Image output device, method, program, recording medium

Abstract

To visualize a signal source such as a magnetic field.SOLUTION: An image output device 20 comprises: a signal source specification unit 22 which receives a signal expressed by a vector having a prescribed direction from a plurality of signal sources S1, S2, receives measurement results of a plurality of sensors MS that measure components of three axes orthogonal to each other and specifies the positions of the signal sources S1, S2 and the direction of the vector; and a signal source image addition unit 24 which adds an image showing the signal sources S1, S2 to a portion corresponding to the positions of the signal sources S1, S2 derived by the signal source specification unit 22 in the imaging result of an imaging unit 2 that images the signal sources S1, S2 for each object OBJ.SELECTED DRAWING: Figure 8

Description

Technical Field

[0001] The present invention relates to the visualization of a signal source that emits signals such as a magnetic field.

Background Art

[0002] There are objects that include a signal source that emits signals such as a magnetic field. Examples of the signal source include a magnetic marker (such as a permanent magnet) and a magnetic material (such as a reinforcing bar).

[0003] Conventionally, various techniques have been known for the position measurement and display of a magnetic signal source (see, for example, Patent Document 1, Patent Document 3, Patent Document 4, Non-Patent Document 1, and Non-Patent Document 2). Also, although not a magnetic signal source, various techniques have been known for the position measurement and display of a sound source (see, for example, Patent Document 2).

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Non-Patent Documents

[0005]

Non-Patent Document 1

[0006] However, even if you visually observe or image the object containing the signal source, you cannot determine the location of the signal source or the direction of the signal vector.

[0007] Therefore, the present invention aims to visualize signal sources such as magnetic fields. [Means for solving the problem]

[0008] The image output device according to the present invention is configured to include a signal source identification unit that receives signals represented by vectors having a predetermined direction from a plurality of signal sources and the measurement results of a plurality of sensors that measure components of three mutually orthogonal axes, and identifies the position of the signal source and the direction of the vector; and a signal source image adding unit that adds an image showing the signal source to the portion of the imaging result of an imaging unit that images the signal source that corresponds to the position of the signal source identified by the signal source identification unit.

[0009] The image output device configured as described above has a signal source identification unit that receives signals represented by vectors having a predetermined direction from multiple signal sources, and receives measurement results from multiple sensors that measure components of three mutually orthogonal axes to identify the position of the signal source and the direction of the vector. The signal source image addition unit adds an image showing the signal source to the portion of the imaging result of the imaging unit that images the signal source that corresponds to the position of the signal source identified by the signal source identification unit.

[0010] Furthermore, the image output device according to the present invention may also have the signal source image addition unit further add coordinate axes to the imaging result.

[0011] Furthermore, the image output device according to the present invention may be configured such that the image showing the signal source indicates the direction of the vector.

[0012] Furthermore, the image output device according to the present invention may have a signal source image addition unit that adds images showing the signal source for multiple time points.

[0013] Furthermore, the image output device according to the present invention may be configured such that the signal source image addition unit outputs the additional result when the viewpoint is changed, based on the coordinates of the position of the signal source and the coordinates of the viewpoint of imaging by the imaging unit.

[0014] Furthermore, the image output device according to the present invention may be configured such that the measurement result of the sensor is proportional to the sum of the values ​​obtained by multiplying each of the three axis components of the vector by a first coefficient, and the signal source identification unit derives a spectrum obtained based on the measurement result of the sensor and the sum of the values ​​obtained by multiplying the first coefficient by a second coefficient, the spectrum which takes a maximum value at the voxel where the signal source that outputs the signal is located, a direction derivation unit which derives the direction of the vector based on the second coefficient used to obtain the spectrum, and a position derivation unit which derives the position of the voxel where the signal source is located based on the spectrum.

[0015] Furthermore, in the image output device according to the present invention, the position derivation unit may derive the position of the voxel in which the signal source is located based on the maximum value of each of the spectra taken in each voxel.

[0016] Furthermore, the image output device according to the present invention includes a signal source identification unit which includes a relation matrix recording unit which records a relation matrix representing the relationship between the measurement results, which are grouped for each of the sensors for each axis, and the vector, and a position / vector derivation unit which derives the position of the signal source and the vector such that the cost function is minimized based on the measurement results and the relation matrix, wherein the components of the vector are grouped for each of the grid points in the space where the signal source is located for each axis, the cost function is the sum of an error function and a regularization term, the error function represents the error between the true value of the position of the signal source and the vector and a candidate value of the true value, the regularization term is a function of a regularization parameter and the L1 norm of the vector, and the position of the signal source and the vector may be identified based on the derivation result of the position / vector derivation unit.

[0017] Furthermore, the image output device according to the present invention may be configured to specify that the derivation result of the position / vector derivation unit is the position of the signal source and the vector.

[0018] Furthermore, the image output device according to the present invention includes a clustering unit that classifies the positions of the signal sources derived by the position / vector derivation unit into clusters of the number of signal sources; a centroid derivation unit that derives the centroid of the signal sources for each cluster; and a weighted average unit that averages the vectors derived by the position / vector derivation unit for each cluster in inverse proportion to the distance between the signal sources and the centroid, wherein the position of the signal sources is identified as the centroid, and the vectors are identified as the results derived by the weighted average unit.

[0019] Furthermore, the image output device according to the present invention may be configured such that the classification into clusters is performed in accordance with the K-means method.

[0020] The present invention receives signals represented by vectors having a predetermined direction from a plurality of signal sources, receives measurement results of a plurality of sensors that measure components of three mutually orthogonal axes, and determines the position of the signal sources and the direction of the vectors. A signal source identification step, and a signal source image addition step of adding an image indicating the signal source to a portion corresponding to the position of the signal source identified in the signal source identification step in the imaging result of an imaging unit that images the signal source. It is an image output method provided with.

[0021] The present invention is a program for causing a computer to execute image output processing, wherein the image output processing receives signals represented by vectors having a predetermined direction from a plurality of signal sources, and measures components of three mutually orthogonal axes. A signal source identification step of receiving the measurement results of a plurality of sensors and identifying the position of the signal source and the direction of the vector, and a signal source image addition step of adding an image indicating the signal source to a portion corresponding to the position of the signal source identified in the signal source identification step in the imaging result of an imaging unit that images the signal source. It is a program provided with.

[0022] The present invention is a computer-readable recording medium recording a program for causing a computer to execute image output processing, wherein the image output processing receives signals represented by vectors having a predetermined direction from a plurality of signal sources, and measures components of three mutually orthogonal axes. A signal source identification step of receiving the measurement results of a plurality of sensors and identifying the position of the signal source and the direction of the vector, and a signal source image addition step of adding an image indicating the signal source to a portion corresponding to the position of the signal source identified in the signal source identification step in the imaging result of an imaging unit that images the signal source. It is a recording medium provided with.

Brief Description of the Drawings

[0023] [Figure 1] It is a perspective view of a voxel V and a magnetic sensor MS according to a first embodiment of the present invention. [Figure 2] It is a functional block diagram showing the configuration of a signal source identification device 1 according to a first embodiment of the present invention. [Figure 3]This is an example of a graph of the maximum value P. [Figure 4] This is a perspective view of a voxel V and magnetic sensor MS according to a second embodiment of the present invention. [Figure 5] This is a functional block diagram showing the configuration of a signal source identification device 1 according to a second embodiment of the present invention. [Figure 6] This is a functional block diagram showing the configuration of a signal source identification device 1 according to a third embodiment of the present invention. [Figure 7] This figure shows the clustering of the signal sources S1 to S4 by the clustering unit 180a (Figure 7(a)), the derivation of the centroid of the cluster by the centroid derivation unit 180b (Figure 7(b)), and the derivation of the weighted average of the vectors by the weighted average unit 180c (Figure 7(c)). [Figure 8] This is a functional block diagram showing the configuration of the image output device 20 according to the fourth embodiment. [Figure 9] This figure shows an example of the display of the image display unit 26. [Figure 10] This figure shows an example of the display of the image display unit 26 in a modified example 1 of the fourth embodiment. [Figure 11] This figure shows an example of the display of the image display unit 26 in a modified example 2 of the fourth embodiment. [Modes for carrying out the invention]

[0024] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0025] First Embodiment Figure 1 is a perspective view of a voxel V and magnetic sensor MS according to a first embodiment of the present invention. Figure 2 is a functional block diagram showing the configuration of a signal source identification device 1 according to a first embodiment of the present invention.

[0026] Referring to Figure 1, signal sources S1 and S2 output signals. The signals are represented by a vector m having a predetermined direction. Vector m is, for example, a magnetic dipole moment. The number of signal sources is, for example, two, but it may be three or more, as long as it is less than the number of magnetic sensors MS. However, the signals output by each signal source are assumed to have different frequencies or phases from each other.

[0027] Furthermore, the spatial positions of signal sources S1 and S2 are represented by voxels V (for example, 10 × 10 × 10 = 1000 voxels). Signal sources S1 and S2 are located in different voxels V. Note that each of the 1000 voxels V will be denoted as V1 to V1000.

[0028] Multiple magnetic sensors (for example, 64 sensors arranged in an 8x8 grid) receive a signal (for example, a magnetic dipole moment) and measure the mutually orthogonal components Bx, By, and Bz along the three axes X, Y, and Z. Each of the 64 magnetic sensors is denoted as MS1 through MS64.

[0029] Here, if vector r is the direction vector from the signal source (magnetic dipole) to the magnetic sensor MS, then the magnetic flux density B (a function of vector r) measured by the magnetic sensor MS is expressed by the Biot-Savart law as shown in equation (1). Here, μ0 is the magnetic constant. Furthermore, vector r can be said to represent the positional relationship between each of the voxels V (V1 to V1000) and each of the magnetic sensors MS1 to MS64.

[0030]

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[0031]

number

[0032] From equation (1), By can be expressed as shown in equation (3) below.

[0033]

number

[0034] From equation (1), Bz can be expressed as shown in equation (4) below.

[0035]

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[0036] Note that vx1, vx2, vx3, vy1, vy2, vy3, vz1, vz2, and vz3 (the first coefficient) are determined based on the vector r by referring to equations (2) to (4) and equations (2') to (4').

[0037] Referring to Figure 2, the signal source identification device 1 according to the first embodiment of the present invention comprises a relative position recording unit 11, a first coefficient derivation unit 12, a transfer function derivation unit 13, a noise eigenvector derivation unit 14, a spectrum derivation unit 16, a direction derivation unit 18, and a position derivation unit 19.

[0038] The signal source identification device 1 receives measurement results from multiple sensors MS1 to MS64 and derives the direction of vector m.

[0039] The relative position recording unit 11 records a vector r, which is the relative position between each of the 1000 voxels V and each of the magnetic sensors MS1 to MS64.

[0040] The first coefficient derivation unit 12 reads the vector r from the relative position recording unit 11 and derives the first coefficients vx1, vx2, vx3, vy1, vy2, vy3, vz1, vz2, and vz3 (see equations (2) to (4) and equations (2') to (4')).

[0041] For example, the first coefficient vx1 can be expressed as shown in equation (5) below.

[0042]

number

[0043] Similarly, the other first coefficients vx2, vx3, vy1, vy2, vy3, vz1, vz2, and vz3 can take on 1000 × 64 different values.

[0044] The first coefficient vx1 can be used as is, but it is normalized as shown in equation (6) below and used in subsequent processing.

[0045]

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[0046] The other first coefficients, vx2, vx3, vy1, vy2, vy3, vz1, vz2, and vz3, are also normalized in the same way.

[0047] The first coefficient derivation unit 12 outputs the first coefficient normalized as described above.

[0048] The noise eigenvector derivation unit 14 obtains eigenvectors of the noise subspace from the measurement results Bx, By, and Bz of the magnetic sensor MS, in accordance with the MUSIC method.

[0049] First, X(t)x is calculated from the measurement result Bx of the magnetic sensor MS using the following equation (7). Here, t is the time the measurement was performed. T represents the transpose.

[0050]

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[0051] Using X(t)x, we obtain the correlation matrix as shown in equation (8) below.

[0052]

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[0053] The eigenvectors ey of the noise subspace can be found in a similar manner. First, replace Bx with By in equation (7), and replace X(t)x with X(t)y in equations (7) and (8), and obtain the correlation matrix using equation (8). Then, similarly, find the eigenvectors corresponding to the small eigenvalues ​​and use these as the eigenvectors ey of the noise subspace. The eigenvectors ey of the noise subspace are 64 x 1 vectors. There are 62 eigenvectors ey of the noise subspace, corresponding to the small eigenvalues.

[0054] Similarly, the eigenvectors ez of the noise subspace can be found. First, replace Bx with Bz in equation (7), and replace X(t)x with X(t)z in equations (7) and (8), and obtain the correlation matrix using equation (8). Then, similarly, find the eigenvectors corresponding to the small eigenvalues ​​and use these as the eigenvectors ez of the noise subspace. The eigenvectors ez of the noise subspace are 64 x 1 vectors. There are 62 eigenvectors ez of the noise subspace, corresponding to the small eigenvalues.

[0055] The transfer function derivation unit 13 derives the transfer functions vx, vy, and vz as shown in equations (9), (10), and (11) below. It derives the sum of the values ​​obtained by multiplying the first coefficients vx1, vx2, and vx3 by the second coefficients ax, bx, and cx, respectively (see equation (9)). The derived result is called the transfer function vx. It derives the sum of the values ​​obtained by multiplying the first coefficients vy1, vy2, and vy3 by the second coefficients ay, by, and cy, respectively (see equation (10)). The derived result is called the transfer function vy. It derives the sum of the values ​​obtained by multiplying the first coefficients vz1, vz2, and vz3 by the second coefficients az, bz, and cz, respectively (see equation (11)). The derived result is called the transfer function vz.

[0056]

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[0057] However, one or two of the second coefficients may be zero. For example, ax=1, bx=cx=0 (i.e., vx=vx1), or ax=bx=1, cx=0 (i.e., vx=vx1+vx2).

[0058] Here, we assume that there are 13 types of (ak, bk, ck) (where k = x, y, z) which are (1,0,0), (0,1,0), (0,0,1), (1,1,0), (1,-1,0), (0,1,1), (0,1,-1), (1,0,1), (-1,0,1), (1,1,1), (-1,1,1), (1,-1,1), and (1,1,-1). Let the corresponding vk be vk1, vk2, ..., vk13.

[0059] For example, if (ax, bx, cx) is (1,0,0), then vx = vx1. If (ax, bx, cx) is (1,1,0), then vx = vx4 = vx1 + vx2. If (ax, bx, cx) is (1,1,-1), then vx = vx13 = vx1 + vx2 - vx3.

[0060] For example, if (ay, by, cy) is (1,0,0), then vy = vy1. If (ay, by, cy) is (1,1,0), then vy = vy4 = vy1 + vy2. If (ay, by, cy) is (1,1,-1), then vy = vy13 = vy1 + vy2 - vy3.

[0061] For example, if (az, bz, cz) is (1,0,0), then vz = vz1. If (az, bz, cz) is (1,1,0), then vz = vz4 = vz1 + vz2. If (az, bz, cz) is (1,1,-1), then vz = vz13 = vz1 + vz2 - vz3.

[0062] The spectrum derivation unit 16 derives a spectrum in which the signal sources S1 and S2 have a maximum value in voxel V. Such a spectrum is obtained according to the MUSIC method. There are two maximum values ​​in the spectrum, corresponding to the number of signal sources. If there are three or more signal sources, there will be three or more maximum values ​​in the spectrum.

[0063] The spectrum is derived by the spectrum derivation unit 16 based on the measurement results Bx, By, Bz of the magnetic sensor MS (and the eigenvectors of the noise subspace obtained from them, ex, ey, ez) and the sum of the values ​​obtained by multiplying the first coefficient by the second coefficient (i.e., the transfer function vx, vy, vz) (equations (9), (10), (11)). The spectrum derivation unit 16 derives the spectrum based on the transfer function vx, vy, vz output by the transfer function derivation unit 13 and the eigenvectors of the noise subspace ex, ey, ez output by the noise eigenvector derivation unit 14.

[0064] The spectrum derivation unit 16 derives the spectrum Px1 as follows. (1) There are 62 eigenvectors ex (64 x 1 vectors) in the noise subspace. Arrange these vectors ex in 62 columns to make ex a 64 x 62 matrix. (2) Transpose the matrix ex and multiply it by the transfer function vx1 (a matrix of 64 rows and 1000 columns). That is, ex T We calculate vx1. This will be a matrix with 62 rows and 1000 columns. (3) Square each element of the matrix obtained in (2). (4) Sum the elements of the matrix obtained in (3) column by column and arrange them in a row to obtain a 1x1000 matrix. For example, the 1st row Q column + 2nd row Q column + ... + 62nd row Q column of the matrix obtained in (3) will be the 1st row Q column of the 1x1000 matrix obtained in (4) (where Q is an integer from 1 to 1000). (5) Taking the reciprocal of each component of the matrix obtained in (4) yields the spectrum Px1 (a 1x1000 matrix).

[0065] Note that each column in spectrum Px1 corresponds to voxels V1 to V1000. The same applies to the other spectra.

[0066] The spectrum derivation unit 16 also derives spectra Px2, Px3, ..., Px13. Spectra Px2, Px3, ..., Px13 can be derived by replacing the transfer function vx1 in (2) above with vx2, vx3, ..., vx13.

[0067] The spectrum derivation unit 16 derives spectra Py1, Py2, Py3, ..., Py13. By replacing the eigenvector ex of the noise subspace in (1) above with ey, and replacing the transfer function vx1 in (2) above with vy1, vy2, vy3, ..., vy13, spectra Py1, Py2, Py3, ..., Py13 can be derived.

[0068] The spectrum derivation unit 16 derives spectra Pz1, Pz2, Pz3, ..., Pz13. By replacing the eigenvector ex of the noise subspace in (1) above with ez, and replacing the transfer function vx1 in (2) above with vz1, vz2, vz3, ..., vz13, spectra Pz1, Pz2, Pz3, ..., Pz13 can be derived.

[0069] The position derivation unit 19 derives the positions of voxels V where signal sources S1 and S2 are located, based on the spectra Px1, Px2, Px3, ..., Px13, Py1, Py2, Py3, ..., Py13, Pz1, Pz2, Pz3, ..., Pz13.

[0070] The spectrum output by the spectrum derivation unit 16 is expressed as shown in equation (12) below.

[0071]

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[0072]

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[0073] Figure 3 shows an example of a graph of the maximum value P. In Figure 3, the vertical axis represents the spectral value, and the horizontal axis represents the voxel (V1 to V1000).

[0074] Referring to Figure 3, assume that the maximum value of P (spectrum) in voxel V750 is SP1 (maximum), and the maximum value of P (spectrum) in voxel V250 is SP2 (maximum). However, assume that SP1 is greater than SP2.

[0075] The position derivation unit 19 determines the centroid of voxels that take values ​​within a predetermined range from the maximum value SP1 within the maximum value P (for example, the value of the maximum value P is 0.95SP1 or greater), while increasing the predetermined range (for example, expanding the predetermined range by 0.05SP1 each time, such as from 0.95SP1 or greater → 0.90SP1 or greater → 0.85SP1 or greater → ...) until the number of times the centroid changes by more than a predetermined amount plus 1 equals the number of signal sources (2).

[0076] Within the maximum value P, the centroid of voxels in the vicinity of the largest value SP1 is approximately voxel V750. However, as the predetermined range expands from the largest value SP1 to include SP2, the centroid of the voxels becomes considerably smaller than voxel V750. Since the centroid changes by more than a predetermined amount, the number of times this occurs (1) plus 1 equals the number of signal sources (2), and thus the calculation of the voxel centroid is terminated.

[0077] Next, the voxels whose centroids have been found are clustered according to the number of signal sources (2). For example, unsupervised machine learning K-means clustering is performed, and the same number of clusters are labeled as there are signal sources.

[0078] Finally, among the clustered voxels, the location of the voxel with the maximum spectral value is defined as the location of the signal source.

[0079] Furthermore, the position derivation unit 19 may further reduce the size of the voxel based on the position of the voxel where the signal source is located, as derived in this manner, to derive the position of the voxel where the signal source is located. In this way, the position of the voxel where the signal source is located can be calculated with high accuracy and speed.

[0080] The direction derivation unit 18 receives Pkj (where k=x, y, z and j=1, 2, 3, ...) corresponding to the signal sources S1 and S2 from the position derivation unit 19 (i.e., taking a maximum value at P). Furthermore, the direction derivation unit 18 derives the direction of vector m based on the second coefficient used to obtain the Pkj corresponding to the signal sources S1 and S2.

[0081] For example, suppose the orientation derivation unit 18 is given Px13 (Py13 or Pz13) of the 750th column (voxel V750) and Px4 (Px4 or Pz4) of the 250th column (voxel V250) as spectra corresponding to signal sources S1 and S2 from the position derivation unit 19.

[0082] The direction derivation unit 18 then determines that the second coefficient (ak, bk, ck) (where k=x, y, z) used to obtain Px13 (Py13 or Pz13) as the direction of vector m in the signal source S1 of voxel V750 is (1,1,-1). Therefore, the direction derivation unit 18 derives that the direction of vector m in the signal source S1 of voxel V750 is parallel to vector (1,1,-1). Here, vector (1,1,-1) is a vector with an X component of 1, a Y component of 1, and a Z component of -1.

[0083] Furthermore, the direction derivation unit 18 determines that the second coefficient (ak, bk, ck) (where k=x, y, z) used to obtain Px4 (Px4 or Pz4) as the direction of vector m in the signal source S2 of voxel V250 is (1,1,0). Therefore, the direction derivation unit 18 derives that the direction of vector m in the signal source S2 of voxel V250 is parallel to vector (1,1,0). Here, vector (1,1,0) is a vector with an X component of 1, a Y component of 1, and a Z component of 0.

[0084] Next, the operation of the first embodiment of the present invention will be described.

[0085] The first coefficient derivation unit 12 reads the vector r from the relative position recording unit 11, and derives the first coefficients vx1, vx2, vx3, vy1, vy2, vy3, vz1, vz2, and vz3 (see equations (2) to (4) and equations (2') to (4')).

[0086] The first coefficient can take 1000 × 64 different values ​​(see equation (5)), and is normalized (see equation (6)) before being given to the transfer function derivation unit 13.

[0087] The transfer function derivation unit 13 derives the transfer functions vx, vy, and vz based on the first and second coefficients ax, bx, cx, ay, by, cy, az, bz, and cz (see equations (9), (10), and (11)).

[0088] The noise eigenvector derivation unit 14 derives the eigenvectors ex, ey, and ez of the noise subspace from the measurement results Bx, By, and Bz of the magnetic sensor MS, in accordance with the MUSIC method.

[0089] The spectrum derivation unit 16 derives spectra Px1, Px2, Px3, ..., Px13, Py1, Py2, Py3, ..., Py13, Pz1, Pz2, Pz3, ..., Pz13 based on the transfer functions vx, vy, vz and the eigenvectors ex, ey, ez of the noise subspace (see equation (12)).

[0090] The position derivation unit 19 determines the maximum value P that each of the spectra can take in each voxel (i.e., the maximum value in each column of equation (12)) (see equation (13) and Figure 3). Based on the maximum value P, voxels 250 and 750, where the signal sources S1 and S2 are located, are derived.

[0091] The direction derivation unit 18 derives the direction of vector m based on the second coefficient used to obtain Pkj corresponding to the signal sources S1 and S2.

[0092] According to the first embodiment of the present invention, the measurement accuracy of signals such as magnetic fields is improved.

[0093] For example, if the transfer function vk consists only of vk1, vk2, and vk3, the orientation of vector m can only be measured if its orientation is parallel to the X, Y, or Z direction. If the orientation of vector m is in any other direction, for example, parallel to the vector (1,1,0) (i.e., a vector with X component 1, Y component 1, and Z component 0), the orientation of vector m cannot be measured.

[0094] However, according to the first embodiment of the present invention, since there are many types of transfer functions vk, such as vk1, vk2, vk3, ..., vk13, the direction of vector m can be measured even when the direction of vector m is not parallel to the X, Y, and Z directions.

[0095] In the first embodiment of the present invention, the signal vector has been defined as a magnetic dipole moment, but the signal vector is not limited to a magnetic dipole moment. The signal vector may be, for example, an electric dipole moment (vector p).

[0096] The magnetic flux density B (a function of vector r) measured by the magnetic sensor MS is expressed as shown in equation (14).

[0097]

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[0098]

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[0099] From equation (14), By can be expressed as shown in equation (16).

[0100]

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[0101] From equation (14), Bz can be expressed as shown in equation (17).

[0102]

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[0103] The configuration and operation of the signal source identification device 1 are the same as when the signal vector is a magnetic dipole moment (vector m), and therefore the explanation is omitted.

[0104] Second Embodiment Figure 4 is a perspective view of a voxel V and magnetic sensor MS according to a second embodiment of the present invention. Figure 5 is a functional block diagram showing the configuration of a signal source identification device 1 according to a second embodiment of the present invention.

[0105] Referring to Figure 4, signal sources S1 and S2 output signals. The signals are represented by a vector a having a predetermined direction. Vector a is, for example, a magnetic dipole moment. The number of signal sources is, for example, two, but there may be three or more, as long as it is less than the number of magnetic sensors MS. The signals output by each signal source may have different frequencies or phases, or they may not. That is, the signals output by each signal source may have the same frequency and phase. Furthermore, the signals output by each signal source may be DC (direct current) signals.

[0106] Furthermore, the spatial positions of signal sources S1 and S2 are represented by voxels V (for example, 10 × 10 × 10 = 1000 voxels). Signal sources S1 and S2 are located in different voxels V. Note that each of the 1000 voxels V will be denoted as V1 to V1000.

[0107] Multiple magnetic sensors (for example, 64 sensors arranged in an 8x8 grid) receive a signal (for example, a magnetic dipole moment) and measure the components bx, by, and bz of the three mutually orthogonal axes X, Y, and Z. Each of the 64 magnetic sensors is denoted as MS1 to MS64. The signal is represented by a vector a with a predetermined direction. The multiple magnetic sensors receive signals from multiple signal sources S1 and S2.

[0108] Here, if vector r is the direction vector from the signal source (magnetic dipole) to the magnetic sensor MS, then the magnetic flux density B (a function of vector r) measured by the magnetic sensor MS is expressed by the Biot-Savart law as shown in equation (21). Here, μ0 is the magnetic constant. Furthermore, vector r can be said to represent the positional relationship between each of the voxels V (V1 to V1000) and each of the magnetic sensors MS1 to MS64.

[0109]

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[0110]

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[0111] From equation (21), by can be expressed as shown in equation (23).

[0112]

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[0113] From equation (21), bz can be expressed as shown in equation (24).

[0114]

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[0115] Here, bx, by, and bz are expressed as shown in equation (25) below.

[0116]

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[0117] Here, the measurement results b, aggregated for each of the X, Y, and Z axes (64 magnetic sensors), are a single-column matrix consisting of bx, by, and bz. (See the left-hand side of equation (28) and the left-hand side of equation (28').

[0118] Furthermore, ax, ay, and az can be expressed as shown in equation (26) below.

[0119]

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[0120] Here, vector a is a single-column matrix. Moreover, in vector a, its components ax, ay, and az are grouped together for each of the X, Y, and Z axes, corresponding to the number of grid points in the space where the signal source is located (1000 points) (see the matrix on the right side of the right-hand side in equations (28) and (28')).

[0121] Referring to Figure 5, the signal source identification device 1 according to the second embodiment includes a relative position recording unit 110, a read field matrix derivation unit 120, a read field matrix recording unit 130, and a position vector derivation unit 150.

[0122] The signal source identification device 1 receives measurement results from multiple sensors MS1 to MS64 and identifies the positions and vectors a of signal sources S1 and S2.

[0123] The relative position recording unit 110 records a vector r, which is the relative position between each of the 1000 voxels V and each of the magnetic sensors MS1MS64.

[0124] The read-field matrix derivation unit 120 reads the vector r from the relative position recording unit 110 and calculates hxx, hxy, hxz, hyx, hyy, hyz, hzx, hzy, hzz (with the vector r as the argument) (components of the relation matrix H (e.g., the read-field matrix) described later) (see equations (22) to (24) and equations (22') to (24').

[0125] For example, hxx can be expressed as shown in equation (27) below.

[0126]

number

[0127] Similarly, hxy, hxz, hyx, hyy, hyz, hzx, hzy, and hzz can each take on 1000 × 64 possible values.

[0128] Here, equations (22') to (24') can be expressed as equation (28) below.

[0129]

number

[0130] Furthermore, let the matrix on the right side of the right-hand side of equation (28) be vector a (in vector a, its components ax, ay, and az are grouped together for each of the X, Y, and Z axes, corresponding to the number of grid points in the space where the signal sources S1 and S2 are located (1000)). Vector a is a single-column matrix.

[0131] Furthermore, let H be the matrix on the left side of the right-hand side in equation (28). H is a relation matrix (for example, a read field matrix) that represents the relationship between the measurement result b and the vector a.

[0132] Then, equation (28) can be expressed as equation (28'). That is, the measurement result b is the product of the relation matrix H and the vector a.

[0133] As explained earlier, the read-field matrix derivation unit 120 finds the components of the relation matrix H and further derives the relation matrix (read-field matrix) H.

[0134] The lead field matrix recording unit 130 receives the relation matrix (lead field matrix) H from the lead field matrix derivation unit 120 and records it.

[0135] The position / vector derivation unit 150 derives the positions and vectors a of signal sources S1 and S2 that minimize the cost function, based on the measurement result b and the relation matrix H.

[0136] In other words, the position vector derivation unit 150 derives a vector a that satisfies the following equation (29).

[0137]

number

[0138] The error function represents the error between the true value of the vector a and a candidate value of the true value, based on the positions of signal sources S1 and S2. The error function is a function of the measurement result b, the relation matrix H, and the candidate value a (of the true value of the vector). For example, the error function can be expressed as (1 / 2)(b-Ha). T (b-Ha)

[0139] The regularization term is a function of the regularization parameter λ and the L1 norm of vector a. For example, the regularization term is the product of the regularization parameter λ and the L1 norm of vector a.

[0140] Based on the derivation result a of the position / vector derivation unit 150, the positions and vectors a of signal sources S1 and S2 are identified. For example, the derivation result a of the position / vector derivation unit 150 is identified as the position and vector of the signal source. For example, if signal source S1 is located at voxel V500 and signal source S2 is located at voxel V600, then (ax500, ay500, az500) in the derivation result a is the vector of the signal output by signal source S1, and (ax600, ay600, az600) is the vector of the signal output by signal source S2.

[0141] Next, the operation of the second embodiment will be described.

[0142] The read-field matrix derivation unit 120 reads the vector r from the relative position recording unit 110, and derives the components hxx, hxy, hxz, hyx, hyy, hyz, hzx, hzy, and hzz of the relation matrix (read-field matrix) H (see equations (22) to (24) and equations (22') to (24')).

[0143] The read field matrix recording unit 130 receives the relation matrix H from the read field matrix derivation unit 120 and records it.

[0144] The position / vector derivation unit 150 derives the positions and vectors a of signal sources S1 and S2 that minimize the cost function, based on the measurement result b and the relation matrix H (see equation (29)).

[0145] According to the second embodiment, the accuracy of position estimation for multiple signal sources (including coherent signal sources) is improved. That is, since the second embodiment conforms to the Lasso method, position estimation is possible even for coherent signal sources. Moreover, according to the second embodiment, the measurement result b and vector a are grouped for each of the X, Y, and Z axes (see equations (28) and (28')), and the measurement results for all three axes can be used, thus improving the accuracy of position estimation for multiple signal sources.

[0146] Third Embodiment The signal source identification device 1 according to the third embodiment differs from the signal source identification device 1 according to the second embodiment in that it includes a clustering unit 180a, a centroid derivation unit 180b, and a weighted average unit 180c.

[0147] Figure 6 is a functional block diagram showing the configuration of a signal source identification device 1 according to a third embodiment of the present invention. The signal source identification device 1 according to the third embodiment comprises a relative position recording unit 110, a read field matrix derivation unit 120, a read field matrix recording unit 130, a position vector derivation unit 150, a clustering unit 180a, a centroid derivation unit 180b, and a weighted average unit 180c.

[0148] The relative position recording unit 110, the read field matrix derivation unit 120, the read field matrix recording unit 130, and the position vector derivation unit 150 are the same as in the second embodiment and will not be described.

[0149] Figure 7 shows the clustering of the signal sources S1 to S4 by the clustering unit 180a (Figure 7(a)), the derivation of the centroid of the cluster by the centroid derivation unit 180b (Figure 7(b)), and the derivation of the weighted average of the vectors by the weighted average unit 180c (Figure 7(c)). However, in Figures 7(b) and 7(c), the signal sources S1 and S2 are omitted from the illustration.

[0150] Referring to Figure 7(c), position G1 is the true position of the signal source, and the signal vector is ag1. However, if position G1 does not match the voxel, the signal source positions are derived to be S1 and S2. Furthermore, the signal vectors are also derived to be A1 and A2.

[0151] Furthermore, position G2 is the true position of the signal source, and the signal vector is ag2. However, if position G2 does not coincide with a voxel, the signal source positions are derived to be S3 and S4. Furthermore, the signal vectors are also derived to be A3 and A4.

[0152] From the derivation results of the position vector derivation unit 150 (S1-S4 and A1-A4), the true signal source positions G1 and G2 and the true signal vectors ag1 and ag2 are determined.

[0153] First, referring to Figure 7(a), the clustering unit 180a classifies the signal source positions S1 to S4, derived by the position vector derivation unit 150, into clusters corresponding to the number of signal sources (2). In the example in Figure 7(a), signal source positions S1 and S2 are classified into cluster C1, and signal source positions S3 and S4 are classified into cluster C2. The distance between signal source positions S1 and S2 is D1, and the distance between signal source positions S3 and S4 is D2.

[0154] Next, referring to Figure 7(b), the centroid derivation unit 180b derives the centroid of the signal source for each cluster. The centroid G1 of the signal source in cluster C1 lies on the line segment connecting the signal source positions S1 and S2. Note that S1G1 / S2G1 = size of A2 / size of A1. The centroid G2 of the signal source in cluster C2 lies on the line segment connecting the signal source positions S3 and S4. Note that S3G2 / S4G2 = size of A4 / size of A3.

[0155] Furthermore, the clustering can be performed according to the K-means method. In this case, first, two centroids are randomly placed, and then the locations S1 to S4 of the signal sources are classified into clusters according to the proximity of the centroids to the locations S1 to S4 of the signal sources.

[0156] Furthermore, the centroid of the signal source is derived for each cluster, and then the signal source locations S1 to S4 are classified into clusters according to the proximity of the derived centroid to the signal source locations S1 to S4. This derivation of the centroid and classification into clusters is repeated until the derived centroid is in the same position as the centroid immediately before derivation.

[0157] The location of the signal source is identified as the centroids G1 and G2 derived in this manner.

[0158] Furthermore, referring to Figure 7(c), the weighted average unit 180c averages the vector a derived by the position vector derivation unit 150 for each cluster, inversely proportional to the distance between the signal source and the centroid.

[0159] Taking cluster C2 as an example, if vector A3 is (P, Q, 0) and vector A4 is (R, S, 0), then the true signal vector ag2 is ((P*D22+R*D21) / D2, (Q*D22+S*D21) / D2, 0). The same applies to cluster C1, so the explanation is omitted.

[0160] The signal vector is identified as the weighted average ((P*D22+R*D21) / D2, (Q*D22+S*D21) / D2, 0) derived in this way.

[0161] Next, the operation of the third embodiment will be described.

[0162] First, the operation of the relative position recording unit 110, the read field matrix derivation unit 120, the read field matrix recording unit 130, and the position vector derivation unit 150 is the same as in the second embodiment, so a description will be omitted.

[0163] The output of the position vector derivation unit 150 is supplied to the clustering unit 180a, where the positions of signal sources S1 to S4 are clustered (see Figure 7(a)). Next, the centroid derivation unit 180b derives the centroids of clusters C1 and C2 (see Figure 7(b)). These centroids G1 and G2 are the true signal source positions. Finally, the weighted average unit 180c derives the weighted average of the vectors (see Figure 7(c)). The weighted averages ag1 and ag2 are the true signal vectors.

[0164] According to the third embodiment, the position of the signal source and the signal vector can be determined even when the position of the signal source does not coincide with a voxel.

[0165] In the above embodiment, the signal was a magnetic dipole moment, but it may also be an electric dipole moment.

[0166] Furthermore, in the above embodiment, the measurement result b was the product of the relation matrix H and the vector a, but the κ-power of the measurement result b may be the product of the κ-power of the relation matrix H and the vector a (where κ > 1) (see equation (30) below).

[0167]

number

[0168] Fourth Embodiment The fourth embodiment relates to an image output device 20 equipped with a signal source identification device 1 according to the first, second, and third embodiments as a signal source identification unit 22.

[0169] Figure 8 is a functional block diagram showing the configuration of the image output device 20 according to the fourth embodiment. The image output device 20 according to the fourth embodiment includes a signal source identification unit 22, a signal source image addition unit 24, and an image display unit 26.

[0170] The signal source identification unit 22 receives signals represented by vectors having a predetermined direction from multiple signal sources S1 and S2, and, based on the measurement results of multiple sensors (magnetic sensors MS) that measure components of three mutually orthogonal axes, identifies the positions of the signal sources S1 and S2 and the direction of the vectors. The positions of the signal sources S1 and S2 and the direction of the vectors are provided to the signal source image addition unit 24.

[0171] As the signal source identification unit 22, the signal source identification device 1 according to the first, second, and third embodiments can be used. Note that the object OBJ contains multiple signal sources S1 and S2. Examples of signal sources S1 and S2 include magnetic markers (such as permanent magnets) and magnetic materials (such as reinforcing bars). Generally, even if the object OBJ is visually inspected, neither the signal sources S1 and S2 nor the direction of the signal vectors can be perceived.

[0172] The imaging unit 2 is, for example, a camera, and it images the signal sources S1 and S2 together with the object OBJ. Generally, even when looking at the imaging results from the imaging unit 2, it is not possible to perceive the signal sources S1 and S2 or the direction of the signal vectors. The imaging results from the imaging unit 2 only show the object OBJ and the magnetic sensor MS. The imaging results from the imaging unit 2 are provided to the signal source image addition unit 24.

[0173] The signal source image addition unit 24 adds images indicating the signal sources S1 and S2 to the portion of the imaging result from the imaging unit 2 corresponding to the positions of the signal sources S1 and S2 identified by the signal source identification unit 22.

[0174] The image display unit 26 displays the results of the signal source image addition unit 24.

[0175] Figure 9 shows an example of the display of the image display unit 26. Images showing signal sources S1 and S2 (rectangles colored in black and white) are added to the imaging results of the imaging unit 2 (object OBJ and magnetic sensor MS). In the images showing signal sources S1 and S2, the black areas represent the north pole and the white areas represent the south pole. Since the north and south poles are known in the images showing signal sources S1 and S2, the direction of the magnetic vector can also be determined.

[0176] Next, the operation of the fourth embodiment will be described.

[0177] The signal sources S1 and S2 are imaged by the imaging unit 2, object OBJ, and the results are provided to the signal source image addition unit 24.

[0178] When the magnetic sensor MS receives signals from signal sources S1 and S2, represented by magnetic vectors having predetermined directions, it measures components in three mutually orthogonal axes. The measurement results are provided to the signal source identification unit 22, which obtains the positions of signal sources S1 and S2 and the orientation of their vectors. The positions of signal sources S1 and S2 and the orientation of their vectors are provided to the signal source image addition unit 24.

[0179] The signal source image addition unit 24 adds images representing signal sources S1 and S2 to the portion of the imaging result from the imaging unit 2 corresponding to the positions of signal sources S1 and S2 identified by the signal source identification unit 22. The added result is provided to the image display unit 26 and displayed as an image (see Figure 9).

[0180] According to the fourth embodiment, signal sources S1 and S2, such as magnetic fields, can be visualized.

[0181] Furthermore, the following modifications 1, 2, and 3 are possible for the fourth embodiment.

[0182] Variation 1 Figure 10 shows an example of the display of the image display unit 26 in a modified example 1 of the fourth embodiment. The signal source image addition unit 24 further adds coordinate axes X, Y, and Z to the imaging result.

[0183] Variation 2 Figure 11 shows an example of the display of the image display unit 26 in a modified example 2 of the fourth embodiment. The signal source image addition unit 24 adds images showing signal sources S1 and S2 for multiple time points (for example, time points t1 and t2). For example, referring to Figure 11, let's assume that signal sources S1 and S2 moved in the direction of the dashed arrows along with the object OBJ. In this case, images showing signal sources S1 and S2 are added to the imaging result (object OBJ and magnetic sensor MS) at time point t1, and further images showing signal sources S1 and S2 are added to the imaging result (object OBJ and magnetic sensor MS) at time point t2 (>t1).

[0184] Variation 3 Furthermore, it is conceivable that the signal source image addition unit 24 may output an additional result when the viewpoint is changed, based on the coordinates of the positions of the signal sources S1 and S2 and the coordinates of the viewpoint of imaging performed by the imaging unit 2.

[0185] Furthermore, the above embodiment can be realized as follows: A computer equipped with a CPU, a hard disk, and a media (USB memory, CD-ROM, etc.) reader is made to read a media containing a program that implements each of the above parts, for example, the signal source identification unit 22 and the signal source image addition unit 24, and install it on the hard disk. The above functions can also be realized by this method. [Explanation of Symbols]

[0186] 1 Signal source identification device 2 Imaging Unit 20 Image output device 22 Signal source identification section 24. Signal source image addition section 26 Image display section OBJ object MS Magnetic Sensor S1, S2 signal source X, Y, and Z coordinate axes Time points t1 and t2

Claims

1. A signal source identification unit receives signals represented by vectors having a predetermined direction from multiple signal sources, and, based on the measurement results of multiple sensors that measure the components of three mutually orthogonal axes, identifies the position of the signal source and the direction of the vector. A signal source image adding unit adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified by the signal source identification unit, Equipped with, The measurement result of the sensor is proportional to the sum of the results obtained by multiplying each of the three axis components of the vector by a first coefficient. The signal source identification unit, A spectrum derivation unit that derives a spectrum obtained based on the measurement results of the sensor and the sum of the values ​​obtained by multiplying the first coefficient by the second coefficient, wherein the spectrum takes a maximum value in the voxel where the signal source that outputs the signal exists, A direction derivation unit that derives the direction of the vector based on the second coefficient used to obtain the spectrum, A position derivation unit that derives the position of the voxel where the signal source is located based on the spectrum, An image output device equipped with an image output device.

2. A signal source identification unit receives signals represented by vectors having a predetermined direction from multiple signal sources, and, based on the measurement results of multiple sensors that measure the components of three mutually orthogonal axes, identifies the position of the signal source and the direction of the vector. A signal source image adding unit adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified by the signal source identification unit, Equipped with, The signal source identification unit, A relation matrix recording unit records a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A position / vector derivation unit that derives the position of the signal source and the vector that minimize the cost function based on the measurement results and the relation matrix, Equipped with, In the aforementioned vector, its components are grouped together according to the number of grid points in the space where the signal source is located, for each of the three axes. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the position of the signal source and the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the position / vector derivation unit, the position of the signal source and the vector are identified. Image output device.

3. An image output device according to claim 1 or 2, The signal source image addition unit is an image output device that further adds coordinate axes to the imaging result.

4. An image output device according to claim 1 or 2, An image output device in which the image showing the signal source indicates the direction of the vector.

5. An image output device according to claim 1 or 2, The signal source image addition unit adds images showing the signal source for multiple time points in time to the image output device.

6. An image output device according to claim 1 or 2, An image output device in which the signal source image addition unit outputs an additional result when the viewpoint is changed, based on the coordinates of the position of the signal source and the coordinates of the viewpoint of imaging by the imaging unit.

7. An image output device according to claim 1, An image output device in which the position derivation unit derives the position of the voxel in which the signal source is located based on the maximum value of each of the spectra taken in each voxel.

8. An image output device according to claim 2, The derivation result of the position / vector derivation unit is identified as the position of the signal source and the vector. Image output device.

9. An image output device according to claim 2, A clustering unit classifies the positions of the signal sources derived by the position / vector derivation unit into clusters of the number of signal sources, Each of the clusters includes a centroid derivation unit for deriving the centroid of the signal source, For each cluster, a weighted average unit averages the vectors derived by the position / vector derivation unit inversely proportional to the distance between the signal source and the centroid, Equipped with, The position of the signal source is identified as the centroid, The aforementioned vector is identified as the result of the derivation of the weighted average section. Image output device.

10. An image output device according to claim 9, The classification into the aforementioned clusters is performed according to the K-means method. Image output device.

11. A signal source identification step involves receiving signals represented by vectors having a predetermined direction from multiple signal sources, and receiving measurement results from multiple sensors that measure the components of three mutually orthogonal axes to determine the position of the signal source and the direction of the vector, A signal source image addition step adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified in the signal source identification step, An image output method comprising, The measurement result of the sensor is proportional to the sum of the results obtained by multiplying each of the three axis components of the vector by a first coefficient. The signal source identification step is, A spectrum derivation step of deriving a spectrum obtained based on the measurement result of the sensor and the sum of the values ​​obtained by multiplying the first coefficient by the second coefficient, wherein the spectrum takes a maximum value in the voxel where the signal source that outputs the signal is located, A direction derivation step in which the direction of the vector is derived based on the second coefficient used to obtain the spectrum, A position derivation step of deriving the position of the voxel where the signal source is located based on the spectrum, A method for outputting images.

12. A signal source identification step involves receiving signals represented by vectors having a predetermined direction from multiple signal sources, and receiving measurement results from multiple sensors that measure the components of three mutually orthogonal axes to determine the position of the signal source and the direction of the vector, A signal source image addition step adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified in the signal source identification step, An image output method comprising, The signal source identification step is, A relation matrix recording step involves recording a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A position and vector derivation step is performed to derive the position of the signal source and the vector that minimize the cost function based on the measurement results and the relation matrix, Equipped with, In the aforementioned vector, its components are grouped together according to the number of grid points in the space where the signal source is located, for each of the three axes. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the position of the signal source and the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the position and vector derivation process, the position of the signal source and the vector are identified. Image output method.

13. A program that causes a computer to perform image output processing, The aforementioned image output process, A signal source identification step involves receiving signals represented by vectors having a predetermined direction from multiple signal sources, and receiving measurement results from multiple sensors that measure the components of three mutually orthogonal axes to determine the position of the signal source and the direction of the vector, A signal source image addition step adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified in the signal source identification step, A program equipped with, The measurement result of the sensor is proportional to the sum of the results obtained by multiplying each of the three axis components of the vector by a first coefficient. The signal source identification step is, A spectrum derivation step of deriving a spectrum obtained based on the measurement result of the sensor and the sum of the values ​​obtained by multiplying the first coefficient by the second coefficient, wherein the spectrum takes a maximum value in the voxel where the signal source that outputs the signal is located, A direction derivation step in which the direction of the vector is derived based on the second coefficient used to obtain the spectrum, A position derivation step of deriving the position of the voxel where the signal source is located based on the spectrum, A program equipped with [features / equipment].

14. A program that causes a computer to perform image output processing, The aforementioned image output process, A signal source identification step involves receiving signals represented by vectors having a predetermined direction from multiple signal sources, and receiving measurement results from multiple sensors that measure the components of three mutually orthogonal axes to determine the position of the signal source and the direction of the vector, A signal source image addition step adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified in the signal source identification step, A program equipped with, The signal source identification step is, A relation matrix recording step involves recording a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A position and vector derivation step is performed to derive the position of the signal source and the vector that minimize the cost function based on the measurement results and the relation matrix, Equipped with, In the aforementioned vector, its components are grouped together according to the number of grid points in the space where the signal source is located, for each of the three axes. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the position of the signal source and the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the position and vector derivation process, the position of the signal source and the vector are identified. program.

15. A computer-readable recording medium that contains a program for causing a computer to perform image output processing, The aforementioned image output process, A signal source identification step involves receiving signals represented by vectors having a predetermined direction from multiple signal sources, and receiving measurement results from multiple sensors that measure the components of three mutually orthogonal axes to determine the position of the signal source and the direction of the vector, A signal source image addition step adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified in the signal source identification step, A recording medium comprising, The measurement result of the sensor is proportional to the sum of the results obtained by multiplying each of the three axis components of the vector by a first coefficient. The signal source identification step is, A spectrum derivation step of deriving a spectrum obtained based on the measurement result of the sensor and the sum of the values ​​obtained by multiplying the first coefficient by the second coefficient, wherein the spectrum takes a maximum value in the voxel where the signal source that outputs the signal is located, A direction derivation step in which the direction of the vector is derived based on the second coefficient used to obtain the spectrum, A position derivation step of deriving the position of the voxel where the signal source is located based on the spectrum, A recording medium equipped with the following features.

16. A computer-readable recording medium that contains a program for causing a computer to perform image output processing, The aforementioned image output process, A signal source identification step involves receiving signals represented by vectors having a predetermined direction from multiple signal sources, and receiving measurement results from multiple sensors that measure the components of three mutually orthogonal axes to determine the position of the signal source and the direction of the vector, A signal source image addition step adds an image indicating the signal source to the portion of the imaging result of the imaging unit that images the signal source, corresponding to the position of the signal source identified in the signal source identification step, A recording medium comprising, The signal source identification step is, A relation matrix recording step involves recording a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A position and vector derivation step is performed to derive the position of the signal source and the vector that minimize the cost function based on the measurement results and the relation matrix, Equipped with, In the aforementioned vector, its components are grouped together according to the number of grid points in the space where the signal source is located, for each of the three axes. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the position of the signal source and the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the position and vector derivation process, the position of the signal source and the vector are identified. Recording medium.

Images