibility that the hand is likely to exist is the same skin color information, The score value is calculated so that the score value is higher than that of a pixel at a position considered to be unlikely to exist. In this way, the hand area can be detected with higher accuracy.

  In the score value map obtained in this way, pixels having colors close to the color information of the face area extracted by the face area extracting unit 21 have a high score value, and a high score is given to an area considered to be a hand area. Pixels with values will be collected.

  The detection start point determination unit 24 determines a plurality of positions (detection start points) as base points when the candidate region detection unit 25 detects a candidate region of the hand region based on a predetermined condition. As a method of determining the detection start point, there is a method of determining based on the score value of each pixel on the score value map. For example, a predetermined number of pixels are determined as detection start points in descending order of score values from all pixels.

  For example, the detection start point may be determined by the following method. That is, when a square area whose size is determined by a predetermined method is prepared and the entire score value map is scanned by this square area, the average value of the score values of the pixels included in the square area is high. A predetermined number of such positions are determined in descending order of the average value. Then, the center of the square area at that position is determined as the detection start point. In this case, the size of the square area may be set to be 0.4 times the size of the face area, for example, based on the size of the face area extracted by the face area extraction unit 21. Thereby, compared with the case where the detection start point is simply determined based on a pixel having a high score value, it is possible to reduce the influence of noise caused by a pixel having a high score value although it is not a hand region.

  In addition, when the original image data is image data of a frame included in the moving image, if the hand area has already been detected for the image data of the previous frame in time, the previous image can be obtained. The detection start point may be determined based on the position of the hand region. In the case of a moving image, the position of the hand region is unlikely to change suddenly in the preceding and following frame images, and according to this method, a position that is more likely to be a hand region can be determined as a detection start point. it can. Alternatively, based on the position and size of the face area, the orientation of the face, etc., the detection start point is determined from areas that are likely to have a hand area based on the relative positional relationship with the face. May be.

  Furthermore, when the detection start point determination unit 24 determines a plurality of detection start points, the detection start point determination unit 24 may determine that the detection start points are separated by a predetermined distance or more. For example, the size estimated as the size of the hand region is estimated based on the size of the face region, and a predetermined distance is determined based on the estimated size. This facilitates detection of a plurality of hand regions that are separated from each other.

  The candidate area detection unit 25 has a purpose of detecting, on the score value map generated by the map generation unit 23, using each detection start point on the score value map determined by the detection start point determination unit 24 as a base point. A hand region candidate region that is an image region is detected. Specifically, the candidate area detection unit 25 identifies, for each detection start point, an area in which a pixel having a high score value near the detection start point is gathered on the score value map. Is detected. A plurality of candidate areas are detected according to a plurality of detection start points.

  The method for detecting the candidate area by the candidate area detection unit 25 is not particularly limited, but here, a cam shift algorithm (Gary R. Bradski, Computer Vision Face Tracking For Use in a Perceptual User Interface: Intel Technology Journal Q2, 1998) is used. The used example will be described.

  When using the cam shift algorithm, first, a square area having a certain size (hereinafter referred to as a template) is set with the detection start point as the center, and information on score values of pixels included therein is used to determine a predetermined area. A value (hereinafter referred to as a moment) for determining the possibility of a hand region is calculated by the function of Candidate area detection unit 25 determines the center of gravity of the template based on this moment, moves the center of the template to the determined center of gravity, and recalculates the moment at that position. Similarly, until the distance between the newly obtained center of gravity and the previously obtained center of gravity is equal to or smaller than a predetermined value (that is, the position of the center of gravity converges) or until the number of repetitions reaches a predetermined value. Repeat the process. Thereby, the position of the center of gravity of the finally obtained template is provisionally determined as the center of the candidate area.

  Subsequently, the size and inclination of the template are changed based on the value of the moment, and the above processing is repeated until the position of the center of gravity converges again. By repeating this series of processing until all of the position, size and inclination converge or the number of repetitions reaches a predetermined value, the position, size and inclination of the template finally obtained are the positions of the candidate areas. , Determined as size and slope.

The hand region specifying unit 26 specifies a region satisfying a predetermined condition as a hand region from among a plurality of candidate regions detected by the candidate region detecting unit 25 according to a plurality of detection start points. Below, the procedure in which the hand region specifying unit 26 specifies the hand region will be described based on the flowchart of FIG. Here, the number of candidate areas detected by the candidate area detection unit 25 is N, and the average value of the score values of the pixels included in each candidate area T _k (k = 1, 2,..., N). _Is represented by Sk.

First, the hand region specifying unit 26, the size of the candidate region T _k is determined whether a predetermined condition is satisfied, excluded from further processing the candidate region does not satisfy a predetermined condition (S1). Specifically, for example, it is determined whether or not the width and height of the candidate area are included in a predetermined range. If not included, the candidate area is determined not to be a hand area. The predetermined range may be determined based on the size of the entire image data or the size of the face area, for example. Further, when the original image data is image data of a frame included in the moving image data, a predetermined range is determined based on the size of the hand area detected with respect to the frame temporally prior to the frame. May be determined.

Next, for the candidate regions T _k that remain without being excluded in the processing of S1, the hand region specifying unit 26 selects a candidate region having the highest average score S _k of the pixels included in each region as the first candidate. Set as region T _s . Further, the candidate area with the second highest average score value is set as the second candidate area _Tf (S2). The first candidate area and the second candidate area are candidates that are finally determined to be hand areas among the plurality of candidate areas detected by the candidate area detection unit 25. Here, the average value of the score values of the pixels included in the first candidate region is S _f , and the average value of the score values of the pixels included in the second candidate region is S _s .

Subsequently, the hand region specifying unit 26 first determines whether or not S _s is larger than a predetermined threshold (S3). Here, the predetermined threshold value is set to a value such as 0.005 based on data such as an average value of score values of hand regions detected in the past. When the value is equal to or smaller than the predetermined threshold, it is estimated that the second candidate region T _s is not a hand region.

When S _s is equal to or smaller than the predetermined threshold, the hand region specifying unit 26 next determines whether or not S _f is larger than the predetermined threshold (S4). Here, it is assumed that the predetermined threshold is the same value as that used in S4. When _{Sf is} also equal to or smaller than a predetermined threshold, it is estimated that the first candidate region _Tf is not a hand region. Therefore, the hand area specifying unit 26 determines that the hand area is not included in the image data, and ends the process (S5). On the other hand, when S _f is greater than a predetermined threshold value is considered the first candidate region T _f is a hand region. Accordingly, it is determined that only one hand region is included in the image data, and the first candidate region _Tf is specified as the hand region (S6).

On the other hand, when it is determined in the process of S3 that S _s is larger than the predetermined threshold, the hand region specifying unit 26 determines that both the first candidate region T _f and the second candidate region T _s are hand regions. You may judge. However, here, in order to further increase the detection accuracy, it is determined whether or not the ratio of S _s to S _f is greater than a predetermined threshold (S7). Specifically, it is determined whether S _f / S _s is greater than 2.0, for example. If this, for example S _f there is a large difference in the average value of the score values of the two candidate regions such that twice the S _s, one of the candidate region is not the very hand region. As described above, when determining whether or not the hand region is a ratio using the ratio of S _f and S _s , even if the candidate region is larger than the threshold used in S3, it may be determined that it is not a hand region. It will be.

_If the ratio of S _s to S _f is greater than a predetermined threshold, it is determined that the second candidate region T _s is not a hand region, and the hand region specifying unit 26 specifies only the first candidate region T _f as a hand region ( S6). On the other hand, when the ratio of S _s to S _f is equal to or smaller than a predetermined threshold, both the first candidate region T _f and the second candidate region T _s are considered to be hand regions. Accordingly, the hand region specifying unit 26 determines that the hand region is included two in the image data, identifying a first candidate region T _f and the second candidate region T _s as the hand region (S7).

  Information on the hand region obtained by the above processing is recorded in the storage unit 12 as information on the posture and state of the person, or used for other processing. In addition, when the image data to be processed is frame image data that is a part of a moving image, a hand region is detected for each frame of the moving image data, and difference information of the hand region for each frame is detected. It becomes possible to grasp the movement of a person's hand.

  According to the embodiment of the present invention described above, it is possible to know in advance the number of hand regions included in image data by determining whether a candidate region is a hand region based on a predetermined threshold. Even if it is not possible or when detecting a hand area from a moving image including occlusion (hidden area), the hand area can be detected according to the number of hands included in the image data, and the detection accuracy of the hand area is improved. It can be improved.

  In addition, by applying this embodiment to the foot region, the number of feet included in the image data even when the number of foot regions cannot be known in advance, as in the case of detecting the hand region. The foot region can be detected according to In this case, the candidate area may be detected and the foot area may be specified using a map of score values different from that used for detecting the hand area calculated including information on the positional relationship with the face area. . In addition, the candidate area is detected by a map of score values based on the skin color distribution of the face area, similar to that used for detecting the hand area, and the positional relationship with the face area or the positional relationship with the already detected hand area, and The foot region may be specified based on a predetermined threshold set to specify the foot region. Furthermore, in this case, based on the ratio between the average score value of the pixels included in the hand region in the image data and the average score value of the pixels included in the candidate region of the foot region, the candidate region is You may perform the process which determines whether it is a foot area | region.

  In the above description, an example in which a score value is set for each pixel included in the image data and a score value map is generated has been described. However, the score value map generated by the map generation unit 23 is not necessarily a unit. Pixels may not be used as regions. For example, by setting a set of a plurality of pixels such as 2 × 2 4 pixels as a unit region and setting a score value for each unit region, information that is coarser than when a score value is set for each pixel A map of score values with quantities is obtained. Although the detection start point determination unit 24 and the candidate region detection unit 25 detect the candidate region for the score value map, the accuracy of the detected attention region is reduced, but the attention region is detected with a smaller calculation amount. can do.

  In the above description, the face area extraction unit 21 first extracts a face area, and the color histogram generation unit 22 generates a color histogram from the pixels included in the obtained face area. It is not restricted to such a form. That is, the color histogram may be given in advance as a color distribution of a predetermined skin color, or learning data obtained by a process of detecting a past attention area may be used. In addition, when a region of interest is detected from image data of each frame included in the moving image, a score value map is generated using the color histogram generated by the color histogram generation unit 22 for the image data of the previous frame. It is good.

It is a block diagram showing the structure of the image processing apparatus which concerns on embodiment of this invention. It is a functional block diagram showing the function of the image processing apparatus which concerns on embodiment of this invention. It is a flowchart which shows an example of the process performed by the image processing apparatus which concerns on embodiment of this invention.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 10 Image processing apparatus, 11 Control part, 12 Storage part, 13 Operation part, 14 Display part, 15 Imaging part, 21 Face area extraction part, 22 Color histogram generation part, 23 Map generation part, 24 Detection start point determination part, 25 Candidate area detection unit, 26 hand area identification unit.

Claims (5)

An image processing device for detecting a region of interest including a portion related to a hand or a foot of the person from the image data generated by imaging at least a part of the person,
For each unit area included in the image data, a map acquisition is performed for acquiring a score value map in which a score value related to the degree to which the unit area is included in the attention area is associated with a position in the image data of the unit area. Means,
Detection start point determination means for determining a plurality of detection start points based on a predetermined condition;
Candidate area detection means for detecting candidate areas that are candidates for a plurality of attention areas respectively associated with the respective detection start points based on the map of score values;
For each candidate area, an area for determining whether or not the candidate area is an attention area based on a relationship between an average value of the score values associated with the unit areas included in the candidate area and a predetermined threshold value Specific means,
An image processing apparatus comprising: The image processing apparatus according to claim 1.
The area specifying unit determines whether the candidate area is an attention area based on a ratio of the average values of the score values related to the two candidate areas for the two candidate areas in descending order of the average value of the score values. An image processing apparatus characterized by determining whether or not. The image processing apparatus according to claim 1 or 2,
The image processing apparatus according to claim 1, wherein the detection start point determination means determines the detection start points such that a plurality of the detection start points are separated by a predetermined distance or more on the score value map. An image processing method for detecting a region of interest including a portion related to a hand or a foot of the person from the image data generated by imaging at least a part of the person using a computer,
For each unit area included in the image data, obtaining a score value map in which a score value related to the degree to which the unit area is included in the attention area is associated with a position in the image data of the unit area; ,
Determining a plurality of detection start points based on a predetermined condition;
Detecting candidate regions that are candidates for a plurality of attention regions respectively associated with the respective detection start points based on the map of score values;
For each of the candidate regions, a step of determining whether or not the candidate region is a region of interest based on a relationship between an average value of the score values associated with the unit regions included in the candidate region and a predetermined threshold value When,
An image processing method comprising: An image processing program for causing a computer to detect a region of interest including a portion related to a person's hand or foot from the image data generated by imaging at least a part of the person,
For each unit area included in the image data, obtaining a score value map in which a score value related to the degree to which the unit area is included in the attention area is associated with a position in the image data of the unit area; ,
Determining a plurality of detection start points based on a predetermined condition;
Detecting candidate regions that are candidates for a plurality of attention regions respectively associated with the respective detection start points based on the map of score values;
For each of the candidate regions, a step of determining whether or not the candidate region is a region of interest based on a relationship between an average value of the score values associated with the unit regions included in the candidate region and a predetermined threshold value When,
An image processing program for causing the computer to execute.

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