JP6379651B2 - Apparatus, method, and program for measuring light distribution of light source and bidirectional reflectance distribution function of object - Google Patents

Description

  The present invention relates to an apparatus, method, and program for measuring a light distribution of a light source from a group of captured images of an object illuminated with a light source, and to an apparatus, method, and program for measuring a bidirectional reflectance distribution function of an object. is there.

  The appearance of an object is affected by the illumination / observation environment. Therefore, it is very useful to reproduce the appearance of an object in an arbitrary illumination / observation environment as an image.

  As one method of image reproduction, physical information such as reflection characteristics and shape, which are the elements of object appearance, is recorded, and an image of object appearance in an arbitrary illumination / observation environment is generated using computer graphic technology based on the physical information. There is a way to do it.

  As a method for measuring / recording the reflection characteristic of an object among physical information, there is a method for estimating the reflection characteristic by analyzing reflected light from a plurality of captured images having different illumination directions. However, when the light sources are discretely arranged to illuminate from different directions, the sampling of the illumination direction is rough, and there may be cases where the reflected light sufficient for analyzing the direction-dependent reflection characteristics such as sharp glossiness cannot be obtained. is there. Although a method of increasing the number of light sources is conceivable, it is difficult to determine an appropriate number of light sources for an object whose reflection characteristics are unknown.

  Therefore, for example, as in Non-Patent Document 1, an approach method in which sampling in the illumination direction is made dense by illuminating in different directions from each point on the surface of the light source using a fluorescent lamp is conceivable. In this approach method, it is necessary to grasp the radiance of light rays from each point on the surface of the light source to each point on the surface of the target object. However, the light distribution curve (Non-Patent Document 2) provided by the light source manufacturer, which is the angular distribution of the luminous intensity of the emitted light, represents only the distribution of the entire light source, and the emitted light is emitted from each point on the surface of the light source. You cannot get brightness.

  In Patent Document 1, there is a method in which a camera is placed on a sphere centered on a light source, and the light distribution at each point on the surface of the light source is acquired by photographing the light source at a high resolution at each position. ing. However, in this method, since the directional resolution of the light distribution depends on the camera arrangement interval, it is necessary to reduce the camera arrangement interval in order to obtain a high directional resolution.

  Furthermore, in Patent Document 2, there is a method of estimating a light distribution by illuminating a curved or concave screen with a light source that estimates the light distribution and photographing the radiance of reflected light with a camera. . By photographing the screen at a high resolution using a camera, a higher directional resolution of the light distribution than the light distribution obtained at the camera arrangement interval described in Patent Document 1 can be obtained.

  However, in Patent Document 2, since light rays incident on the same point on the screen are not separated from each point on the light source surface, it is not possible to obtain a light distribution at each point on the light source surface.

JP 2013-217651 A Japanese Patent No. 5350906

Gardner (GARDNER, A.), Cho (TCHOU, C.), Hawkins (HAWKINS, T.), and Devevec (DEBEVEC, P.), "Linear light source reflectometry", ACM Transactions Graphics (ACM Transactions On Graphics), 2003, Vol. 22, No. 3, p. 749-758 "Z8113 Lighting terminology", Japanese Industrial Standard (JIS)

  The present invention has been made in view of the above problems, and an object thereof is to provide a method, an apparatus, and a program for measuring a light distribution at each point on a light source surface with high directional resolution.

  One aspect of the present invention for solving the above problems is an apparatus for measuring a light distribution of a light source, which is a target light source that is a light source to be measured, and has an object having a diffuse reflection component and a known reflection characteristic A photographing means for photographing at least an object with a camera and obtaining an actual sensor response value, an object posture measuring means for obtaining the position and normal of each point on the object surface in a three-dimensional space, and a target The target light source approximation means for approximating the light source as a set of one or more infinitesimal light sources, and the position and orientation of the target light source are represented by rotation parameters and movement parameters in a three-dimensional space. A target light source posture calculating means for calculating a posture that is an orientation, a light distribution distribution model in which the light distribution of an infinitely small light source is modeled with mathematical formulas and / or measurement data, Is based on the light distribution model parameter that is a parameter of the measurement data, the emitted light calculating means for calculating the radiance of the emitted light in an arbitrary direction, the position of the infinitesimal light source calculated by the target light source attitude calculating means, Distance calculation means for calculating the distance between the position of the infinitesimal light source and each point on the object surface from the position of each point on the object surface obtained by the object posture measuring means, a light distribution distribution model, and a light distribution Model parameters, the attitude of the infinitesimal light source calculated by the target light source attitude calculation means, the position and normal of each point on the object surface obtained by the object attitude measurement means, the position of the infinitesimal light source and the object surface The incident light calculation means for calculating the direction and radiance of the light ray incident on the position of each point on the object surface from the distance of each point, and the direction and radiation of the light ray incident on the position of each point on the object surface The luminance and each point on the object surface Sensor response value when the object is illuminated with the target light source from the correspondence relationship between the position, normal and reflection characteristics, the position of the camera, the radiance of the light incident on the camera, and the sensor response value of the camera. An error for calculating an error based on a difference between a sensor response value calculation means for calculating a calculated value, an actual measurement value of the sensor response value acquired by the imaging means, and a calculated value of the sensor response value obtained by the sensor response value calculation means A light distribution distribution measuring apparatus comprising: a calculation unit; a parameter estimation unit that optimizes a rotation parameter, a movement parameter, and a light distribution distribution model parameter, and estimates a parameter that minimizes an error.

  Further, the error calculation means obtains the measured value of the sensor response value and the calculated value of the sensor response value for two or more objects having different reflection characteristics, and calculates the measured value of the sensor response value for each of the objects as an error and You may calculate the sum total of the error based on the difference with the calculated value of a sensor response value.

  Further, the error calculation means obtains the measured value of the sensor response value and the calculated value of the sensor response value for two or more objects having different reflection characteristics, and calculates the measured value of the sensor response value for each of the objects as an error and You may calculate the sum total of the error based on the difference with the calculated value of a sensor response value.

  The emitted light calculation means calculates the radiance of the emitted light for different light distribution distribution models, the sensor response value calculation means calculates the sensor response value for each light distribution distribution model, and the error calculation means calculates the light distribution. The error for each distribution model is calculated, and the parameter estimation means optimizes the rotation parameter, movement parameter, light distribution model, and light distribution model parameter, and estimates the parameter that minimizes the error. May be.

Another aspect of the present invention is an apparatus for measuring a bidirectional reflectance distribution function of an object, and is bidirectional with the first object for measuring the light distribution using the above-described light distribution distribution measuring apparatus. For each state in which the second object whose reflectance distribution function is to be measured is illuminated by light sources having different postures, the sensor response values of the first and second objects are measured by photographing means. Value is obtained, and based on the measured value of the sensor response value of the first object, the light distribution distribution model of the light source, the light distribution distribution model parameter, and the position and orientation of the infinitesimal light source approximating the light source are determined for each posture of the light source. Based on the light distribution distribution estimation means to be estimated, the second object posture measurement means for obtaining the position and normal of each point on the second object surface in the three-dimensional space, the light distribution distribution model and the light distribution distribution model parameters The radiance of the emitted light to each point on the second object surface The position of the infinitesimal light source and the position of each point on the second object surface obtained by the second object posture measurement means are calculated from the second emission light calculation means for calculating, the position of the infinitesimal light source, and the position of each point on the second object surface. Obtained by a second distance calculating means for calculating the distance to each point on the object surface, the light distribution distribution model and the light distribution distribution model parameters, the attitude of the infinitesimal light source, and the second object attitude measuring means. Incident on the position of each point on the second object surface from the position and normal of each point on the second object surface and the distance between the position of the infinitesimal light source and each point on the second object surface Second incident light calculation means for calculating the direction and radiance of the light beam to be emitted, the direction and radiance of the light beam incident on the position of each point on the second object surface, and each point on the second object surface Bidirectional reflectance distribution function that models the position, normal, and reflection characteristics to be measured with mathematical formulas and / or measurement data Based on the correspondence between Dell, the position of the camera, the radiance of the light incident on the camera, and the sensor response value of the camera, the calculated value of the sensor response value is calculated when the second object is illuminated with the light source and shot. Based on the second sensor response value calculating means, the measured value of the sensor response value of the second object acquired by the imaging means, and the calculated sensor response value obtained by the second sensor response value calculating means. A second error calculating means for calculating an error, and a normal of each point on the surface of the second object, which is a parameter of the bidirectional reflectance distribution function model , and a reflection characteristic to be measured ; A bidirectional reflectance distribution function measuring apparatus comprising: a second parameter estimating unit that estimates a parameter that minimizes an error calculated by the second error calculating unit.

  The present invention is also directed to a method and program for measuring the light distribution of a light source and measuring the bidirectional reflectance distribution function of an object.

  According to the present invention, an object having a diffuse reflection component is illuminated with a light source that measures a light distribution, and a sensor response value of a photographed image obtained by photographing the target object with a camera is used. Optimizing each parameter with the orientation of the light source expressed by parameters of rotation and movement in three-dimensional space when approximated by a set, and the light distribution of the light source modeled by parameters based on mathematical formulas and measurement data It is possible to provide a method, an apparatus, and a program that are derived by a non-linear optimization process as an object to be converted and measure the light source orientation and the light distribution at each point on the light source surface.

Explanatory drawing showing the example of a structure of the 1st measurement system using the light distribution distribution measuring apparatus which concerns on this invention. Explanatory drawing showing the structural example of the 2nd measurement system using the light distribution distribution measuring apparatus which concerns on this invention. Explanatory drawing of the light distribution distribution estimation process which concerns on this invention

  Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the drawings.

  First, a first configuration example of the present invention will be described with reference to FIG. FIG. 1 is an explanatory diagram illustrating a state of light distribution distribution measurement using the light distribution distribution measurement system 10 according to this configuration example. The light distribution distribution measuring system 10 includes a light source 11, an object 12 having a reflection characteristic of a diffuse reflection component, a digital camera 13 (hereinafter referred to as a camera as appropriate), a computer 14, a monitor 15, and a keyboard 16. Yes. The light source 11 is a measurement target light source for which the posture and the light distribution are to be acquired, and is arranged in a posture capable of illuminating the object 12. The digital camera 13 is a photographing unit, and includes a lens, an optical sensor (hereinafter referred to as a sensor), a storage unit, and the like. The digital camera 13 focuses on the object 12 and captures a digital image obtained by photographing the object 12. It outputs to the computer 14 as a sensor response value. The computer 14 includes storage means such as a hard disk as an external storage device and a memory as a primary storage device, a CPU as an arithmetic device, etc., controls the digital camera 13, and saves a photographed image (sensor response value) in the storage means. Then, the estimation process of the attitude of the light source 11 and the light distribution is performed based on the photographed image. The monitor 15 is an output interface for displaying a control screen of the computer 14 and a processing result. The keyboard 16 is an input interface for the user to operate the computer 14. In addition to the digital camera 13, the computer 14, the monitor 15, and the keyboard 16, the light distribution distribution measuring device may include means for installing the light source 11 and the object 12, or may include a predetermined object 12.

  There may be a plurality of objects 12 in photographing. In that case, a plurality of objects may be sequentially arranged in the same posture and photographed by the digital camera 13, or a plurality of objects may be arranged in different postures and a plurality of objects may be photographed simultaneously or sequentially by the digital camera 13. May be. However, the plurality of objects must be arranged at positions within the range where the digital camera 13 is in focus.

  In order to perform control of the digital camera 13 and measurement processing of the light distribution with different computers, the computer 14 may be composed of a plurality of computers. The digital camera 13 may be directly controlled by the user without being controlled by the computer 14, and the captured image stored in the storage device in the digital camera 13 may be transferred to the computer 14.

  A second configuration example of the present invention will be described with reference to FIG. FIG. 2 is an explanatory diagram illustrating a state of light distribution distribution measurement using the light distribution distribution measurement system 20 according to this configuration example. The light distribution measurement system 20 includes a light source 21, an object 22 having a diffuse reflection component as a reflection characteristic, a digital camera 23, a computer 24, a monitor 25, and a keyboard 26. The light source 21 is a measurement target light source for which the posture and the light distribution are to be acquired, and is arranged in a posture capable of illuminating the object 22. The digital camera 23 is a photographing unit, and includes a lens, a sensor, a storage unit, and the like. The digital camera 23 focuses on the light source 21 and the object 22 and takes a digital image obtained by photographing the light source 21 and the object 22 as a sensor. The response value is output to the computer 24. The computer 24 includes a storage means such as a hard disk as an external storage device and a memory as a primary storage device, a CPU as an arithmetic device, etc., controls the digital camera 23, and stores a photographed image (sensor response value) in the storage means. Then, the estimation process of the attitude of the light source 21 and the light distribution is performed based on the photographed image. The monitor 25 is an output interface for displaying a control screen of the computer 24 and processing results. The keyboard 26 is an input interface for the user to operate the computer 24. The light distribution measurement device may include means for installing the light source 21 and the object 22 in addition to the digital camera 23, the computer 24, the monitor 25, and the keyboard 26, or may include a predetermined object 22.

  There may be a plurality of objects 22 in photographing. In that case, a plurality of objects may be sequentially arranged in the same posture and photographed by the digital camera 23, or a plurality of objects may be arranged in different postures and a plurality of objects may be photographed simultaneously or sequentially by the digital camera 23. May be. However, the plurality of objects must be arranged at positions within the range where the digital camera 23 is in focus.

  In order to perform control of the digital camera 23 and measurement processing of the light distribution by different computers, the computer 24 may be configured by a plurality of computers. Further, the digital camera 23 may be directly controlled by the user without being controlled by the computer 24, and the captured image stored in the storage device in the digital camera 23 may be transferred to the computer 24.

  Next, an outline of the data processing method according to the present embodiment will be described. Assuming that the light source is composed of a set of one or more infinitesimal light sources, the sensor response value obtained by illuminating an object with the light source and taking a picture with the camera is the orientation of the light source in three-dimensional space and the infinitesimal The value depends on the light distribution of the light source. Therefore, by modeling the calculation of the rotation parameter and the movement parameter representing the attitude of the light source, the light distribution model parameter representing the light distribution of the infinitesimal light source, and the sensor response value based on the reflection characteristics of the target object The sensor response value at any parameter and reflection characteristic can be calculated.

  In the data processing according to the present invention, the target is to acquire a sensor response value obtained by photographing an object, and each parameter is estimated by nonlinear optimization processing based on the above model. In the nonlinear optimization process, an arbitrary parameter is set, and a sensor response value for the parameter is calculated. It measures the attitude of the light source and the light distribution of the infinitesimal light source by estimating the parameters that minimize the error between the sensor response value obtained by calculation and the actual sensor response value obtained by actual shooting. .

  Below, the detail of the parameter estimated by a nonlinear optimization process is demonstrated first. Next, processing to be performed in advance of photographing an object will be described, and then estimation processing by nonlinear optimization will be described.

Parameter details
First, in the modeling of the light source, the light source is a set of k infinitesimal light sources, the three-dimensional coordinates of the kth infinitesimal light source in the reference posture of the light source are _represented by a vector q _k of 3 rows and 1 column, and the infinitesimal light source k. A unit vector of 3 rows and 1 column representing a predetermined direction is defined as a normal vector _nk .

The radiance I of the emitted light from the infinitely small light source k includes a light distribution distribution model h _k representing the directional distribution of the emitted light, its model parameter vector γ _k , a normal vector _nk, and the direction of the emitted light. It is determined by the relationship with the emission direction vector l which is a unit vector of 3 rows and 1 column representing

Here, γ _k is a vector of W rows and 1 column having W model parameters γ ₁ , γ ₂ ,..., Γ _w of the infinitesimal light source k as elements.

Then the vector p _k of 3 rows and one column representing the three-dimensional coordinates of the infinitesimal light source k on the basis of the rotation parameter and the movement parameter of the light source when illuminating the object by rotating and moving the light source is represented by the following formula .

  Here, R is a 3-by-3 rotation matrix representing rotation in the three-dimensional space, and t is a 3-by-1 movement vector representing movement in the three-dimensional space.

The rotation matrix R in the three-dimensional space can be defined by three rotation parameters, for example, rotation angles θ _x , θ _y, and θ _z with the X, Y, and Z axes as rotation axes. Further, the movement vector t is, X-axis, can be defined Y-axis and the elements of the Z-axis respectively _t x, the three movement parameter of _{t y} and _{t z.} Since the relative position of each infinitesimal light sources are known, the position of all the infinitesimal light _{source, θ x, θ y, θ} z, can be described by six parameters t _x, t _y and t _z. Therefore, in the process according to the present invention, 6 + kW parameters are estimated by the nonlinear optimization process.

  Hereinafter, processing in the present embodiment will be described.

  In the processing according to the present embodiment, the light source is modeled as a set of infinitesimal light sources (target light source approximation means). In modeling, it is necessary to determine the arrangement and number of infinitesimal light sources k and the light distribution model. The arrangement of the infinitesimal light source k is preferably determined in accordance with the shape of the light source, and it is conceivable that the shape is obtained from CAD data or three-dimensional shape restoration by a known method. The number of infinitesimal light sources k is appropriately determined in consideration of the complexity of the shape and the speeding up of data processing. For the light distribution model, it is conceivable to use the deflection angle measurement data of the emitted light from the minute region of the light source and the emitted light distribution based on the light emission principle and structure of the light source.

  For example, in a straight tube fluorescent lamp, a minute point light source is arranged isotropically on the outer periphery. Alternatively, a minute point light source is arranged on the central axis of a straight tube fluorescent lamp, and the light distribution of the minute point light source is different from the surface including the longitudinal direction and the surface perpendicular to the surface according to the shape of the fluorescent lamp. May be.

  In the processing according to the present embodiment, the sensor response value is calculated assuming that the shape, posture, and reflection characteristics of the object illuminated by the light source are known. Therefore, based on measurement and object shape / reflection data, the object shape, the posture of the object when illuminated by the light source (ie, the position and normal of each point on the object surface), and the object reflection characteristics It is necessary to grasp (object posture measuring means).

  Here, a planar object having a uniform surface reflection characteristic is considered. Since it is a planar object, its shape is known. Also, in grasping the orientation of a planar object when illuminated by a light source, the markers placed at the four corners of the planar object are photographed, and the orientation of the planar object is determined from the relationship between the marker position on the image and the actual marker position. presume. In obtaining the reflection characteristics, a known variable angle illumination / measurement device can be used.

  When the target object is not a plane, three-dimensional shape restoration by a known method can be used for shape and posture acquisition. In the acquisition of the reflection characteristic, the target object can be subjected to variable-angle illumination / photographing, and the reflection characteristic can be estimated from the restored shape and posture.

  In the following, the sensor response value when an object is illuminated / photographed with a light source that estimates the light distribution is virtually calculated, and the distribution of the light source is calculated from the error between the calculated sensor response value and the measured sensor response value. Nonlinear optimization processing for estimating the light distribution will be described with reference to FIG.

[Step S31]
The position and orientation of the target light source are represented by rotation parameters and movement parameters in a three-dimensional space, and the attitude (position and orientation) of the infinitesimal light source is calculated using the rotation parameters and movement parameters (target light source attitude calculation means).

[Step S32]
Among G number of points on the object surface, when the vector r _g of g-th three rows and one column of the three-dimensional coordinates (position vector) of a point, from the three-dimensional coordinates p _k infinitesimal light source to the point r _g The heading vector v _{g, k} is expressed by (Equation 3), and the outgoing light vector l _{g, k} is expressed by (Equation 4) (distance calculation means). However, the double line represents the norm of the vector.

Infinitesimal source p _k from the exit optical vector l _g, radiance of the rays of light outgoing to the _k I _{g, k} is expressed by the following formula (outgoing light calculating means).

[Step S33]
Emitted light vector _{l g, when k} is incident on a point _{r g,} the incident light vector _{l g} from point _{r g} to infinitesimal light source _k, 'and, radiance _{I g} of the light _{beam, k' k,} respectively ( These are expressed by (Equation 6) and (Equation 7) (incident light calculation means).

Also, if vector s of three rows and one column of the three-dimensional coordinates of the camera for observing the point r _g, the point r _g viewing direction vector from the three-dimensional coordinates s camera l _{g ''} is represented by the following formula .

Point r _g radiance I _g of the reflected light to the three-dimensional coordinates s located in the camera when illuminated with infinitesimal light source k _'' is expressed by the following equation.

Here, f is a bidirectional reflectance distribution function of the object, the n _g a normal vector of the point r _g, brackets for binomial vector argument represents the inner product of vectors. f can be measured by a known variable angle illumination / measurement technique. In addition, the normal vector _ng can be obtained by a known shape restoration technique or a technique for detecting a marker placed at a predetermined position in the case of a planar object and estimating the posture of the object.

When the reflected light observed by the camera is radiance I _g ″, the sensor response value d _g ′ obtained by the following equation (sensor response value calculation means) is recorded as a digital image in the camera storage device. It is estimated to be.

  Here, α is a normalization coefficient based on the ratio between the radiance of reflected light and the sensor response value.

[Step S34]
Error E of the sensor response value from the sensor response values d _g obtained by actual measurement Oyobi sensor response values d _{g 'obtained} by the above calculation is calculated by the following equation (error calculating means).

[Step S35]
The obtained error E is determined by the rotation parameters (θ _x , θ _y , θ _z ), the movement parameters (t _x , t _y , t _z ), and the light distribution model parameter γ _k , and the error E becomes closer to the actual state. Becomes smaller. Therefore, by estimating a parameter for reducing the error E in the nonlinear optimization process, the actual attitude of the light source and the light distribution of the infinitesimal light source can be estimated (parameter estimation means).

  Note that the number of parameters estimated in the nonlinear optimization process is 6 + kW, and the number of sensor response values G for obtaining an optimal solution is at least 6 + kW.

  The case where there is one target object has been described so far. Here, a case where a plurality of target objects having different reflection characteristics are used will be described.

The sensor response value d _g ′ is a weighted linear sum of the radiances I _{g, k} ′ of incident light, and the weight is determined by the bidirectional reflectance distribution function f of the target object. For example, for a target object such as a mirror that reflects only the incident light vector l _{g, k} ′ from the regular reflection direction of the observation direction vector l _g ″, the outgoing light vector l _{g, k} corresponding to the direction is measured. be able to.

That is, by changing the bidirectional reflectance distribution function f, sampling in the direction of the emitted light of the light distribution distribution model h _k can be changed. Since it is easy to obtain an optimal solution by nonlinear optimization by using sensor response values of different samplings, it is preferable to photograph objects having different bidirectional reflectance distribution functions f. For example, it is preferable to use a plurality of target objects having different surface roughnesses.

At this time, each object is illuminated, and an error E _j of the sensor response value of the j-th target object is calculated. In the nonlinear optimization process, each parameter is estimated by minimizing the sum E ′ of error weighting errors expressed by the following equation.

Here, β _j represents the weight of the j-th error E _j .

The case where there is one light distribution distribution model has been described so far. The use of the light distribution model can reduce the number of directions of the outgoing light vectors lg _{and k} to be measured in order to estimate the light distribution of the infinitesimal light source k. When the light distribution models are different, there is a problem that the estimation accuracy of the light distribution is lowered. Therefore, a case where an optimal light distribution distribution model is estimated from a plurality of light distribution distribution models will be described.

Assuming that the m-th light distribution model of the infinitesimal light source k is h _{k, m} , the error E _{j, m} of the sensor response value of the j-th target object in the light distribution model h _{k , m} is expressed by the following equation. Then, the light distribution distribution model, the model parameter, the rotation parameter, and the movement parameter that minimize the error E _{j, m} are estimated by nonlinear optimization processing.

  When using the light distribution distribution measurement system 20, the target object and the light source can be photographed in the same field of view as shown in FIG. 2, and not only the reflected light of the target object but also the sensor response value of the emitted light of the light source. An actual measurement value is obtained. In addition, while calculating the sensor response value of the image obtained by photographing the target object using (Equation 2) to (Equation 10), in the calculation of the sensor response value of the image obtained by photographing the light source, Instead, (Equation 8) and (Equation 9) can be replaced with (Equation 14) and (Equation 15), respectively, so that the sensor response value can be obtained from the light emitted from the light source.

Here, l _k is an output light vector of 3 rows and 1 column from the infinitesimal light source k, and I _k is the radiance of the output light vector l _k .

  So far, the method for estimating the light distribution of the light source has been described. By using the estimated light distribution, it is possible to calculate the direction vector and radiance of incident light at the position when the position of an arbitrary three-dimensional coordinate is illuminated by the light source.

  Here, a method for estimating a bidirectional reflectance distribution function of an object using a linear light source, which is described in Non-Patent Document 1, will be referred to. In this method, a target object is photographed by a camera at a position of a different line light source while moving the line light source on the target object. For each point on the surface of the target object corresponding to each pixel of the obtained captured image, the incident light from the linear light source, the direction and radiance of the reflected light to the camera, and the bidirectional reflectance distribution function are expressed by mathematical formulas and measurement data. The bi-directional reflectance distribution function of the target object is estimated from the bi-directional reflectance distribution function model modeled in. In this method, in addition to photographing for estimating the bidirectional reflectance distribution function, it is necessary to estimate the attitude of the line light source and the light distribution at each point on the surface of the line light source.

  That is, in the light distribution distribution measurement system according to the present invention, the object and the line light source for estimating the attitude of the line light source and the light distribution are photographed together with the target object for estimating the bidirectional reflectance distribution function. The bidirectional reflectance distribution function of the target object can be estimated simultaneously with the orientation of the light source and the light distribution. As a configuration of such a bidirectional reflectance distribution function measuring device, in addition to the above-described components, each point on the object surface of the target object to be measured for the bidirectional reflectance distribution function in a three-dimensional space A second object posture measuring means for obtaining a position and a normal, a second light intensity distribution model and a light distribution distribution model parameter to calculate the radiance of the emitted light to each point on the target object surface; From the position of the infinitesimal light source and the position of each point on the target object surface from the position of the infinitesimal light source and the position of each point on the target object surface obtained by the target object posture measuring means A second distance calculation means for calculating a distance, a light distribution distribution model and a light distribution distribution model parameter, an attitude of an infinitesimal light source, and each point on the target object surface obtained by the second object attitude measurement means; Position and normal, position and object of infinitesimal light source From the distance of each point on the body surface to the position of each point on the target object surface, second incident light calculation means for calculating the direction and radiance of light rays incident on the position of each point on the target object surface A bi-directional reflectance distribution function model in which the direction and radiance of the incident light beam, the position of each point on the surface of the target object, the normal, and the reflection characteristics to be measured are modeled with mathematical formulas and / or measurement data; A second sensor response for calculating a calculated value of the sensor response value when the target object is illuminated and photographed from the correspondence relationship between the position, the radiance of the light beam incident on the camera, and the sensor response value of the camera A second error for calculating an error based on the value calculation means, the measured value of the sensor response value of the target object acquired by the imaging means, and the calculated value of the sensor response value obtained by the second sensor response value calculation means Calculation means and bidirectional reflectance distribution function It optimizes the model parameters as a target, an example and a second parameter estimating means for estimating a parameter which minimizes the error by the second error calculation means has calculated the like.

  With this configuration, an object with known reflection characteristics is photographed, the light distribution distribution model of the light source is estimated, and the measurement target object of the bidirectional reflectance distribution function is measured in two or more states where the position or orientation of the light source is different. Bidirectional reflectance distribution based on the calculated sensor response value obtained from the light distribution distribution model of the light source, the bidirectional reflectance distribution function model, and the measured sensor response value obtained from the imaging result By optimizing the function model, the bidirectional reflectance distribution function of the target object can be estimated. An object with a known reflection characteristic and a target object may be photographed simultaneously in the same field of view.

  The present invention can be understood as a program executed by a computer including an apparatus, a method, and a processor for measuring a light distribution of a light source. Further, it can be understood as a program executed by a computer including an apparatus, a method, and a processor for measuring a bidirectional reflectance distribution function of an object.

In addition, each vector described in the text is written in bold in the mathematical formula. For example, the vectors γ _k , l _g ″, q _k , n _k , l, t, r _g , v _{g, k} , l _{g, k} , l _{g, k} ′, s, _ng , l _k Among these, it corresponds to each vector shown in the following (Equation 16).

  The present invention is useful for measuring the light distribution of a light source and measuring the bidirectional reflectance distribution function of an object.

10, 20 Light distribution measurement system 11, 21 Light source 12, 22 Object 13, 23 Digital camera 14, 24 Computer 15, 25 Monitor 16, 26 Keyboard

Claims (15)

An apparatus for measuring a light distribution of a light source,
An imaging unit that captures at least the object with a camera and obtains an actual measurement value of a sensor response value in a state in which an object having a diffuse reflection component and a reflection characteristic is illuminated with a target light source that is a light source to be measured;
Object posture measuring means for obtaining the position and normal of each point on the object surface in a three-dimensional space;
Target light source approximation means for approximating the target light source as a set of one or more infinitely small light sources;
A target light source attitude calculation means for expressing the position and orientation of the target light source by a rotation parameter and a movement parameter in a three-dimensional space, and calculating an attitude that is the position and orientation of the infinitesimal light source from the rotation parameter and the movement parameter;
Based on the light distribution distribution model in which the light distribution of the infinitely small light source is modeled with mathematical formulas and / or measurement data, and the light distribution distribution model parameters that are parameters of the mathematical formula and / or measurement data, An emitted light calculating means for calculating the radiance of the incident light;
From the position of the infinitesimal light source calculated by the target light source attitude calculation means and the position of each point on the object surface obtained by the object attitude measurement means, the position of the infinitesimal light source and the object surface Distance calculating means for calculating the distance to each point of
The light distribution distribution model and the light distribution distribution model parameters, the posture of the infinitesimal light source calculated by the target light source posture calculation means, the position of each point on the object surface obtained by the object posture measurement means, and Incident light calculation means for calculating the direction and radiance of light rays incident on the position of each point on the object surface from the normal line, the position of the infinitesimal light source and the distance of each point on the object surface;
The direction and radiance of light rays incident on each point on the object surface, the position, normal and reflection characteristics of each point on the object surface, the position of the camera, and the ray incident on the camera. From the correspondence between the radiance and the sensor response value of the camera, sensor response value calculation means for calculating the calculated value of the sensor response value when the object is illuminated and photographed with the target light source;
An error calculation means for calculating an error based on a difference between an actual measurement value of the sensor response value acquired by the imaging means and a calculated value of the sensor response value obtained by the sensor response value calculation means;
A light distribution distribution measuring apparatus, comprising: parameter estimation means that optimizes the rotation parameter, the movement parameter, and the light distribution distribution model parameter and estimates a parameter that minimizes the error.   The error calculation means obtains an actual measurement value of the sensor response value and a calculated value of the sensor response value for two or more objects having different reflection characteristics, and the sensor response value for each of the objects as the error. The light distribution distribution measuring apparatus according to claim 1, wherein a total sum of errors based on a difference between an actual measurement value of the sensor and a calculated value of the sensor response value is calculated. The imaging means images the object and the target light source in the same field of view, and further acquires an actual measurement value of the sensor response value of the target light source,
The sensor response value calculation means further calculates a calculated value of the sensor response value when the target light source is photographed,
The error calculation means calculates, as the error, a sum of an error for the object and an error based on a difference between the measured value of the sensor response value and the calculated value of the sensor response value for the target light source. Characterized by the
The light distribution distribution measuring apparatus according to claim 1 or 2. The emission light calculation means calculates the radiance of the emission light for different light distribution distribution models,
The sensor response value calculation means calculates a sensor response value for each light distribution model,
The error calculation means calculates an error for each light distribution model,
The parameter estimation unit performs optimization on the rotation parameter, the movement parameter, the light distribution model, and the light distribution model parameter, and estimates a parameter that minimizes the error. The light distribution distribution measuring apparatus according to any one of claims 1 to 3. An apparatus for measuring a bidirectional reflectance distribution function of an object,
Using the light distribution distribution measuring device according to any one of claims 1 to 4, a first object for measuring a light distribution and a second object for measuring a bidirectional reflectance distribution function For each state illuminated by light sources of different postures, and by taking an image of the sensor response values of the first object and the second object to obtain measured values of the first object, Light distribution distribution estimation for estimating the light distribution distribution model of the light source, the light distribution distribution model parameters, and the position and orientation of an infinitesimal light source approximating the light source based on the measured value of the sensor response value of the light source Means,
Second object posture measuring means for obtaining the position and normal of each point on the surface of the second object in a three-dimensional space;
Second emitted light calculation means for calculating a radiance of emitted light to each point on the second object surface based on the light distribution model and the light distribution model parameter;
From the position of the infinitesimal light source and the position of each point on the second object surface obtained by the second object posture measuring means, the position of the infinitesimal light source and the position of the second object surface A second distance calculating means for calculating the distance to each point;
The light distribution distribution model and the light distribution distribution model parameter, the attitude of the infinitesimal light source, the position and normal of each point on the second object surface obtained by the second object attitude measuring means, Second incident light for calculating the direction and radiance of light rays incident on the position of each point on the second object surface from the distance between the position of the infinitesimal light source and each point on the second object surface Calculation means;
Equations and / or measurements of the direction and radiance of rays incident on the position of each point on the second object surface and the position, normal and reflection characteristics to be measured on each point on the second object surface From the correspondence relationship between the bidirectional reflectance distribution function model modeled by data, the position of the camera, the radiance of the light ray incident on the camera, and the sensor response value of the camera, the second object by the light source A second sensor response value calculation means for calculating a calculated value of the sensor response value when photographing and
A second error for calculating an error based on the measured value of the sensor response value of the second object acquired by the imaging unit and the calculated value of the sensor response value obtained by the second sensor response value calculation unit. Calculation means;
Optimization is performed on the normal of each point on the surface of the second object and the reflection characteristics to be measured, which are parameters of the bidirectional reflectance distribution function model , and the second error calculation means calculates the A bi-directional reflectance distribution function measuring device comprising: second parameter estimating means for estimating a parameter that minimizes an error. A method for measuring a light distribution of a light source,
A photographing step of photographing at least the object with a camera and obtaining an actual measurement value of a sensor response value in a state in which an object having a diffuse reflection component and a reflection characteristic is illuminated with a target light source that is a light source to be measured;
An object orientation measurement step for obtaining the position and normal of each point on the object surface in a three-dimensional space;
A target light source approximating step for approximating the target light source as a set of one or more infinitesimal light sources;
A target light source posture calculation step for expressing the position and orientation of the target light source by a rotation parameter and a movement parameter in a three-dimensional space, and calculating a posture that is the position and orientation of the infinitely small light source from the rotation parameter and the movement parameter;
Based on the light distribution distribution model in which the light distribution of the infinitely small light source is modeled with mathematical formulas and / or measurement data, and the light distribution distribution model parameters that are parameters of the mathematical formula and / or measurement data, An outgoing light calculation step for calculating the radiance of the incident light;
From the position of the infinitesimal light source calculated in the target light source attitude calculation step and the position of each point on the object surface obtained in the object attitude measurement step, the position of the infinitesimal light source and the object surface A distance calculating step for calculating the distance to each point of
The light distribution distribution model and the light distribution distribution model parameters, the posture of the infinitesimal light source calculated in the target light source posture calculation step, the position of each point on the object surface obtained in the object posture measurement step, and An incident light calculation step for calculating the direction and radiance of light rays incident on the position of each point on the object surface from the normal line, the position of the infinitesimal light source and the distance of each point on the object surface;
The direction and radiance of light rays incident on each point on the object surface, the position, normal and reflection characteristics of each point on the object surface, the position of the camera, and the ray incident on the camera. From a correspondence relationship between radiance and the sensor response value of the camera, a sensor response value calculation step for calculating a calculated value of the sensor response value when the object is illuminated and photographed with the target light source;
An error calculation step for calculating an error based on a difference between an actual measurement value of the sensor response value acquired in the imaging step and a calculated value of the sensor response value obtained in the sensor response value calculation step;
A light distribution distribution measuring method, comprising: a parameter estimating step of performing optimization on the rotation parameter, the movement parameter, and the light distribution distribution model parameter to estimate a parameter that minimizes the error.   In the error calculation step, an actual measurement value of the sensor response value and a calculated value of the sensor response value are obtained for two or more objects having different reflection characteristics, and the sensor response value for each of the objects is obtained as the error. The light distribution distribution measuring method according to claim 6, wherein a total sum of errors based on a difference between the actually measured value and the calculated sensor response value is calculated. In the photographing step, the object and the target light source are photographed within the same field of view, and an actual measurement value of the sensor response value of the target light source is further acquired,
In the sensor response value calculation step, further calculate a calculated value of the sensor response value when the target light source is photographed,
In the error calculation step, as the error, a sum of an error for the object and an error based on a difference between the measured value of the sensor response value and the calculated value of the sensor response value for the target light source is calculated. The light distribution distribution measuring method according to claim 6 or 7, wherein: In the emission light calculation step, calculate the radiance of the emission light for different light distribution distribution models,
In the sensor response value calculation step, calculate a sensor response value for each light distribution model,
In the error calculation step, an error for each light distribution model is calculated,
In the parameter estimation step, optimization is performed on the rotation parameter, the movement parameter, the light distribution model, and the light distribution model parameter to estimate a parameter that minimizes the error. Item 9. The light distribution distribution measuring method according to any one of Items 6 to 8. A method for measuring a bidirectional reflectance distribution function of an object, comprising:
Using the light distribution distribution measuring method according to any one of claims 6 to 9, a first object for measuring a light distribution and a second object for measuring a bidirectional reflectance distribution function For each state illuminated with light sources of different postures to obtain measured values of sensor response values of the first object and the second object in the photographing step, and to obtain the first object Light distribution distribution estimation for estimating the light distribution distribution model of the light source, the light distribution distribution model parameters, and the position and orientation of an infinitesimal light source approximating the light source based on the measured value of the sensor response value of the light source Steps,
A second object posture measurement step for obtaining the position and normal of each point on the second object surface in a three-dimensional space;
A second emission light calculation step of calculating a radiance of the emission light to each point on the second object surface based on the light distribution distribution model and the light distribution distribution model parameters;
From the position of the infinitesimal light source and the position of each point on the second object surface obtained in the second object posture measurement step, the position of the infinitesimal light source and the position of the second object surface A second distance calculating step for calculating the distance to each point;
The light distribution distribution model and the light distribution distribution model parameters, the posture of the infinitesimal light source, the position and normal of each point on the second object surface obtained in the second object posture measurement step, Second incident light for calculating the direction and radiance of light rays incident on the position of each point on the second object surface from the distance between the position of the infinitesimal light source and each point on the second object surface A calculation step;
Equations and / or measurements of the direction and radiance of rays incident on the position of each point on the second object surface and the position, normal and reflection characteristics to be measured on each point on the second object surface From the correspondence relationship between the bidirectional reflectance distribution function model modeled by data, the position of the camera, the radiance of the light ray incident on the camera, and the sensor response value of the camera, the second object by the light source A second sensor response value calculating step for calculating a calculated value of the sensor response value when the image is taken and
A second error for calculating an error based on the measured value of the sensor response value of the second object acquired in the photographing step and the calculated value of the sensor response value obtained in the second sensor response value calculation step. A calculation step;
Optimization is performed on the normal of each point on the second object surface and the reflection characteristics to be measured, which are parameters of the bidirectional reflectance distribution function model , and the calculation is performed in the second error calculation step. A bidirectional reflectance distribution function measurement method comprising: a second parameter estimation step that estimates a parameter that minimizes an error. In order to measure the light distribution of the light source,
An imaging unit that captures at least the object with a camera and obtains an actual measurement value of a sensor response value in a state in which an object having a diffuse reflection component and a reflection characteristic is illuminated with a target light source that is a light source to be measured;
Object posture measuring means for obtaining the position and normal of each point on the object surface in a three-dimensional space;
Target light source approximation means for approximating the target light source as a set of one or more infinitely small light sources;
A target light source attitude calculation means for expressing the position and orientation of the target light source by a rotation parameter and a movement parameter in a three-dimensional space, and calculating an attitude that is the position and orientation of the infinitesimal light source from the rotation parameter and the movement parameter;
Based on the light distribution distribution model in which the light distribution of the infinitely small light source is modeled with mathematical formulas and / or measurement data, and the light distribution distribution model parameters that are parameters of the mathematical formula and / or measurement data, An emitted light calculating means for calculating the radiance of the incident light;
From the position of the infinitesimal light source calculated by the target light source attitude calculation means and the position of each point on the object surface obtained by the object attitude measurement means, the position of the infinitesimal light source and the object surface Distance calculating means for calculating the distance to each point of
The light distribution distribution model and the light distribution distribution model parameters, the posture of the infinitesimal light source calculated by the target light source posture calculation means, the position of each point on the object surface obtained by the object posture measurement means, and Incident light calculation means for calculating the direction and radiance of light rays incident on the position of each point on the object surface from the normal line, the position of the infinitesimal light source and the distance of each point on the object surface;
The direction and radiance of light rays incident on each point on the object surface, the position, normal and reflection characteristics of each point on the object surface, the position of the camera, and the ray incident on the camera. From the correspondence between the radiance and the sensor response value of the camera, sensor response value calculation means for calculating the calculated value of the sensor response value when the object is illuminated and photographed with the target light source;
An error calculation means for calculating an error based on a difference between an actual measurement value of the sensor response value acquired by the imaging means and a calculated value of the sensor response value obtained by the sensor response value calculation means;
A light distribution distribution measurement program that optimizes the rotation parameter, the movement parameter, and the light distribution distribution model parameter, and functions as a parameter estimation unit that estimates a parameter that minimizes the error.   The error calculation means obtains an actual measurement value of the sensor response value and a calculated value of the sensor response value for two or more objects having different reflection characteristics, and the sensor response value for each of the objects as the error. The light distribution distribution measurement program according to claim 11, wherein a sum of errors based on a difference between an actual measurement value of the sensor and a calculated value of the sensor response value is calculated. The imaging means images the object and the target light source in the same field of view, and further acquires an actual measurement value of the sensor response value of the target light source,
The sensor response value calculation means further calculates a calculated value of the sensor response value when the target light source is photographed,
The error calculation means calculates, as the error, a sum of an error for the object and an error based on a difference between the measured value of the sensor response value and the calculated value of the sensor response value for the target light source. Characterized by the
The light distribution distribution measuring program according to claim 11 or 12. The emission light calculation means calculates the radiance of the emission light for different light distribution distribution models,
The sensor response value calculation means calculates a sensor response value for each light distribution model,
The error calculation means calculates an error for each light distribution model,
The parameter estimation unit performs optimization on the rotation parameter, the movement parameter, the light distribution model, and the light distribution model parameter, and estimates a parameter that minimizes the error. The light distribution measurement program according to any one of claims 11 to 13. To measure the bidirectional reflectance distribution function of an object,
A first object for measuring a light distribution and a second object for measuring a bidirectional reflectance distribution function by executing the light distribution measurement program according to any one of claims 11 to 14. For each state illuminated with light sources of different postures, and obtain the measured values of the sensor response values of the first object and the second object by photographing with the photographing means, A light distribution distribution that estimates the position and orientation of an infinitesimal light source that approximates the light source, based on the measured value of the sensor response value of the object, for each light source posture. An estimation means;
Second object posture measuring means for obtaining the position and normal of each point on the surface of the second object in a three-dimensional space;
Second emitted light calculation means for calculating a radiance of emitted light to each point on the second object surface based on the light distribution model and the light distribution model parameter;
From the position of the infinitesimal light source and the position of each point on the second object surface obtained by the second object posture measuring means, the position of the infinitesimal light source and the position of the second object surface A second distance calculating means for calculating the distance to each point;
The light distribution distribution model and the light distribution distribution model parameter, the attitude of the infinitesimal light source, the position and normal of each point on the second object surface obtained by the second object attitude measuring means, Second incident light for calculating the direction and radiance of light rays incident on the position of each point on the second object surface from the distance between the position of the infinitesimal light source and each point on the second object surface Calculation means;
Equations and / or measurements of the direction and radiance of rays incident on the position of each point on the second object surface and the position, normal and reflection characteristics to be measured on each point on the second object surface From the correspondence relationship between the bidirectional reflectance distribution function model modeled by data, the position of the camera, the radiance of the light ray incident on the camera, and the sensor response value of the camera, the second object by the light source A second sensor response value calculation means for calculating a calculated value of the sensor response value when photographing and
A second error for calculating an error based on the measured value of the sensor response value of the second object acquired by the imaging unit and the calculated value of the sensor response value obtained by the second sensor response value calculation unit. Calculation means;
Optimization is performed on the normal of each point on the surface of the second object and the reflection characteristics to be measured, which are parameters of the bidirectional reflectance distribution function model , and the second error calculation means calculates the A bidirectional reflectance distribution function measurement program that functions as second parameter estimation means for estimating a parameter that minimizes an error.

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