Where am I? Using Vanishing Points

Transcription

1 Whee am I? Using Vanishing Points

2 Vanishing point Vanishing line fo hoizon Vanishing point What can vanishing line tell us about me? Hoizon Camea pitch angle (looking down) Camea oll angle (tilted towad ight)

3 Whee am I w..t. Gound Plane? Camea u v 1 X Y K t C W Z 1 How to compute?

4 What can a Vanishing Point tell us about? Camea v

5 What can a Vanishing Point tell us about? Camea Z 1 v

6 What can a Vanishing Point tell us about? Camea Z 1 1 C v K t W 1 v

7 Single Vanishing Point Camea K -1 v 3 Z 1 1 C v K t W 1 v K 3 v

8 Single Vanishing Point Camea K -1 v 3 Z 1 1 C v K t W 1 v K 3 Kv because 3 is a unit vecto. Kv Z vanishing point tells us about the suface nomal of the gound plane v

9 Single Vanishing Point Camea K -1 v 3 Z 1 1 C v K t W 1 v K 3 Kv because 3 is a unit vecto. Kv Z vanishing point tells us about the suface nomal of the gound plane Rotation ambiguity v

10 Single Vanishing Point Camea Kv -1 Kv 3-1 K -1 v 3 Z 1 1 Roll and pitch angle can be computed by the gound plane. v

11 Single Vanishing Point Camea Kv -1 Kv 3-1 K -1 v 3 Z 1 1 Roll and pitch angle can be computed by the gound plane. 3D spatial otation: a sequence of Eule angle otation (oll/pitch/yaw). v

12 Single Vanishing Point Camea Kv -1 Kv 3-1 K -1 v 3 Z 1 1 Roll and pitch angle can be computed by the gound plane. Yaw: otation about z axis: R yaw cos -sin sin cos 1 v

13 Single Vanishing Point Camea Kv -1 Kv 3-1 K -1 v 3 Z 1 1 Roll and pitch angle can be computed by the gound plane. Yaw: otation about z axis: R yaw Pitch: otation about y axis: Rpitch cos -sin sin cos 1 cos sin 1 -sin cos v

14 Single Vanishing Point Camea Kv -1 Kv 3-1 K -1 v 3 Z 1 1 Roll and pitch angle can be computed by the gound plane. Yaw: otation about z axis: R yaw Pitch: otation about y axis: Rpitch cos -sin sin cos 1 cos sin 1 -sin cos Roll: otation about x axis: R oll 1 cos -sin sin cos v

15 Single Vanishing Point Camea Kv -1 Kv 3-1 K -1 v 3 Z 1 1 Roll and pitch angle can be computed by the gound plane. Yaw: otation about z axis: R yaw Pitch: otation about y axis: Rpitch cos -sin sin cos 1 cos sin 1 -sin cos Roll: otation about x axis: R oll 1 cos -sin sin cos v -sin T yaw pitch oll cos sin R R R cos cos

16 Single Vanishing Point Camea Kv -1 Kv 3-1 K -1 v 3 Z 1 1 Roll and pitch angle can be computed by the gound plane. -sin T yaw pitch oll cos sin R R R cos cos Pitch: Roll: tan tan v

17 Single Vanishing Point (Execise) ComputeCameaUsingVanishingPoint.m f = 1224; K = [f size(im,2)/2; f size(im,1)/2; 1]; m1 = [2563;25;1]; m2 = [2439;545;1]; m3 = [571;25;1]; m4 = [723;498;1]; l1 = GetLineFomTwoPoints(m1,m2); l2 = GetLineFomTwoPoints(m3,m4); v1 = GetPointFomTwoLines(l1,l2); v1 = v1/v1(3); 3 = inv(k)*v1/nom(inv(k)*v1) pitch = atan(-3(1)/nom(3(2:3))) oll = atan(3(2)/3(3)) 3 = pitch =.736 oll = 1.116

18 Two Vanishing Points Camea v Y v X

19 Two Vanishing Points Camea X 1 v Y v X Y 1

20 Two Vanishing Points Camea X 1 C v X K t W X K 1 v Y v X Y 1

21 v Y Camea Two Vanishing Points v X X Y 1 1 C v X K t W X K 1 C v Y K t W Y K 2

22 v Y Camea Two Vanishing Points 1 X C v X K t W X 3 K v X Y 1 C v Y K t W Y K v K v -1-1 X 1, -1 2 K v X -1 1 K K v Y Y : Othogonality constaint

23 Geometic Intepetation -1 KvX X 1

24 Geometic Intepetation -1 KvX X 1-1 KvY Y 1

25 Geometic Intepetation -1 KvX X 1-1 KvY Y 1

26 Geometic Intepetation K v K v -1-1 X Y -1 KvX X 1-1 KvY Y 1

27 Geometic Intepetation (Tanslation Ambiguity)

28 Geometic Intepetation (Tanslation Ambiguity)

29 Geometic Intepetation (Tanslation Ambiguity)

30 Two Vanishing Points Camea ComputeCameaUsingTwoVanishingPoints.m f = 4; K = [f size(im,2)/2; f size(im,1)/2; 1]; v Y v X l11 = GetLineFomTwoPoints(m11,m12); l12 = GetLineFomTwoPoints(m13,m14); l21 = GetLineFomTwoPoints(m21,m22); l22 = GetLineFomTwoPoints(m23,m24); v1 = GetPointFomTwoLines(l11,l12); v2 = GetPointFomTwoLines(l21,l22); 1 = inv(k)*v1/nom(inv(k)*v1); 2 = inv(k)*v2/nom(inv(k)*v2); 3 = Vec2Skew(1)*2; R = Not othogonal matix! det(r) =.577 R *R =

31 Two Vanishing Points f = 1224; K = [f size(im,2)/2; f size(im,1)/2; 1]; ComputeCameaUsingTwoVanishingPoints.m Change focal length l11 = GetLineFomTwoPoints(m11,m12); l12 = GetLineFomTwoPoints(m13,m14); l21 = GetLineFomTwoPoints(m21,m22); l22 = GetLineFomTwoPoints(m23,m24); v1 = GetPointFomTwoLines(l11,l12); v2 = GetPointFomTwoLines(l21,l22); 1 = inv(k)*v1/nom(inv(k)*v1); 2 = inv(k)*v2/nom(inv(k)*v2); 3 = Vec2Skew(1)*2; Othogonal matix! R = det(r) =.9948 R *R =