CN104730802B - Calibration, focusing method and the system and dual camera equipment of optical axis included angle - Google Patents

Abstract

The present invention provides a method and system for calibrating and focusing the included angle of the optical axis and a dual camera device, wherein the calibrating method includes: focusing on any feature point of the object to be photographed, and obtaining the first object distance value; determining the The first imaging point coordinate value of the feature point on the first camera; determine the second imaging point coordinate value of the feature point on the second camera; according to the first coordinate value imaging point coordinate value, The second coordinate value imaging point coordinate value, the pre-stored parameters of the dual-camera device, the first object distance value and the pre-stored optical axis angle calculation formula determine the optical axis angle of the dual-camera device . Through the technical solution of the present invention, the self-calibration focusing of the dual-camera device is realized.

Description

Optical axis angle calibration, focusing method and system, and dual-camera device

technical field

The present invention relates to the technical field of optical focusing, in particular to a method and system for calibrating an included angle of an optical axis, a focusing method and system, and a dual-camera device.

Background technique

In related technologies, in order to achieve a better focusing effect during the shooting process, dual cameras are developed and applied to various shooting devices. Point imaging to form two imaging points, according to the distance between the two imaging points and the center point of the optical axis point on the imaging plane and the equivalent focal length, determine the object distance value from the object to be photographed to the lens plane, and then determine the focusing process The distance the camera moves.

However, the above process is based on the ideal situation where the two optical axes are parallel. When the optical axis of the shooting equipment is shifted due to manufacturing process deviation or external force collision, determining the object distance value according to the ideal situation will cause serious focus deviation and affect the user's Shooting effect and user experience.

After the closed-loop motor technology is applied to the dual-lens shooting technology, although the lens displacement can be measured based on the Hall sensor, it cannot self-calibrate the optical axis angle parameters.

Therefore, how to implement the self-calibration process of the dual-lens shooting device to achieve accurate focusing has become an urgent technical problem to be solved.

Contents of the invention

Based on at least one of the above technical problems, the present invention proposes a method and system for calibrating the included angle of optical axes, a focusing method and system, and a dual camera device.

In view of this, according to the embodiment of the first aspect of the present invention, a method for calibrating the included angle of the optical axis is proposed, including: focusing on any feature point of the object to be photographed, and obtaining the first object distance value; determining the The first imaging point coordinate value of the feature point on the first camera; determine the second imaging point coordinate value of the feature point on the second camera; according to the first coordinate value imaging point coordinate value, The second coordinate value imaging point coordinate value, the pre-stored parameters of the dual-camera device, the first object distance value and the pre-stored optical axis angle calculation formula determine the optical axis angle of the dual-camera device .

According to the calibration method of the optical axis angle of the embodiment of the present invention, by obtaining the first object distance value of the first camera, and determining the optical axis angle sampling value of the dual camera device by the optical axis angle calculation formula, to complete the optical The calibration process of the included angle of the optical axis improves the calibration efficiency of the included angle of the optical axis, avoids problems such as inaccurate focusing caused by the deviation of the included angle of the optical axis, and improves the user experience.

Specifically, determine the first coordinate system with the mirror center of the first camera as the origin (wherein, the y-axis of the first coordinate system is perpendicular to the imaging plane, and the x-axis of the first coordinate system is parallel to the imaging plane), and a second The mirror center of the camera is the second coordinate system of the origin (wherein, the y-axis of the second coordinate system is perpendicular to the imaging plane, and the x-axis of the second coordinate system is parallel to the imaging plane), and the formula for calculating the angle between the optical axes is difference, double The equation relationship between the parameters of the camera (equivalent focal length and mirror center distance, etc.), the angle between the optical axis and the object distance value, where the difference between the imaging points is the distance between the two imaging points and the corresponding y-axis Furthermore, after multiple sampling values of optical axis angles are obtained through the difference, the weighted average is calculated as the optical axis angle, which improves the accuracy of optical axis angle calibration.

In addition, the parameters of the dual-camera device can be stored in the register, or in the storage unit of the microprocessor, so as to ensure that the above-mentioned parameters can be quickly read to calculate the angle between the optical axes. At the same time, the acquisition process of the first object distance value can be adopted The single-camera focusing method, such as using a closed-loop motor to obtain the object distance value after focusing, ensures the accuracy of the object distance value and the reliability of the calibration process.

According to an embodiment of the present invention, preferably, obtaining the first object distance value includes the following specific steps: obtaining a pre-stored first mapping table of the lens displacement value and the object distance value, wherein the object distance value includes The first object distance value of the first camera and the second object distance value of the second camera; the first object distance value corresponding to the lens shift value is acquired through the first mapping table.

According to the method for calibrating the included angle of the optical axis in the embodiment of the present invention, by obtaining the lens displacement value and the mapping table, the first object distance value can be quickly obtained, and then the calibration of the included angle of the optical axis can be realized according to the object distance value. The technical process is simple, The efficiency of the calibration process is improved. Specifically, a closed-loop motor can be installed to achieve fast acquisition of the lens shift value through the closed-loop motor after focusing.

According to an embodiment of the present invention, preferably, before focusing on any feature point of the object to be photographed, the following specific steps are further included: storing the parameters of the dual camera device, wherein the parameters include the The equivalent focal length value of the device and the mirror center distance between the center point of the first camera and the center point of the second camera.

According to the method for calibrating the angle of the optical axis in the embodiment of the present invention, by storing parameters such as the equivalent focal length value and the distance between the mirror centers, the above parameters can be directly used in the calculation of the angle of the optical axis, thereby effectively improving the calibration of the optical axis angle. corner efficiency and accuracy.

According to an embodiment of the present invention, preferably, the coordinate value of the first imaging point is represented by x1, the coordinate value of the second imaging point is represented by x2, the object distance value is represented by L, and the dual camera device The parameters include the mirror center distance d and the equivalent focal length value f, and the calculation formula for the included angle of the optical axis specifically includes:

According to the method for calibrating the included angle of the optical axis according to the embodiment of the present invention, the above calculation formula of the included angle of the optical axis is created through the optical geometric relationship, specifically, through the similarity relationship between the triangle where the feature point is located and the triangle where the imaging point is located, create The above formula for calculating the included angle of the optical axis is determined, that is, the sampling value of the included angle of the optical axis is determined by the imaging point. It meets the calculation accuracy requirements of the optical axis angle.

According to an embodiment of the present invention, preferably, determining the optical axis angle of the dual-camera device includes the following specific steps: calculating a weighted average of the optical axis angle sampling values of all the feature points; The average value is stored in the microprocessor of the dual-camera device as an included angle of the optical axes of the dual-camera device.

According to the method for calibrating the included angle of the optical axis in the embodiment of the present invention, by calculating the weighted average value of the sampled values of the included angle of the optical axis as the included angle of the optical axis, the error in the calibration process is reduced, and the included angle of the optical axis is improved. the calibration accuracy.

According to an embodiment of the present invention, preferably, further comprising: after determining the included angle of the optical axis, using the difference between the coordinate value of the second imaging point and the coordinate value of the first imaging point as the imaging point A difference value, creating a second mapping table between the imaging point difference value and the object distance value through the optical axis included angle calculation formula.

According to the method for calibrating the included angle of the optical axis according to the embodiment of the present invention, by creating the second mapping table, data basis is provided for the actual focusing process of the dual-camera device, specifically, through continuous correction of the included angle of the optical axis, timely Correcting the second mapping table can quickly determine the object distance value through the difference of imaging points in the actual focusing process, and then complete the focusing process.

According to an embodiment of the second aspect of the present invention, a focusing method is proposed, including: acquiring the third imaging point coordinate value of any feature point of the subject on the first camera; acquiring the feature point at the The fourth imaging point coordinate value on the second camera; using the difference between the fourth imaging point coordinate value and the third imaging point coordinate value as the imaging point difference, according to the imaging point difference, calibrated The included angle of the optical axis determines the second object distance value; the lens shift value is determined according to the second object distance value and the first mapping table, so as to complete the first focusing.

According to the focusing method of the embodiment of the present invention, by creating a calibration mapping table between the image distance value and the calibration displacement value, the calibration displacement value of the second camera can be directly determined according to the image distance value, reducing the calculation process, wherein, in After calibrating the included angle of the optical axis, according to the included angle of the optical axis and the above calculation formula, the calibration mapping table can be created by measuring the image distance value multiple times, and then in the actual focusing process, only the image distance value needs to be obtained. Quickly determine the calibration displacement value for the second camera.

According to an embodiment of the present invention, preferably, determining the second object distance value according to the imaging point difference value and the calibrated optical axis angle includes the following specific steps: combining the imaging point difference value, calibration The included angle of the optical axis and the parameters of the dual-camera device are substituted into the calculation formula of the included angle of the optical axis to obtain the second object distance value.

According to the focusing method of the embodiment of the present invention, the second object distance value is obtained through the optical axis angle calculation formula, which improves the focusing accuracy of the second camera. Specifically, after the optical axis angle is calibrated, according to the optical The calculation formula of the included angle of the axis, by substituting the average value of the difference between the imaging points measured multiple times, the calibrated optical axis included angle and the parameters of the dual camera device into the calculated formula of the included optical axis angle, the object distance of the second camera can be accurately obtained value, and quickly determine the calibration displacement value of the second camera according to the object distance value and the second mapping table.

According to an embodiment of the present invention, preferably, determining the second object distance value of the second camera according to the imaging point difference value and the calibrated optical axis angle includes the following specific steps: according to the imaging point The difference value and the second mapping table determine the second object distance value corresponding to the imaging point difference value.

According to the focusing method of the embodiment of the present invention, by obtaining the mapping relationship between the second object distance value and the lens displacement value of the second camera, the focusing efficiency and accuracy of the second camera are improved, and the second camera is controlled to complete the process according to the lens displacement value. Focusing process.

According to an embodiment of the present invention, preferably, further comprising: after completing the first focusing, using a contrast focusing method or a phase focusing method to complete the second focusing.

According to the focusing method of the embodiment of the present invention, after the first focusing is completed, the second focusing is performed to achieve a more accurate focusing effect. The maximum lens position is the exact focus position, and the phase focus method is when the focus position is accurate, the phase detection system can accurately know that it is currently in focus.

According to the embodiment of the third aspect of the present invention, a calibration system for the included angle of the optical axis is proposed, including: an acquisition unit, configured to focus on any feature point of the object to be photographed, and acquire the first object distance value; determine A unit configured to determine a first imaging point coordinate value of the feature point on the first camera; the determining unit is also configured to determine a second imaging point coordinate value of the feature point on the second camera value; the determining unit is also used to, according to the coordinate value of the imaging point of the first coordinate value, the coordinate value of the imaging point of the second coordinate value, the pre-stored parameters of the dual camera device and the first object distance value and a pre-stored optical axis angle calculation formula to determine the optical axis angle of the dual-camera device.

According to the optical axis angle calibration system of the embodiment of the present invention, by obtaining the first object distance value of the first camera, and determining the optical axis angle sampling value of the dual camera device by the optical axis angle calculation formula, to complete the optical The calibration process of the included angle of the optical axis improves the calibration efficiency of the included angle of the optical axis, avoids problems such as inaccurate focusing caused by the deviation of the included angle of the optical axis, and improves the user experience.

Specifically, determine the first coordinate system with the mirror center of the first camera as the origin (wherein, the y-axis of the first coordinate system is perpendicular to the imaging plane, and the x-axis of the first coordinate system is parallel to the imaging plane), and a second The mirror center of the camera is the second coordinate system of the origin (wherein, the y-axis of the second coordinate system is perpendicular to the imaging plane, and the x-axis of the second coordinate system is parallel to the imaging plane), and the formula for calculating the angle between the optical axes is difference, double The equation relationship between the parameters of the camera (equivalent focal length and mirror center distance, etc.), the angle between the optical axis and the object distance value, where the difference between the imaging points is the distance between the two imaging points and the corresponding y-axis Furthermore, after multiple sampling values of optical axis angles are obtained through the difference, the weighted average is calculated as the optical axis angle, which improves the accuracy of optical axis angle calibration.

In addition, the parameters of the dual-camera device can be stored in the register, or in the storage unit of the microprocessor, so as to ensure that the above-mentioned parameters can be quickly read to calculate the angle between the optical axes. At the same time, the acquisition process of the first object distance value can be adopted The single-camera focusing method, such as using a closed-loop motor to obtain the object distance value after focusing, ensures the accuracy of the object distance value and the reliability of the calibration process.

According to an embodiment of the present invention, preferably, the obtaining unit is further configured to obtain a pre-stored first mapping table of the lens shift value and the object distance value, wherein the object distance value includes the first The first object distance value of the camera and the second object distance value of the second camera; and used for obtaining the first object distance value corresponding to the lens shift value through the first mapping table.

According to the optical axis angle calibration system of the embodiment of the present invention, by acquiring the lens displacement value and the mapping table, the first object distance value can be quickly obtained, and then the optical axis angle calibration can be realized according to the object distance value, the technical process is simple, The efficiency of the calibration process is improved. Specifically, a closed-loop motor can be installed to achieve fast acquisition of the lens shift value through the closed-loop motor after focusing.

According to an embodiment of the present invention, preferably, it further includes: a storage unit configured to store parameters of the dual-camera device, wherein the parameters include the equivalent focal length value of the dual-camera device and the first camera The distance between the center point and the center point of the second camera.

According to the optical axis angle calibration system of the embodiment of the present invention, by storing parameters such as equivalent focal length and mirror center distance, the above parameters can be directly used in the calculation of the optical axis angle, thereby effectively improving the calibration optical axis angle. corner efficiency and accuracy.

According to an embodiment of the present invention, preferably, the coordinate value of the first imaging point is represented by x1, the coordinate value of the second imaging point is represented by x2, the object distance value is represented by L, and the dual camera device The parameters include the mirror center distance d and the equivalent focal length value f, and the calculation formula for the included angle of the optical axis specifically includes:

According to the optical axis angle calibration system of the embodiment of the present invention, the above optical axis angle calculation formula is established through the optical geometric relationship, specifically, through the similarity relationship between the triangle where the feature point is located and the triangle where the imaging point is located, create The above formula for calculating the included angle of the optical axis is determined, that is, the sampling value of the included angle of the optical axis is determined by the imaging point. It meets the calculation accuracy requirements of the optical axis angle.

According to an embodiment of the present invention, preferably, further comprising: a calculation unit, configured to calculate a weighted average value of the optical axis angle sampling values of all feature points; the storage unit is also configured to calculate the weighted average The value is stored in the microprocessor of the dual-camera device as an included angle of the optical axis of the dual-camera device.

According to the optical axis angle calibration system of the embodiment of the present invention, by calculating the weighted average of the optical axis angle sampling values as the optical axis angle, the error in the calibration process is reduced, and the optical axis angle is improved. the calibration accuracy.

According to an embodiment of the present invention, preferably, further comprising: a creation unit, configured to use the coordinate value between the second imaging point and the first imaging point after determining the included angle of the optical axis The difference is used as an imaging point difference, and a second mapping table between the imaging point difference and the object distance value is created through the optical axis angle calculation formula.

The optical axis angle calibration system according to the embodiment of the present invention provides a data basis for the actual focusing process of the dual-camera device by creating a second mapping table, specifically, and through continuous correction of the optical axis angle, timely Correcting the second mapping table can quickly determine the object distance value through the difference of imaging points in the actual focusing process, and then complete the focusing process.

According to an embodiment of the fourth aspect of the present invention, a focusing system is proposed, including: an acquisition unit, configured to acquire the coordinate value of a third imaging point of any feature point of the subject on the first camera; the acquisition The unit is also used to obtain the coordinate value of the fourth imaging point of the feature point on the second camera; the focusing system further includes: a determination unit used to combine the coordinate value of the fourth imaging point with the The difference between the coordinate values of the third imaging point is used as the difference value of the imaging point, and the second object distance value is determined according to the difference value of the imaging point and the calibrated optical axis angle; The second object distance value and the first mapping table determine the lens shift value to complete the first focusing.

According to the focus system of the embodiment of the present invention, by creating a calibration mapping table between the image distance value and the calibration displacement value, the calibration displacement value of the second camera can be directly determined according to the image distance value, reducing the calculation process, wherein, in After calibrating the included angle of the optical axis, according to the included angle of the optical axis and the above calculation formula, the calibration mapping table can be created by measuring the image distance value multiple times, and then in the actual focusing process, only the image distance value needs to be obtained. Quickly determine the calibration displacement value for the second camera.

According to an embodiment of the present invention, preferably, the determination unit is further configured to substitute the imaging point difference, the calibrated optical axis angle and the parameters of the dual camera device into the optical axis angle calculation formula , to obtain the second object distance value.

According to the focus system of the embodiment of the present invention, the second object distance value is obtained through the calculation formula of the included angle of the optical axis, which improves the focusing accuracy of the second camera. Specifically, after the included angle of the optical axis is calibrated, according to the The calculation formula of the included angle of the axis, by substituting the average value of the difference between the imaging points measured multiple times, the calibrated optical axis included angle and the parameters of the dual camera device into the calculated formula of the included optical axis angle, the object distance of the second camera can be accurately obtained value, and quickly determine the calibration displacement value of the second camera according to the object distance value and the second mapping table.

According to an embodiment of the present invention, preferably, the determining unit is further configured to determine the second object distance corresponding to the imaging point difference according to the imaging point difference and the second mapping table.

According to the focusing system of the embodiment of the present invention, by obtaining the mapping relationship between the second object distance value and the lens displacement value of the second camera, the focusing efficiency and accuracy of the second camera are improved, and the second camera is controlled to complete the process according to the lens displacement value. Focusing process.

According to an embodiment of the present invention, preferably, the focusing unit is further configured to, after completing the first focusing, use a contrast focusing method or a phase focusing method to complete the second focusing.

According to the focusing system of the embodiment of the present invention, a more accurate focusing effect is achieved by performing the second focusing after the first focusing. The maximum lens position is the exact focus position, and the phase focus method is when the focus position is accurate, the phase detection system can accurately know that it is currently in focus.

According to an embodiment of the fifth aspect of the present invention, a dual-camera device is proposed, including: the optical axis angle calibration system described in any of the above technical solutions or the focusing system described in any of the above technical solutions system.

Through the above technical solutions, fast focusing and precise focusing can be achieved. At the same time, the self-calibration of the optical axis angle of the dual-camera device is realized, which avoids focusing errors caused by the deviation of the optical axis angle, and improves the user's control during the shooting process. Use experience.

Description of drawings

Fig. 1 shows a schematic flowchart of a method for calibrating an included angle of an optical axis according to an embodiment of the present invention;

FIG. 2 shows a schematic flowchart of a focusing method according to an embodiment of the present invention;

Fig. 3 shows a schematic block diagram of a calibration system for an included angle of an optical axis according to an embodiment of the present invention;

Fig. 4 shows a schematic block diagram of a focusing system according to an embodiment of the present invention;

Fig. 5 shows a schematic block diagram of a dual camera device according to an embodiment of the present invention;

FIG. 6 shows a schematic diagram of a coordinate system of a dual-camera device according to an embodiment of the present invention;

FIG. 7 shows a schematic diagram of an optical path of a photographing device according to an embodiment of the present invention (the included angle of the optical axis is zero);

FIG. 8 shows a schematic diagram of an optical path of a photographing device according to an embodiment of the present invention (one optical axis is deflected);

FIG. 9 shows a schematic diagram of an optical path of a photographing device according to an embodiment of the present invention (two optical axes are deflected).

detailed description

In order to understand the above-mentioned purpose, features and advantages of the present invention more clearly, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the case of no conflict, the embodiments of the present application and the features in the embodiments can be combined with each other.

In the following description, many specific details are set forth in order to fully understand the present invention. However, the present invention can also be implemented in other ways different from those described here. Therefore, the protection scope of the present invention is not limited by the specific details disclosed below. EXAMPLE LIMITATIONS.

Fig. 1 shows a schematic flowchart of a method for calibrating an included angle of an optical axis according to an embodiment of the present invention.

As shown in Figure 1, the method for calibrating the included angle of the optical axis according to an embodiment of the present invention includes: step 102, focusing on any feature point of the object to be photographed, and obtaining the first object distance value; step 104, determining The first imaging point coordinate value of the feature point on the first camera; Step 106, determine the second imaging point coordinate value of the feature point on the second camera; Step 108, according to the first The coordinate value of the imaging point of the coordinate value, the coordinate value of the imaging point of the second coordinate value, the pre-stored parameters of the dual-camera device, the first object distance value, and the pre-stored optical axis angle calculation formula determine the dual The included angle of the optical axis of the camera device.

According to the calibration method of the optical axis angle of the embodiment of the present invention, by obtaining the first object distance value of the first camera, and determining the optical axis angle sampling value of the dual camera device by the optical axis angle calculation formula, to complete the optical The calibration process of the included angle of the optical axis improves the calibration efficiency of the included angle of the optical axis, avoids problems such as inaccurate focusing caused by the deviation of the included angle of the optical axis, and improves the user experience.

Specifically, determine the first coordinate system with the mirror center of the first camera as the origin (wherein, the y-axis of the first coordinate system is perpendicular to the imaging plane, and the x-axis of the first coordinate system is parallel to the imaging plane), and a second The mirror center of the camera is the second coordinate system of the origin (wherein, the y-axis of the second coordinate system is perpendicular to the imaging plane, and the x-axis of the second coordinate system is parallel to the imaging plane), and the formula for calculating the angle between the optical axes is difference, double The equation relationship between the parameters of the camera (equivalent focal length and mirror center distance, etc.), the angle between the optical axis and the object distance value, where the difference between the imaging points is the distance between the two imaging points and the corresponding y-axis Furthermore, after multiple sampling values of optical axis angles are obtained through the difference, the weighted average is calculated as the optical axis angle, which improves the accuracy of optical axis angle calibration.

In addition, the parameters of the dual-camera device can be stored in the register, or in the storage unit of the microprocessor, so as to ensure that the above-mentioned parameters can be quickly read to calculate the angle between the optical axes. At the same time, the acquisition process of the first object distance value can be adopted The single-camera focusing method, such as using a closed-loop motor to obtain the object distance value after focusing, ensures the accuracy of the object distance value and the reliability of the calibration process.

According to an embodiment of the present invention, preferably, obtaining the first object distance value includes the following specific steps: obtaining a pre-stored first mapping table of the lens displacement value and the object distance value, wherein the object distance value includes The first object distance value of the first camera and the second object distance value of the second camera; the first object distance value corresponding to the lens shift value is acquired through the first mapping table.

According to the method for calibrating the included angle of the optical axis in the embodiment of the present invention, by obtaining the lens displacement value and the mapping table, the first object distance value can be quickly obtained, and then the calibration of the included angle of the optical axis can be realized according to the object distance value. The technical process is simple, The efficiency of the calibration process is improved. Specifically, a closed-loop motor can be installed to achieve fast acquisition of the lens shift value through the closed-loop motor after focusing.

According to an embodiment of the present invention, preferably, before focusing on any feature point of the object to be photographed, the following specific steps are further included: storing the parameters of the dual camera device, wherein the parameters include the The equivalent focal length value of the device and the mirror center distance between the center point of the first camera and the center point of the second camera.

According to the method for calibrating the angle of the optical axis in the embodiment of the present invention, by storing parameters such as the equivalent focal length value and the distance between the mirror centers, the above parameters can be directly used in the calculation of the angle of the optical axis, thereby effectively improving the calibration of the optical axis angle. corner efficiency and accuracy.

According to an embodiment of the present invention, preferably, the coordinate value of the first imaging point is represented by x1, the coordinate value of the second imaging point is represented by x2, the object distance value is represented by L, and the dual camera device The parameters include the mirror center distance d and the equivalent focal length value f, and the calculation formula for the included angle of the optical axis specifically includes:

According to the method for calibrating the included angle of the optical axis according to the embodiment of the present invention, the above calculation formula of the included angle of the optical axis is created through the optical geometric relationship, specifically, through the similarity relationship between the triangle where the feature point is located and the triangle where the imaging point is located, create The above formula for calculating the included angle of the optical axis is determined, that is, the sampling value of the included angle of the optical axis is determined by the imaging point. It meets the calculation accuracy requirements of the optical axis angle.

According to an embodiment of the present invention, preferably, determining the optical axis angle of the dual-camera device includes the following specific steps: calculating a weighted average of the optical axis angle sampling values of all the feature points; The average value is stored in the microprocessor of the dual-camera device as an included angle of the optical axes of the dual-camera device.

According to the method for calibrating the included angle of the optical axis in the embodiment of the present invention, by calculating the weighted average value of the sampled values of the included angle of the optical axis as the included angle of the optical axis, the error in the calibration process is reduced, and the included angle of the optical axis is improved. the calibration accuracy.

According to an embodiment of the present invention, preferably, further comprising: after determining the included angle of the optical axis, using the difference between the coordinate value of the second imaging point and the coordinate value of the first imaging point as the imaging point A difference value, creating a second mapping table between the imaging point difference value and the object distance value through the optical axis included angle calculation formula.

According to the method for calibrating the included angle of the optical axis according to the embodiment of the present invention, by creating the second mapping table, data basis is provided for the actual focusing process of the dual-camera device, specifically, through continuous correction of the included angle of the optical axis, timely Correcting the second mapping table can quickly determine the object distance value through the difference of imaging points in the actual focusing process, and then complete the focusing process.

Fig. 2 shows a schematic flowchart of a focusing method according to an embodiment of the present invention.

As shown in FIG. 2 , the focusing method according to an embodiment of the present invention includes: step 202, obtaining the third imaging point coordinate value of any feature point of the subject on the first camera; step 204, obtaining the The fourth imaging point coordinate value of the feature point on the second camera; step 206, using the difference between the fourth imaging point coordinate value and the third imaging point coordinate value as the imaging point difference, according to the The imaging point difference value and the calibrated optical axis angle determine the second object distance value; step 208, determine the lens shift value according to the second object distance value and the first mapping table, to complete Focusing for the first time.

According to the focusing method of the embodiment of the present invention, by creating a calibration mapping table between the image distance value and the calibration displacement value, the calibration displacement value of the second camera can be directly determined according to the image distance value, reducing the calculation process, wherein, in After calibrating the included angle of the optical axis, according to the included angle of the optical axis and the above calculation formula, the calibration mapping table can be created by measuring the image distance value multiple times, and then in the actual focusing process, only the image distance value needs to be obtained. Quickly determine the calibration displacement value for the second camera.

According to an embodiment of the present invention, preferably, determining the second object distance value according to the imaging point difference value and the calibrated optical axis angle includes the following specific steps: combining the imaging point difference value, calibration The included angle of the optical axis and the parameters of the dual-camera device are substituted into the calculation formula of the included angle of the optical axis to obtain the second object distance value.

According to the focusing method of the embodiment of the present invention, the second object distance value is obtained through the optical axis angle calculation formula, which improves the focusing accuracy of the second camera. Specifically, after the optical axis angle is calibrated, according to the optical The calculation formula of the included angle of the axis, by substituting the average value of the difference between the imaging points measured multiple times, the calibrated optical axis included angle and the parameters of the dual camera device into the calculated formula of the included optical axis angle, the object distance of the second camera can be accurately obtained value, and quickly determine the calibration displacement value of the second camera according to the object distance value and the second mapping table.

According to an embodiment of the present invention, preferably, determining the second object distance value of the second camera according to the imaging point difference value and the calibrated optical axis angle includes the following specific steps: according to the imaging point The difference value and the second mapping table determine the second object distance value corresponding to the imaging point difference value.

According to the focusing method of the embodiment of the present invention, by obtaining the mapping relationship between the second object distance value and the lens displacement value of the second camera, the focusing efficiency and accuracy of the second camera are improved, and the second camera is controlled to complete the process according to the lens displacement value. Focusing process.

According to an embodiment of the present invention, preferably, further comprising: after completing the first focusing, using a contrast focusing method or a phase focusing method to complete the second focusing.

According to the focusing method of the embodiment of the present invention, after the first focusing is completed, the second focusing is performed to achieve a more accurate focusing effect. The maximum lens position is the exact focus position, and the phase focus method is when the focus position is accurate, the phase detection system can accurately know that it is currently in focus.

Fig. 3 shows a schematic block diagram of a system for calibrating an included angle of an optical axis according to an embodiment of the present invention.

As shown in FIG. 3 , the optical axis angle calibration system 300 according to an embodiment of the present invention includes: an acquisition unit 302, configured to focus on any feature point of the object to be photographed, and acquire the first object distance value; The determining unit 304 is configured to determine a first imaging point coordinate value of the feature point on the first camera; the determining unit 304 is also configured to determine a second imaging point of the feature point on the second camera. The coordinate value of the imaging point; the determining unit 304 is further configured to, according to the coordinate value of the imaging point of the first coordinate value, the coordinate value of the imaging point of the second coordinate value, the pre-stored parameters of the dual-camera device, and the The first object distance value and the pre-stored optical axis angle calculation formula determine the optical axis angle of the dual camera device.

According to the optical axis angle calibration system of the embodiment of the present invention, by obtaining the first object distance value of the first camera, and determining the optical axis angle sampling value of the dual camera device by the optical axis angle calculation formula, to complete the optical The calibration process of the included angle of the optical axis improves the calibration efficiency of the included angle of the optical axis, avoids problems such as inaccurate focusing caused by the deviation of the included angle of the optical axis, and improves the user experience.

Specifically, determine the first coordinate system with the mirror center of the first camera as the origin (wherein, the y-axis of the first coordinate system is perpendicular to the imaging plane, and the x-axis of the first coordinate system is parallel to the imaging plane), and a second The mirror center of the camera is the second coordinate system of the origin (wherein, the y-axis of the second coordinate system is perpendicular to the imaging plane, and the x-axis of the second coordinate system is parallel to the imaging plane), and the formula for calculating the angle between the optical axes is difference, double The equation relationship between the parameters of the camera (equivalent focal length and mirror center distance, etc.), the angle between the optical axis and the object distance value, where the difference between the imaging points is the distance between the two imaging points and the corresponding y-axis Furthermore, after multiple sampling values of optical axis angles are obtained through the difference, the weighted average is calculated as the optical axis angle, which improves the accuracy of optical axis angle calibration.

In addition, the parameters of the dual-camera device can be stored in the register, or in the storage unit of the microprocessor, so as to ensure that the above-mentioned parameters can be quickly read to calculate the angle between the optical axes. At the same time, the acquisition process of the first object distance value can be adopted The single-camera focusing method, such as using a closed-loop motor to obtain the object distance value after focusing, ensures the accuracy of the object distance value and the reliability of the calibration process.

According to an embodiment of the present invention, preferably, the acquiring unit 302 is further configured to acquire a pre-stored first mapping table of the lens shift value and the object distance value, wherein the object distance value includes the first A first object distance value of a camera and a second object distance value of the second camera; and used for obtaining the first object distance value corresponding to the lens shift value through the first mapping table.

According to the optical axis angle calibration system of the embodiment of the present invention, by acquiring the lens displacement value and the mapping table, the first object distance value can be quickly obtained, and then the optical axis angle calibration can be realized according to the object distance value, the technical process is simple, The efficiency of the calibration process is improved. Specifically, a closed-loop motor can be installed to achieve fast acquisition of the lens shift value through the closed-loop motor after focusing.

According to an embodiment of the present invention, preferably, further comprising: a storage unit 306, configured to store parameters of the dual-camera device, wherein the parameters include the equivalent focal length value of the dual-camera device and the first The mirror center distance between the center point of the camera and the center point of the second camera.

According to the optical axis angle calibration system of the embodiment of the present invention, by storing parameters such as equivalent focal length and mirror center distance, the above parameters can be directly used in the calculation of the optical axis angle, thereby effectively improving the calibration optical axis angle. corner efficiency and accuracy.

According to an embodiment of the present invention, preferably, the coordinate value of the first imaging point is represented by x1, the coordinate value of the second imaging point is represented by x2, the object distance value is represented by L, and the dual camera device The parameters include the mirror center distance d and the equivalent focal length value f, and the calculation formula for the included angle of the optical axis specifically includes:

According to the optical axis angle calibration system of the embodiment of the present invention, the above optical axis angle calculation formula is established through the optical geometric relationship, specifically, through the similarity relationship between the triangle where the feature point is located and the triangle where the imaging point is located, create The above formula for calculating the included angle of the optical axis is determined, that is, the sampling value of the included angle of the optical axis is determined by the imaging point. It meets the calculation accuracy requirements of the optical axis angle.

According to an embodiment of the present invention, preferably, further comprising: a calculation unit 308, configured to calculate a weighted average of the optical axis angle sampling values of all the feature points; the storage unit 306 is also configured to convert the The weighted average value is stored in the microprocessor of the dual-camera device as an included angle of the optical axis of the dual-camera device.

According to the optical axis angle calibration system of the embodiment of the present invention, by calculating the weighted average of the optical axis angle sampling values as the optical axis angle, the error in the calibration process is reduced, and the optical axis angle is improved. the calibration accuracy.

According to an embodiment of the present invention, preferably, further comprising: a creation unit 310, configured to, after determining the included angle of the optical axis, use the coordinate value between the second imaging point and the first imaging point The difference between the imaging points is used as the imaging point difference, and a second mapping table between the imaging point difference and the object distance value is created through the optical axis angle calculation formula.

The optical axis angle calibration system according to the embodiment of the present invention provides a data basis for the actual focusing process of the dual-camera device by creating a second mapping table, specifically, and through continuous correction of the optical axis angle, timely Correcting the second mapping table can quickly determine the object distance value through the difference of imaging points in the actual focusing process, and then complete the focusing process.

According to the embodiment of the fourth aspect of the present invention, a focusing system 400 is proposed, including: an acquisition unit 402, configured to acquire the coordinate value of the third imaging point of any feature point of the subject on the first camera; The acquiring unit 402 is also used to acquire the fourth imaging point coordinate value of the feature point on the second camera; the focusing system 400 further includes: a determining unit 404 configured to use the fourth imaging point The difference between the coordinate value and the coordinate value of the third imaging point is used as the difference value of the imaging point, and the second object distance value is determined according to the difference value of the imaging point and the calibrated optical axis angle; the focusing unit 406, It is used to determine the lens shift value according to the second object distance value and the first mapping table, so as to complete the first focusing.

According to the focus system of the embodiment of the present invention, by creating a calibration mapping table between the image distance value and the calibration displacement value, the calibration displacement value of the second camera can be directly determined according to the image distance value, reducing the calculation process, wherein, in After calibrating the included angle of the optical axis, according to the included angle of the optical axis and the above calculation formula, the calibration mapping table can be created by measuring the image distance value multiple times, and then in the actual focusing process, only the image distance value needs to be obtained. Quickly determine the calibration displacement value for the second camera.

According to an embodiment of the present invention, preferably, the determining unit 404 is further configured to substitute the imaging point difference, the calibrated optical axis angle and the parameters of the dual camera device into the optical axis angle calculation formula to obtain the second object distance value.

According to the focus system of the embodiment of the present invention, the second object distance value is obtained through the calculation formula of the included angle of the optical axis, which improves the focusing accuracy of the second camera. Specifically, after the included angle of the optical axis is calibrated, according to the The calculation formula of the included angle of the axis, by substituting the average value of the difference between the imaging points measured multiple times, the calibrated optical axis included angle and the parameters of the dual camera device into the calculated formula of the included optical axis angle, the object distance of the second camera can be accurately obtained value, and quickly determine the calibration displacement value of the second camera according to the object distance value and the second mapping table.

According to an embodiment of the present invention, preferably, the determining unit 404 is further configured to determine the second object distance corresponding to the imaging point difference according to the imaging point difference and the second mapping table .

According to the focusing system of the embodiment of the present invention, by obtaining the mapping relationship between the second object distance value and the lens displacement value of the second camera, the focusing efficiency and accuracy of the second camera are improved, and the second camera is controlled to complete the process according to the lens displacement value. Focusing process.

According to an embodiment of the present invention, preferably, the focusing unit 406 is further configured to, after completing the first focusing, use a contrast focusing method or a phase focusing method to complete the second focusing.

According to the focusing system of the embodiment of the present invention, a more accurate focusing effect is achieved by performing the second focusing after the first focusing. The maximum lens position is the exact focus position, and the phase focus method is when the focus position is accurate, the phase detection system can accurately know that it is currently in focus.

Fig. 5 shows a schematic block diagram of a dual camera device according to an embodiment of the present invention.

As shown in FIG. 5 , a dual camera device 500 according to an embodiment of the present invention includes: a calibration system 300 for optical axis angles as described in any of the above technical solutions or a calibration system 300 as described in any of the above technical solutions Focusing system 400 .

The focusing process of the photographing device according to the embodiment of the present invention will be specifically described below with reference to FIGS. 1 to 9 .

After the closed-loop motor and lens of the dual-camera device are adapted, two sets of mapping tables will be output, one of which is the mapping table of object distance and lens displacement (Table 1), and the other is the mapping table of displacement and lens displacement (Table 2 ).

As shown in Figure 6, determine the first coordinate system (wherein, the y-axis of the first coordinate system is perpendicular to the imaging plane, the x-axis of the first coordinate system is parallel to the imaging plane) with the mirror center of the camera 1 as the origin, and the camera The second coordinate system with the mirror center of 2 as the origin (wherein, the y-axis of the second coordinate system is perpendicular to the imaging plane, and the x-axis of the second coordinate system is parallel to the imaging plane), used for the angle between optical axis 1 and optical axis 2 Each parameter of the calculation formula is the value measured in the corresponding coordinate system.

Table 1

Object Distance(m) Lens Shift(mm) ∞ 0.000 10.0 -0.001 5.0 -0.003 4.0 -0.004 3.0 -0.005 2.0 -0.007 1.9 -0.008 1.8 -0.008 1.7 -0.009 1.6 -0.009 1.5 -0.010 1.4 -0.010 1.3 -0.011 1.2 -0.012 1.1 -0.013 1.0 -0.015 0.9 -0.016 0.8 -0.018 0.7 -0.021 0.6 -0.024 0.5 -0.029 0.45 -0.033 0.40 -0.037 0.35 -0.042 0.30 -0.049 0.25 -0.059 0.20 -0.074 0.15 -0.099 0.14 -0.107 0.13 -0.115 0.12 -0.125 0.11 -0.137 0.10 -0.151

As shown in Figure 7, when the optical axis angle parameter of the shooting device is 0, according to the proportional relationship of similar triangles, the formula is as follows:

Among them, d is the mirror center distance, L is the object distance value, f is the equivalent focal length, and x1-x2 is the above-mentioned difference value. Therefore, through the above formula, Table 1 and Table 2, it can be quickly obtained that the angle of the optical axis is 0 is the object distance value L.

The general applicability of the calculation formula for the included angle of the optical axis is illustrated by specific examples below:

Note: Here we define the angle of clockwise rotation of optical axis 2 relative to optical axis 1 as positive, and vice versa as negative.

Embodiment one:

As shown in Figure 8, when one optical axis of the shooting device is deflected, and the included angle parameter of the optical axis is α, similarly, according to the proportional relationship of similar triangles, there are equations (1) as follows:

Among them, d is the mirror center distance, L is the object distance value, f is the equivalent focal length, x2-x1 is the difference, α is the angle between the optical axis, and Δx is the offset distance of the optical axis. Therefore, the above formula can be used to quickly obtain The object distance value L whose optical axis angle is α, the α value is obtained through the above equations, so as to realize the self-calibration of the optical axis angle, and then calculate the object distance value based on the calibrated α, and combine Table 1 and Table 2 to realize Precise focusing process.

After simplifying the equation group (1) and eliminating Δx, the calculation formula for obtaining the angle of the optical axis is:

Embodiment two:

As shown in Figure 9, when the two optical axes of the shooting device are deflected, and the parameters of the included angle of the optical axes are α ₁ and α ₂ respectively, the included angle of the optical axes α=α ₂ -α ₁ , similarly, according to the similar triangle Proportional relationship, there are equations (2) as follows:

Note that the above Δx1, Δx2, Δx, α1, and α2 are all signed, and may be positive or negative.

in addition,

Among them, d is the mirror center distance, L is the object distance value, f is the equivalent focal length, x2-x1 is the difference, α is the angle between the optical axes, Δx1 is the offset distance of the first optical axis, and Δx2 is the second optical axis Offset distance, therefore, the object distance value L with an optical axis angle of α can be quickly obtained through the above formula (eliminating the parameters Δx1 and Δx2), and the α value is obtained through the above equations, thereby realizing the self-calibration of the optical axis angle, Then calculate the object distance value based on the calibrated α, and combine Table 1 and Table 2 to achieve a precise focusing process.

Table 2

(x2-x1) (unit: pixel) Lens Shift(mm) 0 0.000 1 -0.001 2 -0.003 3 -0.004 4 -0.005 5 -0.007 6 -0.008 7 -0.008 8 -0.009 9 -0.009 10 -0.010 11 -0.010 12 -0.011 13 -0.012 14 -0.013 16 -0.015 18 -0.016 20 -0.018 twenty two -0.021 twenty four -0.024 28 -0.029 32 -0.033 36 -0.037 40 -0.042 44 -0.049 50 -0.059 56 -0.074 62 -0.099 70 -0.107 80 -0.115 90 -0.125 110 -0.137 130 -0.151

Simplifying the above equation group (2), we can get:

Optical axis angle:

At small angles:

That is to say, the calculation formula for obtaining the angle between the optical axes when both optical axes are deflected is also: From the above two embodiments, it can be seen that the calculation formula of the included angle of the optical axis according to the embodiment of the present invention is applicable to all cases where the included angle of the optical axis is deflected, and has universal adaptability.

When the above-mentioned shooting equipment adopts fast focusing, when testing the focusing, obtain the difference value of the feature points on the imaging surface (the average value of multiple tests), and determine the lens displacement through Table 2, and the fast focusing process can be completed.

After fast focusing, use contrast focusing or phase focusing to focus on the dual lens more accurately. During the shooting process, Table 1 and Table 2 are updated and optimized after counting the lens shift.

The technical solution of the present invention has been described in detail above in conjunction with the accompanying drawings, considering the technical problem of how to realize the self-calibration process of a dual-lens shooting device to achieve accurate focusing. Therefore, the present invention proposes a new focusing scheme and a dual-camera device, which can achieve fast and precise focusing. The error of the angle parameter causes the focus error, which improves the user experience in the shooting process.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (21)

1. A calibration method of an optical axis angle, the calibration method is applicable to a dual-camera device comprising a first camera and a second camera, wherein the calibration method comprises: Focus on any feature point of the object to be photographed to obtain the first object distance value; determining a first imaging point coordinate value of the feature point on the first camera; determining a second imaging point coordinate value of the feature point on the second camera; According to the coordinate value of the first imaging point, the coordinate value of the second imaging point, the pre-stored parameters of the dual-camera device, the first object distance value and the pre-stored optical axis angle calculation formula to determine the The angle between the optical axes of the dual-camera device. 2. The calibration method of the optical axis angle according to claim 1, wherein obtaining the first object distance value comprises the following specific steps: Obtain a first mapping table of pre-stored lens displacement values and object distance values; The first object distance value corresponding to the lens shift value is acquired through the first mapping table. 3. The method for calibrating the included angle of the optical axis according to claim 1, characterized in that, before focusing on any feature point of the object to be photographed, further comprising the following specific steps: The parameters of the dual-camera device are stored, wherein the parameters include an equivalent focal length value of the dual-camera device and a mirror center distance between a central point of the first camera and a central point of the second camera. 4. The method for calibrating the included angle of the optical axis according to claim 3, wherein the coordinate value of the first imaging point is represented by x1, the coordinate value of the second imaging point is represented by x2, and the object distance is represented by L value, the parameters of the dual-camera device include the mirror center distance d and the equivalent focal length value f, then the calculation formula for the included angle of the optical axis specifically includes: 5. The method for calibrating the included angle of the optical axis according to any one of claims 1 to 4, wherein determining the included angle of the optical axis of the dual-camera device comprises the following specific steps: Calculate the weighted average of the optical axis angle sampling values of all the feature points; The weighted average value is stored in the microprocessor of the dual-camera device as an included angle of the optical axis of the dual-camera device. 6. the calibration method of optical axis angle according to any one of claims 1 to 4, is characterized in that, also comprises: After determining the included angle of the optical axis, the difference between the coordinate value of the second imaging point and the coordinate value of the first imaging point is used as the difference value of the imaging point, and the imaging is created through the calculation formula of the included angle of the optical axis A second mapping table between the point difference value and the object distance value. 7. A focusing method, which is applicable to a dual-camera device in which the calibration method of the optical axis angle according to any one of claims 1 to 6 completes the calibration of the optical axis angle, characterized in that it comprises: Obtain the coordinate value of the third imaging point of any feature point of the subject on the first camera; Acquiring the fourth imaging point coordinate value of the feature point on the second camera; Using the difference between the coordinate value of the fourth imaging point and the coordinate value of the third imaging point as an imaging point difference value, and determining a second object distance value according to the imaging point difference value and the calibrated optical axis angle; Determine a lens shift value according to the second object distance value and the first mapping table of the dual camera device, so as to complete the first focusing. 8. The focusing method according to claim 7, wherein determining the second object distance value according to the imaging point difference and the calibrated optical axis angle comprises the following specific steps: The imaging point difference value, the calibrated optical axis angle and the parameters of the dual camera device are substituted into the optical axis angle calculation formula to obtain the second object distance value. 9. The focusing method according to claim 7, wherein determining the second object distance value of the second camera according to the imaging point difference value and the calibrated optical axis angle includes the following specific steps: The second object distance value corresponding to the imaging point difference value is determined according to the imaging point difference value and the second mapping table of the dual camera device. 10. The focusing method according to claim 8 or 9, further comprising: After completing the first focusing, use the contrast focusing method or the phase focusing method to complete the second focusing. 11. A calibration system for an included angle of an optical axis, the calibration system is suitable for a dual-camera device including a first camera and a second camera, wherein the calibration system includes: an acquisition unit, configured to focus on any feature point of the object to be photographed, and acquire the first object distance value; a determining unit, configured to determine the first imaging point coordinate value of the feature point on the first camera; The determining unit is also used to determine the second imaging point coordinate value of the feature point on the second camera; The determining unit is further configured to, according to the coordinate value of the first imaging point, the coordinate value of the second imaging point, the pre-stored parameters of the dual-camera device, the first object distance value, and the pre-stored light The axis angle calculation formula determines the optical axis angle of the dual camera device. 12. The calibration system for the included angle of the optical axis according to claim 11, wherein the acquisition unit is further configured to acquire a pre-stored first mapping table of lens displacement values and object distance values; and and acquiring the first object distance value corresponding to the lens shift value through the first mapping table. 13. The calibration system for optical axis angle according to claim 11, further comprising: A storage unit configured to store parameters of the dual-camera device, wherein the parameters include an equivalent focal length value of the dual-camera device and a mirror between the center point of the first camera and the center point of the second camera heart distance. 14. The calibration system for the included angle of the optical axis according to claim 13, wherein the coordinate value of the first imaging point is represented by x1, the coordinate value of the second imaging point is represented by x2, and the object distance is represented by L value, the parameters of the dual-camera device include the mirror center distance d and the equivalent focal length value f, then the calculation formula for the included angle of the optical axis specifically includes: 15. The calibration system for the included angle of the optical axis according to claim 13, further comprising: a calculation unit, configured to calculate a weighted average of the optical axis angle sampling values of all the feature points; The storage unit is further configured to store the weighted average value in the microprocessor of the dual-camera device as an included angle of the optical axes of the dual-camera device. 16. The calibration system for the included angle of the optical axis according to any one of claims 11 to 14, further comprising: The creating unit is configured to use the difference between the coordinate value of the second imaging point and the coordinate value of the first imaging point as the difference value of the imaging point after determining the included angle of the optical axis, and pass through the optical axis The angle calculation formula creates a second mapping table between imaging point difference values and object distance values. 17. A focusing system, suitable for the calibration system of the optical axis angle as claimed in any one of claims 11 to 16 to complete the dual camera device for optical axis angle calibration, characterized in that it comprises: An acquisition unit, configured to acquire a third imaging point coordinate value of any feature point of the subject on the first camera; The acquiring unit is further configured to acquire a fourth imaging point coordinate value of the feature point on the second camera; The focusing system also includes: The determination unit is configured to use the difference between the coordinate value of the fourth imaging point and the coordinate value of the third imaging point as the imaging point difference, and determine the second imaging point difference according to the imaging point difference and the calibrated optical axis angle. Object distance value; A focusing unit, configured to determine a lens shift value according to the second object distance value and the first mapping table of the dual-camera device, so as to complete the first focusing. 18. The focusing system according to claim 17, wherein the determination unit is further configured to substitute the imaging point difference, the calibrated optical axis angle and the parameters of the dual camera device into the light The calculation formula of the included axis angle to obtain the second object distance value. 19. The focusing system according to claim 17, wherein the determining unit is further configured to determine, according to the imaging point difference and the second mapping table of the dual-camera device, that the imaging point difference corresponds to The second object distance value. 20. The focusing system according to claim 18 or 19, wherein the focusing unit is further configured to, after completing the first focusing, use a contrast focusing method or a phase focusing method to complete the second focusing. 21. A dual-camera device, characterized by comprising: the calibration system for the angle of the optical axis according to any one of claims 11 to 16 or the focusing system according to any one of claims 17 to 20 .