CN104596502A - Object posture measuring method based on CAD model and monocular vision - Google Patents

Abstract

The invention discloses an object posture measuring method based on a CAD model and monocular vision. The object posture measuring method based on the CAD model and the monocular vision comprises the following steps: after obtaining a movement relationship between a template shooting camera of an assumed movement and a fixed camera by virtue of movement assumption and iterative calculation of the template shooting camera to obtain an outer parameter of a binocular system consisting of the template shooting camera of the assumed movement and the fixed camera, performing three-dimensional reconstruction on a target to obtain three-dimensional point cloud data of the target, and rectifying a CAD model including object three-dimensional structure information to obtain a corresponding relation between the object posture of the target object under a current world coordinate system and the CAD model, and accurately figuring the posture of the target object. A movable camera fixing carrier is not needed and the CAD model and the three-dimensional vision information of the object are combined, so that the cost is low, the precision is high, and the demand of the actual industrial application can be met.

Description

A kind of object pose measuring method based on cad model and monocular vision

Technical field

The present invention relates to a kind of object pose measuring method based on cad model and monocular vision, belong to vision measurement field.

Background technology

Along with industrial machine man-based development, the robot/mechanical arm operation of view-based access control model servo is applied in increasing scene, is at present " machine substitution ", the key problem of industrial transformation.But current industrial vision system is because technology and cost restriction, good simple and easy solution be there is no to the accurate location of three-dimensional body, current vision servo system is caused to be mainly used in two aspects: one is target object regular shape and flat scene, accurately can be located by outline; Two is less demanding to accuracy of identification, has the scene that larger grabbing error is allowed, as food packing, piling etc.But need three-dimensional pinpoint application scenarios then can only rely on the sensors such as the laser of high price for shape and structure complexity, general application cannot be realized.

The monocular vision that utilizes in the past carries out in the method for three-dimensional pose measurement to target, video camera is needed to be fixed on motion carrier, two width images taken by video camera under diverse location, eigenmatrix is calculated according to the match point on image and Epipolar geometry constraint, by carrying out SVD decomposition to eigenmatrix, obtain the position relationship of video camera when shooting two width image.But the result of calculation obtained like this is not unique, the motion control parameter with reference to fixing video camera carrier is needed to determine the normal solution of camera motion.In commercial Application, motion carrier controling parameters is unknowable or when not having a motion carrier, these class methods are infeasible at all.

Summary of the invention

The object of the invention is the deficiency existed in measuring for existing monocular vision, a kind of object pose measuring method based on cad model and monocular vision is provided.

Step based on the object pose measuring method of cad model and monocular vision is as follows:

(1) cad model of object is obtained;

(2) be fixed on above perform region by single camera, carry out intrinsic parameter demarcation to video camera, obtain intrinsic parameter and the distortion factor of video camera, setting world coordinate system, using worktable as the plane of z=0, obtains the outer parameter [R of video camera ₁t ₁], namely camera coordinate system is relative to the rotation of world coordinate system and translation transformation, wherein R ₁represent rotation matrix, t ₁represent translation vector;

(3) object is placed on visual field central authorities, the standard form image of photographic subjects object;

(4) the online captured in real-time of video camera obtains the image of object under current placement pose, if the current pose of object is P _n, the pose of object when carrying out template shooting is P ₀, P _n≠ P ₀;

(5) feature extraction algorithm based on Scale invariant, invariable rotary is utilized, obtain the unique point descriptor in current taken image and template image, unique point descriptor according to image is slightly mated two width images, obtain the feature point pairs of N to coupling, the parameter of adjustment feature extraction algorithm, makes to obtain at least 8 to above matching characteristic point;

(6) according in step (5) two width image at least 8 to above matching characteristic point pair, RANSAC algorithm is utilized to calculate basis matrix F between two width images, reject the Mismatching point in step (5) according to the epipolar-line constraint of basis matrix F and Epipolar geometry, obtain smart matching result;

(7) according to current goal subject image and template image, known camera intrinsic parameter, suppose that object pose immobilizes, obtain the outer parameter of video camera during shooting two width image, just can carry out three-dimensional reconstruction to target object, for calculating the placement pose of current object in world coordinate system, suppose that object is with current pose fixed placement, template image is taken by camera motion and is obtained, the rotational transform of the relatively current fixed position, position of video camera is R, translation transformation is t, for convenience of describing, hereinafter with the video camera of template camera site in this camera motion of template shooting video camera acute pyogenic infection of finger tip hypothesis, if the outer parameter of template shooting video camera is [R ₂t ₂], namely template shooting camera coordinate system is relative to the rotation translation transformation of world coordinate system, wherein R ₂represent rotation matrix, t ₂represent translation vector,

(8) according to template shooting camera motion hypothesis, known fixed external parameters of cameras, needs the outer parameter [R solving template shooting video camera ₂t ₂], the iterative algorithm mated by feature based, complete the estimation to template shooting external parameters of cameras, iterative process comprises two stages: the outer parametric solution stage of template shooting video camera and unique point world coordinates estimation stages;

(9) according to the template shooting external parameters of cameras [R that step (8) obtains ₂t ₂] and the outer parameter [R of fixed cameras ₁t ₁] and image information, camera intrinsic parameter, three-dimensional reconstruction is carried out to target object, obtains the cloud data of object, in the process of three-dimensional reconstruction Stereo matching, because marginal point and angle point grey scale change are obvious, in the three-dimensional point cloud obtained, more marginal information and angle point information can be comprised;

(10) cad model of the cloud data of target object under current pose and object is carried out registration, obtain the world coordinate system measured and the transformational relation that designs a model between coordinate system of CAD, thus obtain the position of the cad model corresponding with object cloud data in our times coordinate system and attitude accurately, complete the measurement to object dimensional pose.

Described step (8) comprising:

(8-1) iterative process comprises two stages: the outer parametric solution stage of template shooting video camera and unique point world coordinates estimation stages;

(8-2) unique point world coordinates initialization: the external parameter [R of known fixed video camera ₁t ₁] and intrinsic parameter M, the initial value of the given unique point depth of field, obtains the world coordinates initial value { p of present image and template image matching characteristic point ₁, p ₂... p _n} ⁽⁰⁾, wherein n represents the number that matching characteristic point is right;

(8-3) template shooting external parameters of cameras solves the stage: according to the picture planimetric coordinates of unique point in template image and the world coordinate point { p of its correspondence ₁, p ₂..., p _n} ^(k)and camera intrinsic parameter M, by solving PnP problem, the outer parameter [R of new template shooting video camera ₂t ₂] ^(k);

(8-4) unique point world coordinates calculation stages: known fixed external parameters of cameras [R ₁t ₁], upgrade after template shooting video camera outer parameter [R ₂t ₂] ^(k)the picture coordinate corresponding with matching characteristic point in the intrinsic parameter of video camera and two width images, according to principle of triangulation, the world coordinates { p of regeneration characteristics point ₁, p ₂..., p _n} ^(k+1);

(8-5) according to the unique point of template image as coordinate { q ₁, q ₂..., q _n, video camera internal reference M and [R ₂t ₂] ^(k), { p ₁, p ₂..., p _n} ^(k+1)calculate re-projection error:

$e^2({R_2}^{\left(k\right)},{t_2}^{\left(k\right)},\{{p_i}^{(k+1)}\left\}\right)=\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{\left|\right|q_i-\frac{M({R_2}^{\left(k\right)}{p_i}^{(k+1)}+{t_2}^{\left(k\right)})}{{r_{23}}^{t\left(k\right)}{p_i}^{(k+1)}+{t_{2z}}^{\left(k\right)}}\left|\right|}^2$

Wherein r ₂₃ ^{t (k)}represent R ₂ ^(k)the third line, t _2z ^(k)represent t ₂ ^(k)the third line, q _ifor the homogeneous form of pixel coordinate, when re-projection error is less than the threshold value of setting, then stop iteration, obtain iterative computation result [R ₂t ₂] ₌[R ₂t ₂] ^(k), otherwise, put k=k+1.

Camera position of the present invention is fixed, and does not need movable carrier, by binding object cad model and Stereo Vision, proposes a kind of low cost, high-precision object pose measures solution.Carry out object observation by monocular vision in different visual angles and form stereoscopic vision, the preliminary object dimensional structural information obtained, although this three-dimensional structure information may exist error or cavity, good complete observation can be possessed in its three-dimensional edges region and precision is higher; Carry out registration by the master pattern of these marginal informations and CAD, the accurate pose that can obtain whole object is estimated.

The present invention is directed to the actual demand of commercial Application scene, although only provide the scheme of monocular vision, if there are two or more cameras, also can apply the thinking combined based on cad model and stereoscopic vision equally and realize the estimation of accurate object pose.

Accompanying drawing explanation

Fig. 1 is the object pose measuring method process flow diagram based on cad model and monocular vision;

Fig. 2 is iterative computation template shooting external parameters of cameras method flow diagram;

Fig. 3 is fixed cameras coordinate system, supposes that Motion mask takes the transformational relation schematic diagram between camera coordinate system and world coordinate system;

Fig. 4 is stereoscopic vision Epipolar geometry relation schematic diagram.

Embodiment

Step based on the object pose measuring method of cad model and monocular vision is as follows:

(1) cad model of object is obtained;

(2) be fixed on above perform region by single camera, carry out intrinsic parameter demarcation to video camera, obtain intrinsic parameter and the distortion factor of video camera, setting world coordinate system, using worktable as the plane of z=0, obtains the outer parameter [R of video camera ₁t ₁], namely camera coordinate system is relative to the rotation of world coordinate system and translation transformation, wherein R ₁represent rotation matrix, t ₁represent translation vector, the inside and outside parameter of video camera is demarcated and by demarcation gridiron pattern, can be adopted Zhang Zhengyou standardization;

(3) object is placed on visual field central authorities, the standard form image of photographic subjects object;

(4) the online captured in real-time of video camera obtains the image of object under current placement pose, and target object appears in the visual field of video camera with random pose, if the current pose of object is P _n, the pose of object when carrying out template shooting is P ₀, P _n≠ P ₀;

(5) feature extraction algorithm based on Scale invariant, invariable rotary is utilized, obtain the unique point descriptor in current taken image and template image, unique point descriptor according to image is slightly mated two width images, obtain the feature point pairs of N to coupling, the parameter of adjustment feature extraction algorithm, makes to obtain at least 8 to above matching characteristic point;

(6) according in two width images in step (5) at least 8 to above matching characteristic point, utilize RANSAC algorithm to calculate basis matrix F between two width images, Fig. 4 represents the Epipolar geometry restriction relation in stereoscopic vision.As shown in Figure 4, baseline is the straight line of connection two video camera photocentre O and O', and antipodal points e and e' is baseline and the intersection point as plane.Be the plane of baseline and specified point p to polar plane, polar curve is to the intersection of polar plane with picture plane, q ₁, q ₂for the projection of p on imaging plane, then in space, the imaging point pixel coordinate of arbitrfary point on two plane pictures meets following Epipolar geometry restriction relation: q ₁fq ₂=0, reject the Mismatching point in thick matching result according to this Epipolar geometry restriction relation, obtain exact matching result.

(7) according to current goal subject image and template image, known camera intrinsic parameter, suppose that object pose immobilizes, obtain the outer parameter of video camera during shooting two width image, just can carry out three-dimensional reconstruction to target object, for calculating the placement pose of current object in world coordinate system, suppose that object is with current pose fixed placement, template image is taken by camera motion and is obtained, the rotational transform of the relatively current fixed position, position of video camera is R, translation transformation is t, for convenience of describing, hereinafter with the video camera of template camera site in this camera motion of template shooting video camera acute pyogenic infection of finger tip hypothesis, if the outer parameter of template shooting video camera is [R ₂t ₂], namely template shooting camera coordinate system is relative to the rotation translation transformation of world coordinate system, wherein R ₂represent rotation matrix, t ₂represent translation vector, then the transformational relation between outer parameter coordinate system as shown in Figure 3,

(8) according to template shooting camera motion hypothesis, known fixed external parameters of cameras, needs the outer parameter [R solving template shooting video camera ₂t ₂], by the iterative algorithm that feature based mates, complete the estimation to template shooting external parameters of cameras, iterative process comprises two stages: the outer parametric solution stage of template shooting video camera and unique point world coordinates estimation stages, and the method flow of iterative computation as shown in Figure 2;

(9) according to the template shooting external parameters of cameras [R that step (8) obtains ₂t ₂] and the outer parameter [R of fixed cameras ₁t ₁], obtain the rotational transform R between template shooting video camera and fixed cameras and translation transformation t.If m ₁, m ₂be respectively world coordinate point p at fixed cameras coordinate points and hypothesis Motion mask shooting camera coordinates point, then m ₁=R ₁p+t ₁, m ₂=R ₂p+t ₂, can m be obtained ₂=R ₂r ₁ ^-1m ₁+ t ₂-R ₂r ₁ ^-1t ₁, so R=R ₂r ₁ ^-1, t=t ₂-R ₂r ₁ ^-1t ₁.The internal reference M of known R, t and video camera, according to current taken image and template image, can carry out stereo vision three-dimensional rebuilding to target object, can obtain the cloud data of object under current pose after reconstruction.In the process of three-dimensional reconstruction Stereo matching, because the grey scale change of marginal point and angle point is obvious, therefore reconstructs the some cloud obtained and can comprise obvious marginal information and angle point information.

(10) cad model of the cloud data of target object under current pose and object is carried out registration, arest neighbors iterative algorithm ICP (Iterative closet point) can be adopted to carry out registration to cloud data and object cad model, obtain the world coordinate system measured and the transformational relation that designs a model between coordinate system of CAD, thus obtain the position of the cad model corresponding with object cloud data in our times coordinate system and attitude accurately, complete the measurement to object dimensional pose.

Described step (8) comprising:

(8-1) iterative process comprises two stages: the outer parametric solution stage of template shooting video camera and unique point world coordinates estimation stages;

(8-2) unique point world coordinates initialization: the external parameter [R of known fixed video camera ₁t ₁] and intrinsic parameter M, the initial value of the given unique point depth of field, according to the imaging model of video camera, obtains the world coordinates initial value of present image and template image matching characteristic point.Because object is placed in world coordinate system near z=0 plane, the initial value of given unique point world coordinates z is z=0, can obtain the initial value { p of unique point world coordinates ₁, p ₂..., p _n} ⁽⁰⁾, wherein n represents the number that matching characteristic point is right;

(8-3) template shooting external parameters of cameras solves the stage: according to the picture planimetric coordinates of unique point in template image and the world coordinate point { p of its correspondence ₁, p ₂..., p _n} ^(k)and camera intrinsic parameter M, solve the outer parameter [R of more new template shooting video camera ₂t ₂] ^(k), this is a typical PnP problem, has the derivation algorithm of many classics, such as, can select to have global convergence and good orthogonal iteration (orthogonal iteration) algorithm of real-time, solve this PnP problem;

(8-4) unique point world coordinates calculation stages: the intrinsic parameter of known video camera is $M=\left[\begin{array}{ccc}{f}_x& 0& c_x\\ 0& f_y& c_y\\ 0& 0& 1\end{array}\right],$ Wherein (f _x, f _y) represent the normalization focal length of video camera, (c _x, c _y) represent the coordinate of photocentre in picture plane.The imaging model of video camera is:

$s\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_x& 0& c_x\\ 0& f_y& c_y\\ 0& 0& 1\end{array}\right]\left[R\right|t]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]$

Wherein [u v 1] ^trepresent the homogeneous coordinates as coordinate plane, [X Y Z 1] ^tthe homogeneous coordinates of representation space point world coordinate system.

Order $R=\left[\begin{array}{c}{r_1}^t\\ {r_2}^t\\ {r_3}^t\end{array}\right],t=\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right],p=\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right],$ Substitute into above camera model and can obtain following three equations:

s·u＝fx·(r ₁ ^t·p+t _x)+cx·(r ₃ ^t·p+t _z)

s·v＝fy·(r ₂ ^t·p+t _y)+cy·(r ₃ ^t·p+t _z)

s＝r ₃ ^t·p+t _z

Cancellation s, arrangement can obtain:

[(u-cx)·r ₃ ^t-fx·r ₁ ^t]·p＝fx·t ₁-(u-cx)·t ₃

[(v-cy)·r ₃ ^t-fy·r ₂ ^t]·p＝fy·t ₂-(v-cy)·t ₃

Matching characteristic point on known present image and template image is to (u ₁, v ₁) _i→ (u ₂, v ₂) _i, the external parameter of fixed cameras the template shooting external parameters of cameras that kth time iteration obtains the world coordinates of the locus that this matching characteristic point is corresponding is p _i ^(k+1), can obtain

$\left[\begin{array}{c}(u_1-\mathrm{cx})\·{r_{13}}^t-\mathrm{fx}\·{r_{11}}^t\\ (v_1-\mathrm{cy})\·{r_{13}}^t-\mathrm{fy}\·{r_{12}}^t\\ (u_1-\mathrm{cx})\·{r_{23}}^t-\mathrm{fx}\·{r_{21}}^t\\ (v_1-\mathrm{cy})\·{r_{23}}^t-\mathrm{fy}\·{r_{22}}^t\end{array}\right]\·{p_i}^{(k+1)}=\left[\begin{array}{c}\mathrm{fx}\·t_{1x}-(u_1-\mathrm{cx})\·t_{1z}\\ \mathrm{fy}\·t_{1y}-(v_1-\mathrm{cy})\·t_{1z}\\ \mathrm{fx}\·t_{2x}-(u_2-\mathrm{cx})\·t_{2z}\\ \mathrm{fy}\·t_{2y}-(v_2-\mathrm{cy})\·t_{2z}\end{array}\right]$

This is the system of linear equations of a Planar Mechanisms, can in the hope of p _i ^(k+1)least square solution.The world coordinates of n matching characteristic point can be upgraded according to this kind of method, obtain { p ₁, p ₂..., p _n} ^(k+1);

(8-5) according to the unique point of template image as coordinate { q ₁, q ₂..., q _n, video camera internal reference M and [R ₂t ₂] ^(k), { p ₁, p ₂..., p _n} ^(k+1)calculate re-projection error:

$e^2({R_2}^{\left(k\right)},{t_2}^{\left(k\right)},\{{p_i}^{(k+1)}\left\}\right)=\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{\left|\right|q_i-\frac{M({R_2}^{\left(k\right)}{p_i}^{(k+1)}+{t_2}^{\left(k\right)})}{{r_{23}}^{t\left(k\right)}{p_i}^{(k+1)}+{t_{2z}}^{\left(k\right)}}\left|\right|}^2$

Wherein r ₂₃ ^{t (k)}represent R ₂ ^(k)the third line, t _2z ^(k)represent t ₂ ^(k)the third line, q _ifor the homogeneous form of pixel coordinate; When re-projection error is less than the threshold value of setting, then stop iteration, obtain iterative computation result [R ₂t ₂]=[R ₂t ₂] ^(k), otherwise, put k=k+1.

Claims (2)

1., based on an object pose measuring method for cad model and monocular vision, it is characterized in that: its step is as follows:

(1) cad model of object is obtained;

(2) be fixed on above perform region by single camera, carry out intrinsic parameter demarcation to video camera, obtain intrinsic parameter and the distortion factor of video camera, setting world coordinate system, using worktable as the plane of z=0, obtains the outer parameter [R of video camera ₁t ₁], namely camera coordinate system is relative to the rotation of world coordinate system and translation transformation, wherein R ₁represent rotation matrix, t ₁represent translation vector;

(3) object is placed on visual field central authorities, the standard form image of photographic subjects object;

(4) the online captured in real-time of video camera obtains the image of object under current placement pose, if the current pose of object is P _n, the pose of object when carrying out template shooting is P ₀, P _n≠ P ₀;

(5) feature extraction algorithm based on Scale invariant, invariable rotary is utilized, obtain the unique point descriptor in current taken image and template image, unique point descriptor according to image is slightly mated two width images, obtain the feature point pairs of N to coupling, the parameter of adjustment feature extraction algorithm, makes to obtain at least 8 to above matching characteristic point;

(6) according in step (5) two width image at least 8 to above matching characteristic point pair, RANSAC algorithm is utilized to calculate basis matrix F between two width images, reject the Mismatching point in step (5) according to the epipolar-line constraint of basis matrix F and Epipolar geometry, obtain smart matching result;

(7) according to current goal subject image and template image, known camera intrinsic parameter, suppose that object pose immobilizes, obtain the outer parameter of video camera during shooting two width image, just can carry out three-dimensional reconstruction to target object, for calculating the placement pose of current object in world coordinate system, suppose that object is with current pose fixed placement, template image is taken by camera motion and is obtained, the rotational transform of the relatively current fixed position, position of video camera is R, translation transformation is t, for convenience of describing, hereinafter with the video camera of template camera site in this camera motion of template shooting video camera acute pyogenic infection of finger tip hypothesis, if the outer parameter of template shooting video camera is [R ₂t ₂], namely template shooting camera coordinate system is relative to the rotation translation transformation of world coordinate system, wherein R ₂represent rotation matrix, t ₂represent translation vector,

(8) according to template shooting camera motion hypothesis, known fixed external parameters of cameras, needs the outer parameter [R solving template shooting video camera ₂t ₂], the iterative algorithm mated by feature based, complete the estimation to template shooting external parameters of cameras, iterative process comprises two stages: the outer parametric solution stage of template shooting video camera and unique point world coordinates estimation stages;

(9) according to the template shooting external parameters of cameras [R that step (8) obtains ₂t ₂] and the outer parameter [R of fixed cameras ₁t ₁] and image information, camera intrinsic parameter, three-dimensional reconstruction is carried out to target object, obtains the cloud data of object, in the process of three-dimensional reconstruction Stereo matching, because marginal point and angle point grey scale change are obvious, in the three-dimensional point cloud obtained, more marginal information and angle point information can be comprised;

(10) cad model of the cloud data of target object under current pose and object is carried out registration, obtain the world coordinate system measured and the transformational relation that designs a model between coordinate system of CAD, thus obtain the position of the cad model corresponding with object cloud data in our times coordinate system and attitude accurately, complete the measurement to object dimensional pose.

2. a kind of object pose measuring method based on cad model and monocular vision according to claim 1, is characterized in that: described step (8) comprising:

(8-1) iterative process comprises two stages: the outer parametric solution stage of template shooting video camera and unique point world coordinates estimation stages;

(8-2) unique point world coordinates initialization: the external parameter [R of known fixed video camera ₁t ₁] and intrinsic parameter M, the initial value of the given unique point depth of field, obtains the world coordinates initial value { p of present image and template image matching characteristic point ₁, p ₂... p _n} ⁽⁰⁾, wherein n represents the number that matching characteristic point is right;

(8-3) template shooting external parameters of cameras solves the stage: according to the picture planimetric coordinates of unique point in template image and the world coordinate point { p of its correspondence ₁, p ₂..., p _n} ^(k)and camera intrinsic parameter M, by solving PnP problem, the outer parameter [R of new template shooting video camera ₂t ₂] ^(k);

(8-4) unique point world coordinates calculation stages: known fixed external parameters of cameras [R ₁t ₁], upgrade after template shooting video camera outer parameter [R ₂t ₂] ^(k)the picture coordinate corresponding with matching characteristic point in the intrinsic parameter of video camera and two width images, according to principle of triangulation, the world coordinates { p of regeneration characteristics point ₁, p ₂..., p _n} ^(k+1);

(8-5) according to the unique point of template image as coordinate { q ₁, q ₂..., q _n, video camera internal reference M and [R ₂t ₂] ^(k),{ p ₁, p ₂..., p _n} ^(k+1)calculate re-projection error:

$e^2({R_2}^{\left(k\right)},{t_2}^{\left(k\right)},\{p_i^{(k+1)}\left\}\right)=\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{\left|\right|q_i-\frac{M({R_2}^{\left(k\right)}{p_i}^{(k+1)}+{t_2}^{\left(k\right)})}{{r_{23}}^{t\left(k\right)}{p_i}^{(k+1)}+{t_{2z}}^{\left(2\right)}}\left|\right|}^2$

Wherein r ₂₃ ^{t (k)}represent R ₂ ^(k)the third line, t _2z ^(k)represent t ₂ ^(k)the third line, q _ifor the homogeneous form of pixel coordinate, when re-projection error is less than the threshold value of setting, then stop iteration, obtain iterative computation result [R ₂t ₂]=[R ₂t ₂] ^(k), otherwise, put k=k+1.