where am i? using vanishing pointscis580/spring2017/lectures/cis580-09-where... · roll and pitch...
TRANSCRIPT
![Page 1: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/1.jpg)
Where am I?Using Vanishing Points
![Page 2: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/2.jpg)
Where was I (how high)?
Taken from my hotel room (6th floor) Taken from beach
![Page 3: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/3.jpg)
![Page 4: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/4.jpg)
![Page 5: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/5.jpg)
![Page 6: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/6.jpg)
![Page 7: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/7.jpg)
![Page 8: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/8.jpg)
Keller Hall
Vanishing point
Vanishing point
What can vanishing line tell us about me?
• Horizon
• Camera pitch angle (looking down)
• Camera roll angle (tilted toward right)
Vanishing line for horizon
![Page 9: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/9.jpg)
Ground plane
Where am I w.r.t. Ground Plane?
3D world
Camera
Xu
Yv
ZK r r r tC
1 2 3 W
11
How to compute?
3D world
r1
r2
r3
![Page 10: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/10.jpg)
What can a Vanishing Point tell us about?Camera
3D world
r1
r2
r3
v
Ground plane
![Page 11: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/11.jpg)
Ground plane
What can a Vanishing Point tell us about?Camera
3D world
r1
r2
r3
v
Z
0
0
1
0
![Page 12: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/12.jpg)
Ground plane
What can a Vanishing Point tell us about?Camera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
C
1 2 3 W
0
0
1
0
v K r r r t
![Page 13: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/13.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
C
1 2 3 W
0
0
1
0
v K r r r t
-1
3
K v r
3
v Kr
![Page 14: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/14.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
C
1 2 3 W
0
0
1
0
v K r r r t
-1
3
K v r
3
v Kr
K v
rK v
-1
3 -1because r3 is a unit vector.
Z vanishing point tells us about the
surface normal of the ground plane
![Page 15: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/15.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
C
1 2 3 W
0
0
1
0
v K r r r t
-1
3
K v r
3
v Kr
K v
rK v
-1
3 -1because r3 is a unit vector.
Z vanishing point tells us about the
surface normal of the ground plane
Ground plane
Rotation ambiguity
![Page 16: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/16.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
![Page 17: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/17.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
Yaw: rotation about z axis:yaw
cos -sin 0
sin cos 0
0 0 1
R
![Page 18: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/18.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
Yaw: rotation about z axis:yaw
cos -sin 0
sin cos 0
0 0 1
R
Pitch: rotation about y axis:pitch
cos 0 sin
0 1 0
-sin 0 cos
R
![Page 19: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/19.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
Yaw: rotation about z axis:yaw
cos -sin 0
sin cos 0
0 0 1
R
Pitch: rotation about y axis:pitch
cos 0 sin
0 1 0
-sin 0 cos
R
Roll: rotation about x axis:roll
1 0 0
0 cos -sin
0 sin cos
R
![Page 20: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/20.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
Yaw: rotation about z axis:yaw
cos -sin 0
sin cos 0
0 0 1
R
Pitch: rotation about y axis:pitch
cos 0 sin
0 1 0
-sin 0 cos
R
Roll: rotation about x axis:roll
1 0 0
0 cos -sin
0 sin cos
R
T
1 2 3 yaw pitch roll
-sin
cos sin
cos cos
r r r R R R ?
![Page 21: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/21.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
Yaw: rotation about z axis:yaw
cos -sin 0
sin cos 0
0 0 1
R
Pitch: rotation about y axis:pitch
cos 0 sin
0 1 0
-sin 0 cos
R
Roll: rotation about x axis:roll
1 0 0
0 cos -sin
0 sin cos
R
T
1 2 3 yaw pitch roll
-sin
cos sin
cos cos
r r r R R R
![Page 22: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/22.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
-1 31
2 2
32 33
-1 32
33
tan
tan
r
r r
r
r
T
1 2 3 yaw pitch roll
-sin
cos sin
cos cos
r r r R R R
Pitch:
Roll:
![Page 23: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/23.jpg)
Ground plane
Single Vanishing PointCamera
3D world
r1
r2
r3
v
0 0
0 0
1
1 0
Z
-1
3
K v r
K v
rK v
-1
3 -1
Roll and pitch angle can be computed by the ground plane.
-1 31
2 2
32 33
-1 32
33
tan
tan
r
r r
r
r
T
1 2 3 yaw pitch roll
-sin
cos sin
cos cos
r r r R R R
Pitch:
Roll:
![Page 24: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/24.jpg)
Single Vanishing Point (Exercise)
f = 1224;
K = [f 0 size(im,2)/2;
0 f size(im,1)/2;
0 0 1];
m1 = [2563;25;1];
m2 = [2439;545;1];
m3 = [571;25;1];
m4 = [723;498;1];
l1 = GetLineFromTwoPoints(m1,m2);
l2 = GetLineFromTwoPoints(m3,m4);
v1 = GetPointFromTwoLines(l1,l2);
v1 = v1/v1(3);
r3 = inv(K)*v1/norm(inv(K)*v1)
pitch = atan(-r3(1)/norm(r3(2:3)))
roll = atan(r3(2)/r3(3))
ComputeCameraUsingVanishingPoint.m
r3 =
-0.07360.89590.4381
pitch =
0.0736
roll =
1.1160
v
![Page 25: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/25.jpg)
Single Vanishing Point (Exercise)
f = 1224;
K = [f 0 size(im,2)/2;
0 f size(im,1)/2;
0 0 1];
m1 = [2563;25;1];
m2 = [2439;545;1];
m3 = [571;25;1];
m4 = [723;498;1];
l1 = GetLineFromTwoPoints(m1,m2);
l2 = GetLineFromTwoPoints(m3,m4);
v1 = GetPointFromTwoLines(l1,l2);
v1 = v1/v1(3);
r3 = inv(K)*v1/norm(inv(K)*v1)
pitch = atan(-r3(1)/norm(r3(2:3)))
roll = atan(r3(2)/r3(3))
ComputeCameraUsingVanishingPoint.m
r3 =
-0.07360.89590.4381
pitch =
0.0736
roll =
1.1160
![Page 26: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/26.jpg)
Ground plane
Two Vanishing Points
3D world
Camera
r1
r2
r3
Yv
v
X
3D world
![Page 27: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/27.jpg)
Ground plane
Two Vanishing PointsCamera
0
1
0
0
Y
X
1
0
0
0
3D world
r1
r2
r3
Yv
v
X
3D world
![Page 28: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/28.jpg)
Ground plane
Two Vanishing PointsCamera
X
1
0
0
0
v K r r r t X
Kr
C
X 1 2 3 W
1
0
1
0
0
Y
3D world
r1
r2
r3
Yv
v
X
3D world
![Page 29: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/29.jpg)
Ground plane
Two Vanishing PointsCamera
X
1
0
0
0
C
Y 1 2 3 W
2
v K r r r t Y
Kr
v K r r r t X
Kr
C
X 1 2 3 W
1
0
1
0
0
Y
3D world
r1
r2
r3
Yv
v
X
3D world
![Page 30: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/30.jpg)
Ground plane
Two Vanishing PointsCamera
X
1
0
0
0
-1 -1
X Y1 2-1 -1
X Y
,
K v K v
r rK v K v
3 1 2 r r r : Orthogonality constraint
C
Y 1 2 3 W
2
v K r r r t Y
Kr0
1
0
0
Y
3D world
r1
r2
r3
v K r r r t X
Kr
C
X 1 2 3 W
1
Yv
v
X
3D world
![Page 31: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/31.jpg)
Ground plane
Geometric Interpretation
3D world
r1
r2
r3
X
1
0
0
0
-1
X
K v
![Page 32: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/32.jpg)
Ground plane
Geometric Interpretation
X
1
0
0
0
-1
X
K v
0
1
0
0
Y-1
Y
K v
3D world
r1
r2
r3
![Page 33: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/33.jpg)
Ground plane
Geometric Interpretation
X
1
0
0
0
-1
X
K v
3D world
r1
r2
r3
-1
Y
K v
0
1
0
0
Y
![Page 34: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/34.jpg)
Ground plane
Geometric Interpretation
X
1
0
0
0
-1
X
K v
-1 -1
X Y K v K v
3D world
r1
r2
r3
-1
Y
K v
0
1
0
0
Y
![Page 35: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/35.jpg)
Ground plane
Geometric Interpretation (Translation Ambiguity)
![Page 36: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/36.jpg)
Ground plane
Geometric Interpretation (Translation Ambiguity)
![Page 37: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/37.jpg)
Ground plane
Geometric Interpretation (Translation Ambiguity)
![Page 38: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/38.jpg)
Ground plane
Two Vanishing Points
3D world
Camera
r1
r2
r3
f = 4000;K = [f 0 size(im,2)/2;
0 f size(im,1)/2;0 0 1];
l11 = GetLineFromTwoPoints(m11,m12);l12 = GetLineFromTwoPoints(m13,m14);
l21 = GetLineFromTwoPoints(m21,m22);l22 = GetLineFromTwoPoints(m23,m24);
v1 = GetPointFromTwoLines(l11,l12);v2 = GetPointFromTwoLines(l21,l22);
r1 = inv(K)*v1/norm(inv(K)*v1);r2 = inv(K)*v2/norm(inv(K)*v2);
r3 = Vec2Skew(r1)*r2;
R =0.2448 -0.5178 0.0424
-0.1737 -0.1960 -0.69780.9539 0.8327 -0.1379
det(R) = 0.5077
R’*R =0.3299 0.0294 -0.20360.0294 0.5555 -0.2327
-0.2036 -0.2327 1.6224
Not orthogonal matrix!
ComputeCameraUsingTwoVanishingPoints.m
Yv
v
X
3D world
![Page 39: Where am I? Using Vanishing Pointscis580/Spring2017/Lectures/cis580-09-where... · Roll and pitch angle can be computed by the ground plane. Yaw: rotation about z axis: yaw cos -sin](https://reader034.vdocument.in/reader034/viewer/2022042811/5fa64ca5128bd2210f127208/html5/thumbnails/39.jpg)
Two Vanishing Pointsf = 1224;K = [f 0 size(im,2)/2;
0 f size(im,1)/2;0 0 1];
l11 = GetLineFromTwoPoints(m11,m12);l12 = GetLineFromTwoPoints(m13,m14);
l21 = GetLineFromTwoPoints(m21,m22);l22 = GetLineFromTwoPoints(m23,m24);
v1 = GetPointFromTwoLines(l11,l12);v2 = GetPointFromTwoLines(l21,l22);
r1 = inv(K)*v1/norm(inv(K)*v1);r2 = inv(K)*v2/norm(inv(K)*v2);
r3 = Vec2Skew(r1)*r2;
ComputeCameraUsingTwoVanishingPoints.m
R =0.5846 -0.8496 0.0508
-0.4149 -0.3216 -0.83670.6972 0.4180 -0.5405
det(R) =0.9948
R’*R =1.0662 -0.0118 0.0250
-0.0118 0.9757 0.02850.0250 0.0285 0.9530
Orthogonal matrix!
Change focal length