JP2006051280A - Digital signal processing method, digital signal processing apparatus, and computer program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To stably perform digital signal interpolation.
The maximum number of terms k of the polynomial is changed in a range of 1 to K, the coefficients of the polynomial are obtained with the respective maximum number of terms, and the interpolation value at the sample point 201 is calculated using the obtained polynomial. At every sample point 201, the sum of squares of the difference between the original value of the sample point 201 and the interpolated value is calculated, and the total error at the sample point is obtained. Then, the interpolation value at the evaluation point 202 inserted evenly between the samples 201 is calculated using the polynomial, and the estimated shift at the evaluation point 202 using a local interpolation method such as nearest neighbor pixel interpolation. A vector value (interpolation value) is calculated, and the sum of squares of the difference between the calculated interpolation values is calculated to obtain a total error at the evaluation point. Then, the total error at the sample point 201 and the total error and sum at the evaluation point are calculated with a predetermined weight, and the goodness of the interpolation polynomial is evaluated.
[Selection] Figure 1

Description

  The present invention relates to a digital signal processing method, a digital signal processing apparatus, and a computer program, and is particularly suitable for use in interpolating digital signal values.

  In the time-dependent CAD (Computer Aided Diagnosis) technique of an X-ray image, first, a first image obtained by imaging a part (for example, lung region) of a common subject (subject). For the second image, a plurality of sets of corresponding points are obtained. Then, a shift vector representing the amount of misalignment between corresponding points is obtained, and further interpolated to correct changes in the lung region caused by various factors such as changes in the posture of the subject and breathing, Difference processing is performed on the image and the second image. In this way, a portion in which both the first image and the second image are changed is depicted in the difference image.

  At this time, by using the temporal difference technique, it is possible to cancel common normal structures such as bones and blood vessels in the two images (first image and second image) and extract only the change in the lesion. Therefore, by using the time-difference CAD technology, it is possible to expect clinically early detection of lesions, particularly lesions hidden in normal structures such as ribs and blood vessels, prevention of missed lesions, and rapid interpretation.

FIG. 13 shows an outline of the algorithm of the time difference CAD.
In FIG. 13, first, a first image and a second image of the same part of a subject photographed at different times are input to the preprocessing units 1100 and 1200 from the non-instructed image storage unit. A set of images consisting of the first and second images is digitized. Next, the registration unit 1300 selects many small regions of interest (ROI), and performs image registration using the selected ROI. Image registration consists of local matching applied to each pair of corresponding ROIs of the two images and a mapping of shift values indicating the amount of local matching between each pair of corresponding ROIs. .

  The shift vector interpolation unit 1400 interpolates the x and y components of the shift vector calculated by the alignment unit 1300 with a two-dimensional polynomial. In the subtraction unit 1500, warping is performed so that one of the first image and the second image is matched with the other, and the difference between the first image and the second image is taken to create a difference image.

The post-processing unit 1600 performs image processing suitable for the difference image, and outputs it to the output unit 1700 such as a monitor.

  Here, in the shift vector interpolation technique performed using a two-dimensional polynomial, each input point is used as a sample point, and each sample point is obtained by using the two-dimensional data at each sample point by the least square error method or the like. The coefficients of each polynomial term are obtained so as to minimize the input data and the interpolation data at, and the input two-dimensional data is approximated. In the interpolation of the shift vector using the two-dimensional polynomial, the coefficient is obtained over the entire region where the corresponding points exist, so that the input two-dimensional data can be smoothly interpolated and is hidden in the two-dimensional data. Noise can also be suppressed to some extent (see Patent Document 1).

JP-A-7-37074

  In the time difference technique, in order to obtain a shift vector at the corresponding point (sample point), for example, a matching technique such as a cross-correlation operation is often used for the template ROI, data, and search ROI. In order to improve the alignment accuracy, it is necessary to obtain shift vectors at many corresponding points. However, when interpreting medical images, it is practical to be able to create differential images at high speed on the spot to improve throughput. This is desirable from the standpoint of optimization, and increasing the number of corresponding points has a problem that it takes time to execute due to an increase in the amount of computation.

  Here, since the distribution of the shift vector tends to change relatively smoothly as a whole image, the number of corresponding points described above, that is, the number of sample points, is reduced, and the maximum number of terms of the interpolation polynomial is reduced, so Calculation time can be suppressed while ensuring accuracy. However, changes in the posture of the subject depicted in images taken at different times may be accompanied by complex deformations. For example, in FIG. 14, the shift vector in the upper right lung field points in the horizontal direction, but this is different from the overall average direction, and it is sufficient to use an interpolation polynomial with a low maximum number of terms. Accurate alignment accuracy cannot be secured.

  If the maximum number of terms of the interpolation polynomial is increased, there is a problem that if the number of sample points is small, the interpolation value will oscillate between the sample points, so it is necessary to select the optimal polynomial while reducing the computation time. It has been difficult to perform an interpolation process that can ensure accurate alignment accuracy.

  The present invention has been made in view of the above circumstances, and an object thereof is to enable stable interpolation of digital signals.

  In order to solve the above-described problems, a digital signal processing method according to the present invention includes a first interpolation value calculation step for obtaining an interpolation value at each sample point of a digital signal, and a first step for obtaining an error of the interpolation value at each sample point. An interpolation value error evaluation step, a second interpolation value calculating step for arranging a predetermined number of evaluation points between the sample points, and obtaining an interpolation value at the arranged evaluation points, and an interpolation value at the evaluation point Based on the second interpolation value error evaluation step for obtaining the error, the error of the interpolation value at each sample point, and the error of the interpolation value at the evaluation point, a total of interpolation equations used to interpolate the digital signal And an overall error evaluation step for obtaining a general error.

  The digital signal processing apparatus of the present invention includes a first interpolation value calculation means for obtaining an interpolation value at each sample point of the digital signal, a first interpolation value error evaluation means for obtaining an error of the interpolation value at each sample point, A second interpolation value calculating means for arranging a predetermined number of evaluation points between the sample points and obtaining an interpolation value at the arranged evaluation points; and a second interpolation value for obtaining an error of the interpolation value at the evaluation point. Comprehensive error evaluation for obtaining a comprehensive error of an interpolation formula used for interpolating the digital signal based on an error evaluation means, an error of an interpolation value at each sample point, and an error of an interpolation value at the evaluation point Means.

  The computer program of the present invention includes a first interpolation value calculation step for obtaining an interpolation value at each sample point of a digital signal, a first interpolation value error evaluation step for obtaining an error of the interpolation value at each sample point, A second interpolation value calculation step for determining a predetermined number of evaluation points between the sample points, obtaining an interpolation value at the arranged evaluation points, and a second interpolation value error evaluation for obtaining an error of the interpolation value at the evaluation point A total error evaluation step for obtaining a total error of an interpolation formula used for interpolating the digital signal based on the error of the interpolation value at each sample point and the error of the interpolation value at the evaluation point; Is executed by a computer.

  According to the present invention, in addition to the evaluation of the interpolation value at the sample points of the digital signal, the evaluation of the interpolation value at the evaluation points arranged between the sample points is performed, and these are comprehensively evaluated. Regardless of only the interpolation accuracy at the point, the vibration of the interpolation data generated by the higher-order interpolation equation can also be measured, and the overall accuracy of the interpolation equation can be evaluated.

  Further, according to the present invention, the maximum number of interpolation polynomials for interpolating the digital signal is determined dynamically, so that the digital signal can be obtained regardless of the magnitude of the data change at the corresponding point (sample point). It is possible to determine the maximum number of polynomial terms that are optimal for interpolating the digital signal, and to perform digital signal interpolation more stably. In addition, when obtaining a time difference signal representing a change over time in a plurality of digital signals, the number of sample points can be reduced, so that the processing speed can be improved.

Next, embodiments of the present invention will be described with reference to the drawings.
<First Embodiment>
FIG. 1 is a block diagram showing an example of an X-ray image processing system according to the first embodiment of the present invention.

In FIG. 1, the image processing system includes an X-ray imaging device 10, an image processing device 20, and a display device 30.
The image processing apparatus 20 is for capturing and processing an X-ray image obtained by the X-ray imaging apparatus 10. The image processing apparatus 20 is a personal computer, for example, and includes a ROM in which a control program for operating the image processing apparatus 20 is recorded, and a CPU for executing the control program and controlling the image processing apparatus in an integrated manner. And a RAM serving as a work area when the CPU executes the control program.
The image processing apparatus 20 includes an image input unit 20a, a matching unit 20b, a shift vector interpolation unit 20c, an image warping unit 20d, and a difference processing unit 20e. It goes without saying that the image processing apparatus 20 has functions other than these.

  The image input unit 20 a inputs an X-ray image obtained by the X-ray imaging apparatus 10. For example, the image input unit 20a inputs two X-ray images of the same part of the subject taken at different times. The matching unit 20b aligns one X-ray image input by the image input unit 20a with the other X-ray image.

  Specifically, the matching unit 20b first roughly aligns both X-ray images and obtains an overall shift amount of the examination site. Based on this shift amount, a plurality of template ROIs (Region Of Interest) are set for one X-ray image, and a plurality of search ROIs are set for corresponding points in the other X-ray image.

  Next, an area that most closely matches the template ROI is searched in the search ROI, and the amount of horizontal and vertical movement between the center of the template ROI and the center of the area is set as a shift vector. By performing this process for each of the plurality of template ROIs, a plurality of shift vectors representing the positional deviation between the two X-ray images at each corresponding point are obtained as shown in FIG.

  The shift vector interpolation unit 20c performs two-dimensional polynomial interpolation on the horizontal and vertical components of the plurality of shift vectors detected by the matching unit 20b. The processing in the shift vector interpolation unit 20c will be described in detail.

  The warping unit 20d calculates the corresponding position in the other X-ray image for each pixel of one X-ray image using the polynomial obtained by the shift vector interpolation unit 20c, performs the warping process, and the difference processing unit 20e One X-ray image warped to the other X-ray image is subtracted from the other X-ray image, and the difference result is displayed on the display device 30.

FIG. 2 is a block diagram illustrating the function of the shift vector interpolation unit 20c.
The shift vector interpolation unit 20c includes an overall error evaluation unit 20c1, an optimum term number measurement unit 20c2, an interpolation formula determination unit 20c3, and an interpolation value calculation unit 20c4.
The total error evaluation unit 20c1 changes the maximum number k of interpolation polynomials for interpolating the shift vector from 1 to K (K is a natural number of 2 or more), and the total error E _k (k = 1, ..., K) is calculated.
The optimum term number measurement unit 20c2 searches for the minimum total error from the total errors E _k (k = 1,..., K) of the respective interpolation polynomials obtained by the total error evaluation unit 20c1, and indicates the minimum total error. The maximum number of terms k of the interpolation polynomial is obtained and set as the optimum number of terms.

The interpolation formula determination unit 20c3 calculates the coefficient of the interpolation polynomial using the optimum number of terms obtained by the optimum term number measurement unit 20c2 as the maximum number of terms of the interpolation polynomial.
The interpolation value calculation unit 20c4 calculates shift vector values of points to be interpolated over the entire image using the coefficients of the interpolation polynomial calculated by the interpolation formula determination unit 20c3.

FIG. 3 is a block diagram illustrating the function of the total error evaluation unit 20c1.
The data input unit 101 receives the shift vector data output from the matching unit 20b, and uses the horizontal and vertical components of the shift vector at each sample point and the coordinate position of the sample point as sample point data. 1 shift vector interpolation unit 102 and evaluation point insertion unit 105 respectively.

The first shift vector interpolation unit 102 obtains the polynomial coefficient c _K by the least square error method using the maximum term number k set by the maximum term number setting unit 104 over the entire area occupying the sample points. The maximum number-of-terms setting unit 104 changes the maximum number of terms k in the range of 1 to K, and the first shift vector interpolation unit 102 is a polynomial coefficient c _K (k = 1) corresponding to the value of each maximum number of terms k. , ..., K).

Here, the interpolation polynomial f (x, y) is shown in Expression (1). Here, m is the maximum number of terms in the abscissa x of each term of the interpolation polynomial x ⁱ y ^j , and n is the maximum number of terms in the ordinate y. k is the maximum number of terms of the interpolation polynomial. Polynomial interpolation uses the coordinate position as a variable, and calculates the value of the coordinate position.

In order to obtain each coefficient of the polynomial, the first shift vector interpolation unit 102 solves the equation shown in Expression (2). In Expression (2), L is the number of sample points. The sample points are arranged in two-dimensional data as shown in FIG. 14, but are rearranged in the scanning order and handled as one-dimensional data. As described above, in this embodiment, in order to compensate for an error in the shift vector obtained in the matching unit 20b, the number L of sample points is larger than the maximum number k of polynomial terms, and the polynomial coefficient c _K (k = 1, …, K) cannot be uniquely determined. For this reason, each coefficient of the interpolation polynomial is obtained by Equation (4) using the least square error method that minimizes the weighted square error S at each sample point shown in Equation (3). Here, w _i is the weight of the i-th sample, and W is a diagonal matrix in which w _i are arranged diagonally. w _i is an amount representing the goodness of matching when ROI matching is calculated by the matching unit 20b. For example, when cross-correlation is used for matching, it is determined based on the magnitude of the cross-correlation coefficient.

  Next, the first shift vector interpolation unit 102 outputs the obtained polynomial coefficients to the sample point error calculation unit 103 and the evaluation point error calculation unit 107, and the sample point polynomial interpolation value and the evaluation point polynomial respectively. Calculate the interpolated value.

The sample point error calculation unit 103 receives the polynomial coefficient from the first shift vector interpolation unit 102 and calculates the interpolation value ν _i at all the sample points from the equation (5). Then, from Equation (6), the horizontal (horizontal) and vertical (vertical) components of the shift vector at each sample point output from the data input unit 101, and the respective interpolated values ν _{i at} each sample point. And the weighted square sum S is taken as the total error of the sample points. Note that the sample point error calculation unit 103 may simply use the sum of squares as the total error instead of the weighted sum of squares.

  On the other hand, the evaluation point insertion unit 105 receives the sample point coordinate position data from the data input unit 101 and equally inserts evaluation points (white circles in FIG. 4) 202 between the sample points (black circles in FIG. 4) 201. . The position coordinate data of the inserted evaluation point 202 is output to the second shift vector interpolation unit 106. As shown in FIG. 4, in this embodiment, intermediate coordinates are obtained from the coordinates of sample points 201 that are adjacent in the vertical, horizontal, and diagonal directions, and these points are used as evaluation points 202.

  The second shift vector interpolation unit 106 receives the coordinates of the sample point data from the data input unit 101 and the coordinates of the evaluation points from the evaluation point insertion unit 105, and uses the local interpolation method to insert the evaluation points. Find the interpolation factor. Here, as a local interpolation method, there are nearest neighbor pixel interpolation obtained by Expression (7), bilinear interpolation and cubic interpolation obtained by Expression (8), and the like. The estimated shift vector of the evaluation point is estimated using the obtained interpolation coefficient, and then output to the evaluation point error calculation unit 107. As a local interpolation method, a known affine transformation or local polynomial interpolation may be used from sample points around the evaluation point.

FIG. 5 shows the difference between polynomial interpolation and local interpolation by taking the horizontal component of a single row of shift vectors as an example. A black circle in FIG. 5 indicates the shift vector value of the sample point 201, and a white circle in FIG. 5 indicates the estimated shift vector value of the local interpolation result at the evaluation point 202.
The smooth curve Q is the result of polynomial interpolation. The difference ν _i −u _i (solid arrow in FIG. 5) between the shift vector value at the sample point and the polynomial interpolation result is taken as the total error of the sample points, and the estimated shift vector value at the evaluation point and the polynomial interpolation result The sum of weighted squares of the difference ν _i −ν ′ _i (broken arrow in FIG. 5) is defined as the total error of the evaluation points.
Weight at the evaluation point, using the weights w _i of sample points, as shown in the formula (9) into equation (10) is determined by calculation similar to the local interpolation method for estimating the shift vector.

In evaluation point error calculation unit 107, by using a polynomial interpolation coefficients from the first shift vector interpolation unit 102 calculates the polynomial interpolation value [nu _i at the evaluation point, at the same time, the local interpolation value Nyu' _i at the evaluation point Received from the second shift vector interpolation unit 106, the total error at the evaluation point is calculated by the equation (11). However, L 'is a score of evaluation points.

Finally, the total error calculation unit 108 calculates an error E _{k obtained} by combining the sample points and the evaluation points in the maximum number of terms _k using Expression (12). Here, w is the weight of the total error at the sample points, and may be determined so that the total error at the evaluation points can be sufficiently considered empirically.

  In the present embodiment, the total error between the sample points and the evaluation points does not need to be limited to Equation (6), and may be an absolute sum of weighted differences or may not be weighted.

  In this way, not only the interpolation results at the sample points of a plurality of images are evaluated, but also evaluation points are inserted between the sample points, and the interpolation results at the evaluation points are also evaluated, and these are comprehensively evaluated. As a result, the interpolation of the shift vector can be performed more stably than before, and the number of sample points can be reduced.

FIG. 6 is a flowchart for explaining the flow of processing in the shift vector interpolation unit 20c. Hereinafter, processing contents will be described for each step.
Step S201: When the shift vector data output from the matching unit 20b is input to the data input unit 101, the data input unit 101 includes the horizontal (horizontal) and vertical (vertical) components of the shift vector. The coordinates of the sample points are output to the first shift vector interpolation unit 102 and the evaluation point insertion unit 105.

Step S202: The maximum term number setting unit 104 sets the maximum term number k of the interpolation polynomial to 1.
Step S203: It is determined whether or not the maximum term number k of the interpolation polynomial is larger than the upper limit value K of the change range. If it is larger, the process of the comprehensive error evaluation unit 20c1 is terminated, and the process proceeds to Step S214. If so, go to step 204.
Step S204: The first shift vector interpolation unit 102 obtains a polynomial coefficient c _k by the least square error method as the maximum number k of terms of the interpolation polynomial.
Step S205: The sample point error calculation unit 103 calculates the interpolation value ν _i at all the sample points.

Step S206: The sample point error calculation unit 103 calculates the total error at the sample points. Weighted sum of squares of the horizontal (horizontal) and vertical (vertical) components of the shift vector at each sample point, which is the output value of the data input unit 101, and the respective polynomial interpolation value ν _{i at} each sample point Is calculated as the total error S sample point of the sample points.
Step S207: The evaluation point insertion unit 105 sets evaluation points based on the sample point coordinates output from the data input unit 101.
Step S208: The second shift vector interpolation unit 106 estimates an estimated shift vector at each evaluation point by a local interpolation method.

Step S209: The second shift vector interpolation unit 106 calculates the weight of each evaluation point by a local interpolation method.
Step S210: The evaluation point error calculation unit 107 calculates the polynomial interpolation value ν _i at each evaluation point using the polynomial interpolation coefficient from the first shift vector interpolation unit 102.
Step S211: The evaluation point error calculation unit 107 receives the local interpolation value ν ′ _i at each evaluation point from the second shift vector interpolation unit 106, and calculates an error S evaluation point at each evaluation point.

Step S212: The total error calculation unit 108 calculates a total error E _k that combines the sample points and the evaluation points in the maximum number of terms _k .
Step S213: The total error E _k is output to the optimum term number measurement unit 20c2, and this total error E _k is stored in the optimum term number measurement unit 20c2.
Step S214: Increment the maximum number of terms k and return to step S203.

Step S215: The maximum term number k is changed in the range of 1 to K (k = 1 to K), and after obtaining the total error E _k for all the maximum term numbers k, the optimum term number measuring unit 20c2 However, the optimum maximum number of terms k ₁ that minimizes the value of the total error E _k is searched.
Step S216: The interpolation formula determination unit 20c3 calculates the optimum interpolation polynomial coefficient c _k1 using the optimum maximum number of terms k ₁ that minimizes the total error E _k obtained in step S214.
Step S217: The interpolation value calculation unit 20c4 calculates a shift vector value of points to be interpolated over the entire image using the polynomial coefficient obtained in step S215.

<Modification of First Embodiment>
FIG. 7 is a diagram for explaining a modification of the first embodiment. When the maximum term number k is changed in the range of 1 to _K and the polynomial coefficient _ck is obtained by the first shift vector interpolation unit 102, the correspondence between the maximum number k and the polynomial coefficient _ck is stored in the storage unit 109. The difference from the first embodiment is that it is stored in the first embodiment.
Therefore, in the operation flow of this modification, instead of calculating the optimum interpolation polynomial coefficient c _{k1 in} step S216, the optimum interpolation polynomial coefficient c _k1 is read from the storage unit 109.

<Second Embodiment>
Next, a second embodiment of the present invention will be described. FIG. 8 is a diagram illustrating an example of the arrangement of corresponding points according to the second embodiment of this invention. As shown in FIG. 8, in this embodiment, the sample points (corresponding points) 301 are arranged at the contour portion of the lung field, which is an anatomically characteristic position. The basic concept for evaluating the shift vector interpolation formula in this embodiment is basically the same as that in the first embodiment as shown in FIGS. The processing in step S207 for arranging is different from that in the first embodiment. Hereinafter, detailed description of the same parts as those in the first embodiment will be omitted.

  FIG. 9 is a flowchart showing in detail an example of evaluation score insertion processing in the evaluation score insertion unit 105 of FIG. FIG. 10 is a diagram illustrating an example of the arrangement of sample points and inserted evaluation points.

Step S301: The evaluation point insertion unit 105 determines whether or not the processing of steps S302 and S303 has been performed for all the sample points. If all the sample points have not been processed, the processing proceeds to step S302. If all sample points have been processed, the evaluation point insertion unit 105 ends the process.
Step S302: The evaluation point insertion unit 105 obtains the closest sample point (for example, the sample point 301b in FIG. 9) located at the lower right of the original sample point to be processed (for example, the sample point 301a in FIG. 9).

Step S303: The evaluation point insertion unit 105 calculates an intermediate point of a line segment connecting the sample point (for example, the sample point 301b in FIG. 9) obtained in Step S302 and the original sample point (for example, the sample point 301a in FIG. 9). Assume that it is an evaluation point (for example, evaluation point 302 in FIG. 9). If there is no sample point at the lower right of the sample point to be processed, there is no evaluation point.
Step S304: Move to the next sample point and return to Step S301.

  In this embodiment, the sample point closest to the lower right of the original sample point to be processed is searched. However, this is not necessarily required, and the upper left, upper right, Alternatively, the closest sample point may be searched in a direction such as the lower left, or the sample point closest to the original sample point to be processed may be searched regardless of the direction.

<Third Embodiment>
Next, a third embodiment of the present invention will be described. In this embodiment, in the evaluation point insertion flow of the second embodiment described above, when the original sample point and the nearest sample point are close, it is considered that there is no oscillation of the polynomial between these sample points. Since it is possible, do not insert evaluation points. As described above, the present embodiment and the second embodiment are different from each other in steps S301 to S304 in FIG.

FIG. 11 is a flowchart showing in detail the example of the operation of the evaluation point insertion unit 105 according to the third embodiment of the present invention.
Step S401: The evaluation point insertion unit 105 determines whether or not the processing of steps S402, S403, S404, and S405 has been performed for all the sample points. If all the sample points have not been processed, the evaluation point insertion unit 105 proceeds to step S402. When all the sample points have been processed, the process of the evaluation point insertion unit 105 is terminated.

Step S402: The evaluation point insertion unit 105 obtains the closest sample point at the lower right of the original sample point to be processed.
Step S403: The evaluation point insertion unit 105 determines whether or not the set distance between the two sample points is larger than a predetermined distance. As a result of this determination, if it is large, the process proceeds to step S404. If it is small, step S403 is omitted and the process proceeds to step S405. By doing so, evaluation points are not inserted between close sample points, and the processing speed is improved by reducing the number of evaluation points.
Step S404: The evaluation point insertion unit 105 arranges evaluation points at the midpoint of the line segment connecting the two set sample points.
Step S405: Move to the next sample point and return to step S401.

  In the present embodiment, the evaluation points are arranged in a well-balanced manner as described above.

As in the second embodiment, in step S401, the closest sample point may be searched for in the direction such as upper left, upper right, or lower left of the original sample point to be processed. The sample point closest to the original sample point to be processed may be searched regardless of the above.
In the second embodiment and the present embodiment, one sample point having the minimum distance is searched for among the sample points that are separated from the original sample point by a predetermined distance. As shown in FIG. , N (n ≧ 1) sample points may be searched, the original sample points may be added to the n sample points, and the center point of the (n + 1) sample points may be used as the evaluation point. In this case, in step S402, it is determined whether the average distance between the sample points is greater than a predetermined distance.

  Further, the present invention may be applied to a system constituted by a plurality of devices (for example, a host computer, an interface device, an imaging device, a web application, etc.) or an apparatus constituted by a single device.

(Other embodiments of the present invention)
In order to operate various devices to realize the functions of the above-described embodiments, program codes of software for realizing the functions of the above-described embodiments are provided to an apparatus or a computer in the system connected to the various devices. What is implemented by operating the various devices according to a program supplied and stored in a computer (CPU or MPU) of the system or apparatus is also included in the scope of the present invention.

  In this case, the program code of the software itself realizes the functions of the above-described embodiments, and the program code itself and means for supplying the program code to the computer, for example, the program code are stored. The recorded medium constitutes the present invention. As a recording medium for storing the program code, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used. When the present invention is applied to the recording medium, the recording medium stores program codes corresponding to the flowcharts described above.

  Further, by executing the program code supplied by the computer, not only the functions of the above-described embodiments are realized, but also the OS (operating system) or other application software in which the program code is running on the computer, etc. It goes without saying that the program code is also included in the embodiment of the present invention even when the functions of the above-described embodiment are realized in cooperation with the embodiment.

  Further, after the supplied program code is stored in the memory provided in the function expansion board of the computer or the function expansion unit connected to the computer, the CPU provided in the function expansion board or function expansion unit based on the instruction of the program code Needless to say, the present invention includes a case where the functions of the above-described embodiment are realized by performing part or all of the actual processing.

It is a block diagram which shows the 1st Embodiment of this invention and shows an example of a time-dependent difference processing system. It is a block diagram which shows the 1st Embodiment of this invention and shows an example of the basic concept at the time of calculating the shift vector value of the point to interpolate. It is a block diagram which shows the 1st Embodiment of this invention and shows an example of the basic concept at the time of comprehensively evaluating the interpolation formula of a shift vector. It is a figure which shows the 1st Embodiment of this invention and shows an example of arrangement | positioning of a sample point and an evaluation point. It is a figure which shows the 1st Embodiment of this invention and shows a nearest neighbor pixel interpolation method and a bilinear interpolation method. It is a flowchart which shows the 1st Embodiment of this invention and shows in detail an example of the basic concept at the time of calculating | requiring a shift vector value. It is a block diagram which shows the 1st Embodiment of this invention and shows the modification of the basic concept at the time of comprehensively evaluating the interpolation formula of a shift vector. It is a figure which shows the 2nd Embodiment of this invention and shows an example of arrangement | positioning of a corresponding point. It is a flowchart which shows the 2nd Embodiment of this invention and shows in detail an example of the basic concept at the time of arrange | positioning evaluation points. It is a figure which shows the 2nd Embodiment of this invention and shows an example of arrangement | positioning of a sample point and an evaluation point. It is a flowchart which shows the 3rd Embodiment of this invention and shows in detail an example of the basic concept at the time of arrange | positioning evaluation points. It is a figure which shows the modification of the 2nd and 3rd embodiment of this invention, and shows the other example of arrangement | positioning of a sample point and an evaluation point. It is a block diagram which shows the prior art and shows a time difference system. It is a figure which shows the prior art and shows an example of the shift vector in a time difference system in detail.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 X-ray imaging apparatus 20 Image processing apparatus 30 Display apparatus 201, 301 Sample point 202, 302, 303 Evaluation point

Claims (17)

A first interpolation value calculating step for obtaining an interpolation value at each sample point of the digital signal;
A first interpolation value error evaluation step for obtaining an error of the interpolation value at each sample point;
A second interpolation value calculating step of arranging a predetermined number of evaluation points between the sample points and obtaining an interpolation value at the arranged evaluation points;
A second interpolation value error evaluation step for obtaining an error of the interpolation value at the evaluation point;
A comprehensive error evaluation step for obtaining a total error of an interpolation formula used for interpolating the digital signal based on the error of the interpolation value at each sample point and the error of the interpolation value at the evaluation point. A digital signal processing method.   The digital signal processing method according to claim 1, wherein the evaluation point is arranged at a center position of a plurality of sample points.   3. The digital signal processing method according to claim 1, wherein the first interpolation value calculation step obtains a polynomial interpolation value at each sample point of the digital signal using a polynomial as the interpolation formula.   4. The digital signal processing method according to claim 3, wherein the first interpolation value error evaluation step obtains a difference between a polynomial interpolation value at each sample point and a digital signal value at the sample point. In the second interpolation value calculation step, the first interpolation value at the evaluation point is obtained using the polynomial, and the digital signal value at the sample point arranged in the vicinity of the evaluation point is used to determine the first interpolation value. To obtain a second interpolated value at the evaluation point,
In the second interpolation value error evaluation step, a difference between a second interpolation value obtained by performing the local interpolation and a first interpolation value obtained by using the polynomial is obtained. The digital signal processing method according to claim 3 or 4. The digital signal is an image signal,
6. The digital signal processing method according to claim 5, wherein the local interpolation is nearest neighbor pixel interpolation, bilinear interpolation, or cubic interpolation. A first interpolation value calculating step for obtaining an interpolation value at each sample point of the digital signal using a polynomial having a maximum number of terms k;
A first interpolation value error evaluation step for obtaining an error of the interpolation value at each sample point;
A second interpolation value calculating step of arranging a predetermined number of evaluation points between the respective sample points and obtaining an interpolation value at the arranged evaluation points by the polynomial;
A second interpolation value error evaluation step for obtaining an error of the interpolation value at the evaluation point;
An overall error evaluation step for obtaining an overall error of a polynomial used for interpolating the digital signal based on the error of the interpolation value at each sample point and the error of the interpolation value at the evaluation point;
The first interpolation value calculation step, the first interpolation value error evaluation step, and the second interpolation value calculation step by changing the maximum term number k of the polynomial in a range of 1 to K (K is a natural number of 2 or more). Repeating the second interpolation value error evaluation step and the total error evaluation step to obtain a total error corresponding to the polynomial in the maximum number of terms, respectively,
An interpolating step for interpolating a digital signal using a polynomial having a maximum number of terms that minimizes the overall error. An interpolation value calculation step for obtaining each sample point of the digital signal and a predetermined number of evaluation points between the sample points, and obtaining an interpolation value at the arranged evaluation points by changing the maximum number of terms of the polynomial ,
An interpolation value error evaluation step for obtaining an interpolation value error at each sample point and an interpolation value error at each evaluation point for each maximum number of terms of the polynomial;
An overall error evaluation step for obtaining an overall error of the polynomial for each maximum number of terms of the polynomial based on an error of the interpolation value at each sample point and an error of the interpolation value at the evaluation point; and A digital signal processing method comprising: an interpolation step for performing interpolation processing of a digital signal using a polynomial having a maximum number of terms with the smallest possible error. First interpolation value calculation means for obtaining an interpolation value at each sample point of the digital signal;
First interpolation value error evaluation means for obtaining an error of an interpolation value at each sample point;
A second interpolation value calculating means for arranging a predetermined number of evaluation points between the sample points and obtaining an interpolation value at the arranged evaluation points;
Second interpolation value error evaluation means for obtaining an error of the interpolation value at the evaluation point;
Comprehensive error evaluation means for obtaining a total error of an interpolation formula used for interpolating the digital signal based on the error of the interpolation value at each sample point and the error of the interpolation value at the evaluation point. A digital signal processing device.   The digital signal processing apparatus according to claim 9, wherein the evaluation point is arranged at a center position of a plurality of sample points.   11. The digital signal processing apparatus according to claim 9, wherein the first interpolation value calculation means obtains a polynomial interpolation value at each sample point of the digital signal using a polynomial as the interpolation formula.   12. The digital signal processing apparatus according to claim 11, wherein the first interpolation value error evaluation unit obtains a difference between a polynomial interpolation value at each sample point and a digital signal value at the sample point. The second interpolation value calculation means obtains a first interpolation value at the evaluation point using the polynomial, and locally uses a digital signal value at a sample point arranged in the vicinity of the evaluation point. To obtain a second interpolated value at the evaluation point,
The second interpolation value error evaluation means obtains a difference between the second interpolation value obtained by performing the local interpolation and the first interpolation value obtained by using the polynomial. The digital signal processing apparatus according to claim 11 or 12. The digital signal is an image signal,
The digital signal processing apparatus according to claim 13, wherein the local interpolation is nearest neighbor pixel interpolation, bilinear interpolation, or cubic interpolation. First interpolation value calculation means for obtaining an interpolation value at each sample point of the digital signal using a polynomial having a maximum number of terms k;
First interpolation value error evaluation means for obtaining an error of an interpolation value at each sample point;
A second interpolation value calculating means for arranging a predetermined number of evaluation points between the respective sample points and obtaining an interpolation value at the arranged evaluation points by the polynomial;
Second interpolation value error evaluation means for obtaining an error of the interpolation value at the evaluation point;
Comprehensive error evaluation means for obtaining an overall error of a polynomial used for interpolating the digital signal based on the error of the interpolation value at each sample point and the error of the interpolation value at the evaluation point;
The first interpolation value calculation means, the first interpolation value error evaluation means, and the second interpolation value calculation means by changing the maximum term number k of the polynomial in a range of 1 to K (K is a natural number of 2 or more). Repeating the second interpolation value error evaluation means and the overall error evaluation means, respectively to obtain a comprehensive error corresponding to the polynomial in each maximum term number,
A digital signal processing apparatus comprising interpolation means for performing interpolation processing of a digital signal using a polynomial having a maximum number of terms that minimizes the total error. Interpolation value calculation means for determining each interpolation point at each sample point of the digital signal and arranging a predetermined number of evaluation points between each of the sample points and changing the maximum number of terms of the polynomial at each of the arranged evaluation points; ,
Interpolation value error evaluation means for obtaining an interpolation value error at each sample point and an interpolation value error at each evaluation point for each maximum number of terms of the polynomial;
A total error evaluation means for determining a total error of the polynomial for each maximum number of terms of the polynomial based on an error of the interpolation value at each sample point and an error of the interpolation value at the evaluation point; A digital signal processing apparatus comprising: interpolation means for performing interpolation processing of a digital signal using a polynomial having a maximum number of terms that minimizes a large error. A first interpolation value calculating step for obtaining an interpolation value at each sample point of the digital signal;
A first interpolation value error evaluation step for obtaining an error of the interpolation value at each sample point;
A second interpolation value calculating step of arranging a predetermined number of evaluation points between the sample points and obtaining an interpolation value at the arranged evaluation points;
A second interpolation value error evaluation step for obtaining an error of the interpolation value at the evaluation point;
Comprehensive error evaluation step for obtaining a total error of an interpolation formula used for interpolating the digital signal based on the error of the interpolation value at each sample point and the error of the interpolation value at the evaluation point. A computer program that is executed.

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