JP2005351869A - Positioning method and system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a positioning method and a positioning system capable of solving problems in a conventional positioning method, being utilized outdoors and indoors, and constantly measuring from a small space of several meters square to a wide space of several 100 meters square with high accuracy, without lowering the accuracy even when a substance disturbing the magnetic field such as metal, exists near the system. <P>SOLUTION: This positioning system comprises indicators emitting the light flashing with various patterns, of which positional coordinates in a three-dimensional space are known, an image pick-up means for picking up an image including at least two or more indicators among the indicators, a calculating means for calculating the positional coordinates in the three-dimensional space of the image pick-up means from the positional coordinates in the image of the indicators, and a storing means for storing the calculated positional coordinates of the image pick-up means. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a technique for acquiring position coordinates of various information devices in a three-dimensional space with high accuracy.

In recent years, a method using GPS is widely used as a technique for acquiring the position coordinates of an object existing in a three-dimensional space.
This method measures the time required to reach the receiver after the radio wave is transmitted from the satellite by receiving information such as the position and time of the satellite transmitted from the GPS satellite with one antenna. It is converted into distance, and the position of the observation point is determined by simultaneously knowing the distance from four or more satellites to the observation point by using a GPS satellite whose position is known as a moving reference point. An error of about 10 m occurs due to an error or a delay of the radio wave when the radio wave from the satellite passes through the troposphere or the ionosphere.

There are methods called DGPS (Differential GPS) positioning and RTK-GPS (Real-time kinematic-GPS) positioning as methods for reducing the measurement error and performing highly accurate position measurement.
Both of these methods simultaneously perform GPS observations at a reference station whose position is known and the observation point for which the position is to be obtained, and transmit the data observed at the reference station to the observation point in real time using radio etc. Based on the results, the position of the observation point is obtained in real time.

DGPS performs independent positioning at both points, obtains the difference between the position result and the observed coordinate value at the reference station, and transmits the difference to the observation point as correction information.
On the other hand, RTK-GPS measures the phase at both points and transmits the phase data observed at the reference station to the observation point. The GPS receiver at the observation point determines the position of the observation point by analyzing the received data and the data transmitted from the reference station in real time.
In these methods, since various error factors are eliminated, it is possible to measure the position with an error of several meters for DGPS and several centimeters for RTK-GPS.
Since the method using GPS described above uses an artificial satellite, it can be used in a wide range of places on a global scale. For this reason, it is used for the position measurement of a moving body including car navigation (for example, refer nonpatent literature 1 and nonpatent literature 2).

  On the other hand, as a position measuring method in a small space of about several meters square, there is a method using a magnetic field whose principle is shown in FIG. In FIG. 7, 71 is a transmitter that generates a magnetic field, and 72 is a sensor that measures the strength of the magnetic field in space. Reference numerals 73 and 74 denote a drive circuit and a detection circuit, 75 denotes a computer, and 76 denotes an output unit. Both the transmitter 71 and the sensor 72 are composed of three coils orthogonal to each other.

The principle is that an alternating magnetic field is first generated by applying an alternating current to a transmitter coil orthogonal to the x, y, and z directions. An alternating current is applied to each coil in order in a time division manner. When a sensor is placed in this alternating magnetic field, a current is induced in each of the x, y, and z coils of the sensor, and the strength of the current is determined by the distance and direction from the transmitter. The three-dimensional position coordinates x, y, z and the direction of the sensor are measured by solving simultaneous equations based on 9 × 3 data obtained by these correlations.
Such a method using a magnetic field is characterized in that it can be measured without contact and can be measured without being affected by a physical obstacle (see, for example, Patent Document 1).

Takey Sakai, “Introduction to GPS Technology”, Tokyo Denki University Press, March 2003, p. 1-p.131 ITS Information Communication System Promotion Conference, “Illustration of GPS”, Morikita Publishing Co., Ltd., March 2004, p.44-p.80 JP-A-10-51711

However, the method using the GPS cannot be used indoors or underground shopping areas where radio waves do not reach. Even in the outdoors, accurate location measurement becomes difficult due to reflection of radio waves in high-rise buildings and the like.
On the other hand, the method using a magnetic field can be used indoors, but there is a problem that accurate measurement becomes difficult when there is an object such as a metal that disturbs the magnetic field in the vicinity of the magnetic sensor. There is also a problem that the maximum measurement range is as narrow as about 3 m from the transmitter.

  In view of such problems, the present invention is intended to solve the problems of the conventional position measurement method, and can be used regardless of whether it is outdoors or indoors, and an object that disturbs a magnetic field such as metal nearby. The present invention also provides a position measurement method that can always perform highly accurate measurement from a small space of several square meters to a wide space of several hundred square meters without causing a decrease in accuracy even in the case where there is a problem.

  In solving the above-described problems, the positioning method and positioning system according to the present invention first uses a plurality of indices whose position coordinates in the three-dimensional space are known using imaging means whose position coordinates in the three-dimensional space are unknown. It is an object of the present invention to provide a positioning method for capturing an image including two or more indices and specifying the position coordinates of the imaging means from the position coordinates of the indices in the image.

  Second, a plurality of indices whose positions in the three-dimensional space are known, imaging means for capturing an image including at least two indices among the indices, and positions of the indices in the captured image in the image Computation means for calculating position coordinates in the three-dimensional space of the image pickup means from the coordinates, and storage means for storing the calculated position of the image pickup means, the image pickup means comprises an image pickup optical system and an image pickup element. A band-pass filter that allows only light of a predetermined width to pass may be disposed in front of the imaging optical system, in the imaging optical system, and anywhere between the rear end of the imaging optical system and the imaging element. The plurality of indicators are light sources that emit light, and each of the plurality of indicators emits light that blinks in different patterns, and the blinking pattern of the indicator represents identification information or position information of the indicator. Of this indicator In the case where at least one of the indicators is composed of a plurality of light sources, the distance and direction of each light source question is determined in a predetermined manner. It serves to specify the index in the captured image.

  In the present invention, the position coordinates of the image pickup means are calculated from the position coordinates of the indices in the image captured by the image pickup means by arranging a plurality of indices serving as light sources in a three-dimensional space. If it exists, it is possible to specify the self-position with high accuracy regardless of whether it is outdoors or indoors, and an inexpensive LED is used as the light source, and a CCD imaging device whose cost is being reduced is used as the imaging means. The positioning system can be constructed at a low cost, and has a remarkable industrial effect.

In the positioning in the present invention, at least two or more indices with known position coordinates are imaged from an imaging means whose position coordinates are unknown, and the position coordinates of the imaging means are specified from the position coordinates of the indices in the captured image. It is.
Hereinafter, the details of the present invention will be described with reference to FIG.

FIG. 1 is a diagram illustrating the principle of a positioning method and positioning system according to the present invention.
In FIG. 1, P ₁ and P ₂ indicate indices, C is the pupil position of the lens constituting the imaging means, and P ₁ ′ and P ₂ ′ are images on which the indices P ₁ and P ₂ are projected onto the imaging surface S. Show.
Here, the space where the imaging means and the index exist is represented by a three-dimensional coordinate system (x, y, z) as shown in FIG. 1A, and the coordinates of the imaging means, more precisely, the pupil position of the lens. Let the coordinates of C be (x ₀ , y ₀ , z ₀ ). These coordinates (x ₀ , y ₀ , z ₀ ) are position coordinates of the imaging means to be specified.

Next, another three-dimensional coordinate system (X, Y, Z) is considered for convenience. In this three-dimensional coordinate system (X, Y, Z), coordinates are selected as follows.
First, the pupil position C of the lens of the imaging unit is set as the origin, and the optical axis of the lens of the imaging unit is arranged to be parallel to the Z axis so that the Z axis is perpendicular to the imaging surface. Further, on the imaging surface, the horizontal scanning direction of the imaging device is made parallel to the X axis, and the vertical scanning direction is made parallel to the Y axis.

These two coordinate systems can be converted into each other by operations of translation and rotation.
Since the position of (x ₀ , y ₀ , z ₀ ) in the coordinate system (x, y, z) is the origin in the coordinate system (X, Y, Z), the amount of movement is the x, y, z axis. X ₀ , y ₀ , and z ₀ , respectively. On the other hand, for rotation, suppose that the coordinate system (X, Y, Z) is obtained by rotating the coordinate system (x, y, z) by θ, φ, ψ about the x-axis, y-axis, and z-axis, respectively. The relationship expressed by Equation 1 is established between the coordinate system (X, Y, Z) and the coordinate system (x, y, z).

Here, since the three-dimensional coordinate system (X, Y, Z) is selected as in paragraph 0015, the coordinate axis, the lens pupil plane, and the imaging plane can be represented by the positional relationship shown in FIG.
In FIG. 1B, the distance f between the pupil position C of the lens and the imaging surface S represents the focal length of the lens, and the coordinates of _three indices P ₁ , P ₂ and P ₃ (omitted in the figure) are respectively shown. (X ₁ , Y ₁ , Z ₁ ), (X ₂ , Y ₂ , Z ₂ ), (X ₃ , Y ₃ , Z ₃ ). Also, the coordinates of the positions where these indexes are formed on the imaging surface by the lens are (x ₁ ′, y ₁ ′), (x ₂ ′, y ₂ ′) as shown in FIG. , (X ₃ ′, y ₃ ′) ((x ₃ ′, y ₃ ′ is omitted in FIG. 1 c)), Equation 2 is established between these coordinates due to a similar relationship. Here, (x ₁ ′, y ₁ ′), (x ₂ ′, y ₂ ′), (x ₃ ′, y ₃ ′) represent two-dimensional coordinates on the imaging surface and represent the optical axis of the lens. Is the coordinate when the horizontal scanning direction is selected as x ′ and the vertical scanning direction is selected as y ′.

Next, (x ₁ ′, y ₁ ′), (x ₂ ′, y ₂ ′), (x ₃ ′, y ₃ ′) are obtained from image signals obtained by imaging the three indexes, and are known coordinates. If (X ₁ , Y ₁ , Z ₁ ), (X ₂ , Y ₂ , Z ₂ ), (X ₃ , Y ₃ , Z ₃ ) are substituted into Formula (2), Formula 2 is The unknown is x ₀ , y ₀ , z ₀ , θ, φ, ψ, and the number of equations becomes six simultaneous equations. Therefore, the position (x ₀ , y ₀ , z ₀ ) of the imaging means can be obtained by solving the simultaneous equations. Further, the orientation (θ, φ, ψ) of the imaging means can be obtained and known.

  The above is based on the premise of six degrees of freedom that the lens optical axis of the image pickup means can be translated in three directions of x, y, and z, and can be rotated around each of the three axes of the x, y, and z axes. However, if the lens optical axis of the image pickup means is always horizontally oriented and only rotation with the y axis as the rotation axis is allowed, the unknowns are x, y, z, and θ, and the indices to be imaged simultaneously. The number is also two.

  As is apparent from the above principle, the present invention can be implemented not only outdoors but also indoors by arranging a predetermined index in the space. In addition, even in high-rise buildings, if there is an indicator in the field of view, it can be implemented without being affected by the building.

  The measurement accuracy of the positioning system of the present invention depends on the resolution of the image sensor, and a value obtained by dividing the distance between the index and the image pickup means by the number of pixels in one direction of the image sensor is an approximate accuracy. In recent years, image sensors with millions of pixels are available at low cost, but in these image sensors, the number of pixels in one direction exceeds 1000. For example, when the distance between the index and the imaging means is several meters, the measurement accuracy is several millimeters, and high-precision measurement is possible.

  Since light is used, even if there is a metal nearby, high-precision measurement is possible without being affected by it. Furthermore, measurement is possible within the reach of light, and the measurement range can be expanded as compared with a method using a magnetic field. Further, the above-described index used in the present invention can be an inexpensive light source such as an LED, and the imaging unit is also inexpensive because the cost of the CCD imaging device has been reduced in recent years. It also has the feature that can be built.

Details of the embodiment of the present invention will be described below with reference to FIGS.
(Example 1)
A first embodiment of the present invention is shown in FIG. FIG. 2 is a block diagram showing the basic configuration of the positioning system. In FIG. 2, the positioning system 1 includes indices 21 to 2n and a positioning device 3.

  The indicator 21 includes a light emitting unit 211, a blinking control unit 212, and a storage unit 213. The light emitting means 211 emits blinking light based on an instruction from the blinking control means 212. The blinking control unit 212 reads the light emission pattern information stored in the storage unit 213, and controls the light emitting unit 211 to blink by the light emission pattern. An example of this light emission pattern is shown in FIG.

In FIG. 3, information encoded by binary values in the time direction, with “1” at the time of light emission and “0” at the time of extinction, or “0” at the time of light emission and “1” at the time of extinction. To do. This information includes at least the unique ID of each index. The blinking cycle of the light emitting means indicated by “T” is equal to or longer than the frame period or field period of the imaging means.
So far, the structure and the light emission pattern of the index 21 have been described, but the same applies to the other indices 22 to 2n. However, a unique ID is assigned to each index, and a light emission pattern considering the unique ID is stored in each storage unit.
Therefore, each indicator emits light with a different light emission pattern. In this embodiment, an LED having an emission spectrum half-width of about several tens of nanometers is used as the indicator light emitting means. In addition, the number and location of the indicators should be taken into consideration such as the angle of view of the imaging so that at least three indicators are always captured in the captured image, regardless of the direction the imaging means can take in normal use. decide.

The positioning device 3 includes an imaging unit 31, a calculation unit 32, and a storage unit 33. The optical band-pass filter 4 is disposed in the imaging means 31 in front of the imaging optical system, in the imaging optical system, and at any location between the imaging optical system and the rear end of the imaging optical system.
The center wavelength of the transmitted light of the optical bandpass filter 4 is the same as or near the center wavelength of the light emission of the LED as the light emitting means, and the half width is equal to or less than the half width of the emission spectrum of the LED. .

The image pickup means 31 of the present embodiment uses the bandpass filter, so that light from the index among the light reaching the image sensor is not greatly affected by the intensity, whereas light from other than the index is not received. The strength is significantly reduced. The image picked up by the image pickup means 31 in this way is transmitted to the calculation means 32. The computing means 32 first binarizes the captured image using an appropriate threshold and extracts an index.
That is, due to the effect of the bandpass filter, since the intensity of light from other than the index is reduced, it is possible to extract only the lit index by setting an appropriate threshold value. Next, the position on the imaging surface is recognized from the coordinates of the extracted index pixel, the index blink pattern is read from the temporally continuous frame image, and the index ID is read.

  The three-dimensional coordinate information of each index is stored in the storage means 33 corresponding to each ID. When the calculation unit 32 reads the ID from the blinking pattern, the calculation unit 32 reads the three-dimensional coordinate information corresponding to the ID from the storage unit 33. By the above method, the three-dimensional coordinate information corresponding to the ID is obtained for each of the three indexes shown in the captured image, and the three-dimensional coordinate information is used to capture an image from the formula (1) and the formula (2). The position of the means is obtained and output. If four or more indices are shown in the captured image, any three are selected and the process is executed.

(Example 2)
An example according to the second embodiment of the present invention will be described with reference to FIGS.
The basic configuration of the positioning system is the same as the basic configuration of the positioning system shown in FIG. 2 of the first embodiment, and includes a plurality of indicators and positioning devices.
In this embodiment, the indicator has two light emitting means 211A and 211B arranged adjacent to each other as shown in FIG. Of these two light emitting means, the light emitting means 211A operates in the same manner as the light emitting means 21 of the first embodiment. That is, blinking light is emitted based on an instruction from the blinking control unit 212. Then, the blinking control unit 212 reads the light emission pattern information stored in the storage unit 213, and controls the light emitting unit 211A to blink by the light emission pattern.

The other light emitting means 211B emits flashing light at the same period as the frame period of the imaging means as shown in FIG. In FIG. 5, T _F is the frame period, f ₀ is the odd field period of the image pickup means, f _e represents an even field period.

By using the index, prevention of erroneous index extraction and position measurement for each frame are realized.
First, since the light emitting means 211B blinks at the same frequency as the frame frequency, if the light emission period is set shorter than the field period, the light emission means 211B is extracted in either the odd field or the even field. Not extracted for consecutive fields. Accordingly, if only one of the fields in one frame is extracted, it is the indicator light emitting means used in this embodiment, and the position information is acquired from the blinking pattern of the light emitting means in the vicinity.

On the other hand, if it is extracted in both fields in one frame, it is recognized as a light emitting object other than the index. In addition, when the light emission period of the light emitting means 211B extends over the odd field and the even field, the light is extracted in both fields. Therefore, when there is an object that is always extracted in both fields in the frame in the screen, the phase of the field frequency of the imaging means is shifted by the light emission period of the light emitting means 211B. As a result, the light emission period falls within either the odd field or the even field, and is not extracted in consecutive fields. Even in this case, the object detected in both fields can be determined to be an object other than the indicator light emitting means used in this embodiment.
As described above, even when there is a high-luminance luminescent object other than the index, only the index can be accurately extracted.

Next, it will be described that position measurement for each frame is possible.
Also in the second embodiment, as in the first embodiment, “1” and “0” are assigned to turn on and off the light emitting means, and the unique ID of each index is represented by a binary code in the time direction. Since at least one field period of the imaging means is required to acquire 1-bit information, for example, if the ID of the index is 8 bits, at least 8 field periods, that is, 4 frame periods are required before reading the ID. I need. Here, if it is possible to identify the index extracted by reading the ID over the first 8 field periods, then tracking this even if the index moves through the screen, it takes 8 field periods to identify There is no need to read 8-bit information.

In the first embodiment, there may be a case where the number of light emitting means is one, the pattern corresponding to the ID is blinked, and “0” continues. In the case of “0”, the light is extinguished and position information cannot be obtained in the field or frame. In addition, if this unlit field or frame continues for a long time, it becomes difficult to track the index.
However, in the second embodiment, since the light emitting means that blinks in the frame period is provided separately from the light emitting means that emits the ID information, the tracking becomes easy. It is possible to acquire the position of the index for each frame.

(Example 3)
A third embodiment of the present invention will be described with reference to FIG.
The basic configuration of the positioning system is composed of a plurality of indicators and positioning devices in the same manner as the basic configuration of the positioning system shown in FIG. 2 of the first embodiment, but the index used in the third embodiment is composed of a plurality of light sources. In addition, the ID assigned to each index is represented by the arrangement pattern of the light sources that are lit among the plurality of light sources.

FIG. 6 shows an example of an index used in the third embodiment. Light sources are arranged at equal intervals indicated by P _{0 to} P ₄ , and light sources at positions P ₀ and P ₁ are always lit. Suppose you are. On the other hand, the light sources at the positions P ₂ , P ₃ and P ₄ represent ID as a three-digit binary number, and represent “1” when turned on and “0” when turned off. In FIG. 6, “101” is represented.

  Next, the method for identifying the self-position of the image pickup means is as follows: first, an image picked up and transmitted by the image pickup means is subjected to binarization of the image and filtering by an optical bandpass filter to constitute an index. The light source to be extracted is extracted. Note that, as in normal imaging, the imaging means is used with the horizontal scanning direction parallel to the horizontal direction, and the inclination is always within ± 90 degrees even if an inclination occurs.

In FIG. 6, the light sources at the positions of P ₀ and P ₁ are lit at any of the indices. Therefore, when a light source group is extracted from the captured image, the light source on the leftmost side and the light source on the right side thereof are first. A light source is extracted. The distance D and direction between the two light sources are obtained. Next, P ₂ , P ₃ , and P ₄ are located at distances of D, 2D, and 3D, respectively, from P ₁ on the extension of the line drawn from P ₀ to P ₁ . Therefore, by checking the luminance of the pixels corresponding to these positions in the binarized image, it is checked whether the light sources arranged at these positions are turned on or off. By performing the above processing, the index ID is obtained.

Next, the three-dimensional coordinate information of each index is stored in the storage unit corresponding to each ID, and when the calculation unit obtains the ID, the three-dimensional coordinate information corresponding to the ID is read from the storage unit.
By the above method, the three-dimensional coordinate information corresponding to the ID is obtained for each of the three indices shown in the image, and the three-dimensional coordinate information is used to capture an image from the equations (1) and (2). The position coordinates of the means are obtained and output. Also in the third embodiment, when four or more indexes are shown in the captured image, arbitrary three indexes are selected and the above process is executed.

  Although the present invention has been described above using three examples, it goes without saying that various embodiments can be adopted within the scope of the present invention. For example, in the three examples, all of the indicator light emitting means are used. The information emitted from the ID is ID information for identifying the index, and the position information is obtained from the storage means stored in correspondence with this ID information. Thus, the position information of the index can be read directly from the light emitting means.

  In the second embodiment, as a method for distinguishing the index from the light emitting object other than the index, a method is described in which two light emitting means are provided and one of them is blinked at a frame period. In addition to the above method, for example, when the luminescent object other than the index is sufficiently larger than the index, the index and the perimeter of the luminescent object can be calculated and obtained by a known method. It is also possible to distinguish from light emitting objects other than the index.

In the above three embodiments, the positioning device 3 is composed of the image pickup means 31, the calculation means 32, and the storage means 33. However, the image pickup means 31, the calculation means 32, and the storage means 33 are each physically independent devices. It is also possible to install them at positions far away from each other.
In addition, the present invention can be implemented by using any light emitting means of any wavelength as the light emitting means as long as there is an imaging means corresponding to the wavelength. Therefore, invisible light such as infrared light can be used, and in this case, the presence of the index can be made inconspicuous.

  In each of the embodiments described above, it goes without saying that the computer can execute a processing procedure for position measurement executed by the computing means, and the computer executes a program for causing the computer to execute the processing procedure. It can be provided and distributed by being recorded on a readable storage medium such as a flexible magnetic disk, a magneto-optical disk, a ROM, a memory card, a CD, a DVD, or a removable disk.

Explanatory drawing of the principle of the present invention (a) xyz coordinate system, (b) XYZ coordinate system. It is a block diagram in Example 1 of this invention. It is the figure which showed the example of the light emission pattern of the light emission means of the parameter | index in Example 1 of this invention. It is a block diagram of the light emission means used in Example 2 of this invention. It is the figure which showed the example of the light emission pattern of one light emission means among the several light emission means of the parameter | index in Example 2 of this invention. It is the figure which showed the example of arrangement | positioning of the some light emission means of the parameter | index in Example 3 of this invention. It is a block diagram of the method using the conventional magnetic field.

Explanation of symbols

P ₁ , P ₂ indices P ₁ ′, P ₂ ′ Images of indices P ₁ and P ₂ projected onto the captured image plane C The pupil position S of the lens constituting the imaging means S Imaging plane _TF Frame period f of the imaging means ₀ Odd-numbered field period _fe Imaging means even-numbered field periods P ₀ , P ₁ , P ₂ , P ₃ , P ₄ Light emitting means 1 Positioning systems 21 to 2n Indicators 211, 211 A, 211 B Light emitting means 212 Flashing control means 213 Storage means 3 Positioning device 31 Imaging means 32 Calculation means 33 Storage means 4 Optical bandpass filter 71 Transmitter 72 that generates a magnetic field Sensor 73 that measures the strength of the magnetic field in the space 73 Drive circuit 74 Detection circuit 75 Computer 76 Output section

Claims (8)

A positioning method for specifying position coordinates of an object whose position in the three-dimensional space is unknown, and a plurality of positions whose coordinates in the three-dimensional space are known by using an imaging means whose position coordinates in the three-dimensional space are unknown A positioning method characterized in that an image including two or more of the indices is picked up from the indices and the position coordinates of the imaging means in a three-dimensional space are specified from the position coordinates of the indices in the picked-up image. A positioning system for identifying position coordinates of an object whose position in the three-dimensional space is unknown, a plurality of indices whose position coordinates in the three-dimensional space are known, and at least two or more indices among the indices An imaging unit that captures an image including the image, a calculation unit that calculates a position coordinate of the imaging unit in a three-dimensional space from a position coordinate of the index in the captured image, and a calculated position coordinate of the imaging unit A positioning system comprising storage means. The imaging means is composed of an imaging optical system and an imaging element, and has a wavelength of a predetermined width at any position in front of the imaging optical system, in the imaging optical system, and between the rear end of the imaging optical system and the imaging element. The positioning system according to claim 2, wherein a band-pass filter that allows only light to pass is disposed. 3. The positioning system according to claim 2, wherein the plurality of indicators are light sources that emit light, and each of the plurality of indicators emits light that blinks in different patterns. The positioning system according to claim 4, wherein the blinking pattern of the index represents identification information or position information of the index. The positioning system according to claim 4, wherein the index is specified by blinking the index. The positioning system according to claim 4, wherein at least one of the indices is composed of a plurality of light sources. The positioning system according to claim 7, wherein, in the index composed of the plurality of light sources, the index is specified from the captured image by predetermining the distance and direction of each light source.

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