Quadrilaterals Quadrilaterals: A Review Game Moody Mathematics.
Inverse Perspective Projection of Convex Quadrilaterals
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Transcript of Inverse Perspective Projection of Convex Quadrilaterals
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Inverse Perspective Projection of Convex Quadrilaterals
Joo-Haeng LeeETRI
KOREA
ACDDE 2011VR and Multimedia WorkshopSession VRM-2 Paper ID116
111년 8월 28일 일요일
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Assume that you have a hand-held projector which can accept an rectangular source image of arbitrary aspect ratio. Which of the following convex quadrilaterals is projectable from this projector?
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #1
2
211년 8월 28일 일요일
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Assume that you have a hand-held projector which can accept an rectangular source image of arbitrary aspect ratio. Which of the following convex quadrilaterals is projectable from this projector?
(a) Rhombus (b) Parallelogram
(c) Trapezoid___ (d)IsoscelesTrapezoid
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #1
2
211년 8월 28일 일요일
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(a) (b)
(c) (d)
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #2
3
311년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Outline• Motivation
- Investigation of a geometric projection property as a theoretic aspect of RSAR (Robotic Spatial AR)
• Main Contribution
- (1) Analytic solution to the inverse perspective projection of a convex quadrilateral
- (2) Geometric interpretation
• Experimental Results + Answer to the Quiz #2
• Discussion
4
411년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
AR, SAR & RSAR• AR
- Augmented Reality
5
511년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
AR, SAR & RSAR• AR
- Augmented Reality
• SAR
- Spatial Augmented Reality
5
511년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
AR, SAR & RSAR• AR
- Augmented Reality
• SAR
- Spatial Augmented Reality
• RSAR
- Robotic Spatial Augmented Reality
5
511년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Examples of AR• World Lens
6
611년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Examples of SAR• SixthSense (2009, MIT)
7
711년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Examples of RSAR• LuminAR (2010; MIT)
8
811년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
FRC: RSAR System in ETRI
9
911년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
FRC: Kinematic Features• 5 Motors: (tilt + pan) x 2 + (center pan)
- Redundancy in Pan Rotation
10!!
1011년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
FRC: Micro Projectors
11
• Microvision SHOWWX
- Laser-based
- No need to control focus
- 10~15 lumen
• Optoma PK-301
- DLP
- Manual focusing required
- 20~50 lumen
1111년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
FRC: Applications
12
! ! ! !
1211년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Control Issues in RSAR• Kinematic Control
- Inverse Kinematics, Redundancy in DOF
• Inverse Projection
- Approximation vs. Analytic Solution
- Image Pre-Warping
• High-Order Control
- Constraints Handling; Collaborative RSAR
13
1311년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Inverse Projection
14
• End Effector (= Goal)
- position, area, shape, intensity, precision, ...
• Parameters
- Internal
- External: Pose Estimation
• High-order Control
- Soft and Hard Collision Avoidance
- Image Pre-Warping
1411년 8월 28일 일요일
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• End Effector: a projected mid-point
Joo-Haeng Lee (joohaeng at etri.re.kr)
Position Control
15
1511년 8월 28일 일요일
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• End Effector: a portion of area
Joo-Haeng Lee (joohaeng at etri.re.kr)
Area Control
16
1611년 8월 28일 일요일
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• End Effector: a certain shape of convex quadrilateral at a certain position
Joo-Haeng Lee (joohaeng at etri.re.kr)
Shape Control
17
1711년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Problem Definition
• Geometric Projectability of a Convex Quad
- Given an arbitrary convex quadrilateral, find external and internal parameters of a projector to project this quad from an imaginary rectangle of an unknown aspect ratio.
- Which type of named convex quadrilateral can be projected from a rectangle?
- Why a certain quad is not projectable?
- How to modify a such quadrilateral to be projectable?
18
1811년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Solution Outline: Analytic Inverse Projection of Convex Quadrilateral
19
1911년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Solution Outline: Analytic Inverse Projection of Convex Quadrilateral
1. Get a diagonal parameterization of a convex quad.
19
1911년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Solution Outline: Analytic Inverse Projection of Convex Quadrilateral
1. Get a diagonal parameterization of a convex quad.
2. Find values of length-related coefficients from inverse line projection for each diagonal.
19
1911년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Solution Outline: Analytic Inverse Projection of Convex Quadrilateral
1. Get a diagonal parameterization of a convex quad.
2. Find values of length-related coefficients from inverse line projection for each diagonal.
3. Check if these coefficients satisfy the basic conditions to solve the solution equations.
19
1911년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Solution Outline: Analytic Inverse Projection of Convex Quadrilateral
1. Get a diagonal parameterization of a convex quad.
2. Find values of length-related coefficients from inverse line projection for each diagonal.
3. Check if these coefficients satisfy the basic conditions to solve the solution equations.
4. Solve the analytic equations to get the projector parameters
19
1911년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Solution Outline: Geometric Inverse Projection of Convex Quadrilateral
1. Get a diagonal parameterization of a convex quad
2. Find two solution spheres from inverse line projection for each diagonal
3. Find an intersection circle of above two spheres
4. Find a point as center-of-projection where two line projections have the same field-of-view
20
2011년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Configuration
21
ds0s2
l0l2
q
yy
v0v2 m
p
ms
2111년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Configuration• External Param:
- center-of-projection:
- projection direction:
21
pms − p
ds0s2
l0l2
q
yy
v0v2 m
p
ms
2111년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Configuration• External Param:
- center-of-projection:
- projection direction:
• Internal Param
- filed-of-view:
21
ψ
pms − p
ds0s2
l0l2
q
yy
v0v2 m
p
ms
2111년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Configuration• External Param:
- center-of-projection:
- projection direction:
• Internal Param
- filed-of-view:
• Imaginary Source Line
21
ψ
pms − p
ds0s2
l0l2
q
yy
v0v2 m
p
ms
2111년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Configuration• External Param:
- center-of-projection:
- projection direction:
• Internal Param
- filed-of-view:
• Imaginary Source Line
• Projected Line Image
- Projected mid-point:
21
ψ
pms − p
md
s0s2
l0l2
q
yy
v0v2 m
p
ms
2111년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Inverse Projection• Input
- A projected line with a projected mid-point
• Output
- Ext param:
• center-of-projection:
- Int param:
• filed-of-view:
22
p = (d,θ )
ψd
s0s2
l0l2
q
yy
v0v2 m
p
ms
2211년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Analytic Solution• Ext Param:
• Int Param:
• Coefficients:
23
cosθ =dl2 − l02 l0l2
=dα
tanψ =l2 − l0l0 + l2
tanθ
=1βtanθ
α and β
ds0s2
l0l2
q
yy
v0v2 m
p
ms
2311년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Coefficients• Coefficients defined by the given configuration:
24
α =l2 − l02l0l2
β =
l0 + l2l2 − l0
γ =αβ =l0 + l22l0l2
ds0s2
l0l2
q
yy
v0v2 m
p
ms
2411년 8월 28일 일요일
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• Observation in 2D
Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Geometric Meaning
25
pc#d ,θ&=d #cosθ ,sinθ&=1αcosθ #cosθ ,sinθ&
cl0l2 v0v2 m l0l2 v0v2 m
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• Solution Space in 2D
Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Geometric Meaning
26
cl0l2 v0v2 m
2611년 8월 28일 일요일
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• Solution Space in 2D
Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Geometric Meaning
26
A circle of radius 1
2α with the center at
1
2α,0
⎛
⎝⎜⎞
⎠⎟
cl0l2 v0v2 m
2611년 8월 28일 일요일
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• Solution Space in 3D
Joo-Haeng Lee (joohaeng at etri.re.kr)
Line: Geometric Meaning
27
A sphere S of radius 1
2α with the center at
l2
l2− l
0
#v0−m&
2711년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Configuration
28
m
pc
v0
v1
v2
v3
Qs
ms
2811년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Configuration
• Ext Params
- center of projection
• Int Params
- filed-of-view
• Source Quad
- rectangle (cf) aspect ratio
• Projected Quad
- convex quadrilateral
• Length-related coefficients:28
m
pc
v0
v1
v2
v3
Qs
ms
2811년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Configuration
• Ext Params
- center of projection
• Int Params
- filed-of-view
• Source Quad
- rectangle (cf) aspect ratio
• Projected Quad
- convex quadrilateral
• Length-related coefficients:28
m
pc
v0
v1
v2
v3
Qs
ms
α i ,βi and γ i for each diagonal
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Diagonal Parameterization
• Transformation of a quad to a canonical form which is defined with simple shape parameters related to diagonals:
29
(d2 , ρ, t1, t 2 )
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Configuration
• 1st diagonal
- Ext Params
• cop:
- Int Params
• filed-of-view:
- Source
• a line segment
- Projected Line
• the 1st diagonal
- Coefficient:30
α0 and β0
m
pc
v0
v1
v2
v3q0
y0
y0
ψ 0
p0 = (d0 ,θ0 )
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Configuration
• 2nd diagonal
- Ext Params
• cop:
- Int Params
• filed-of-view:
- Source
• a line segment
- Projected Line
• the 2nd diagonal
- Coefficient:31
α1 and β1
ψ 1
p1 = (d1,θ1)
m
pc
v0
v1
v2
v3
q1
y1
y1
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
• Input
- a convex quadrilateral
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
• Input
- a convex quadrilateral
• Output
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
3211년 8월 28일 일요일
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
• Input
- a convex quadrilateral
• Output
- Ext param
• center-of-projection (cop)
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
• Input
- a convex quadrilateral
• Output
- Ext param
• center-of-projection (cop)
- Int param
• filed-of-view (fov)m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
• Input
- a convex quadrilateral
• Output
- Ext param
• center-of-projection (cop)
- Int param
• filed-of-view (fov)
• Constraints
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
• Input
- a convex quadrilateral
• Output
- Ext param
• center-of-projection (cop)
- Int param
• filed-of-view (fov)
• Constraints
- same cop:
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
d0 = d1
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Inverse Projection
32
• Input
- a convex quadrilateral
• Output
- Ext param
• center-of-projection (cop)
- Int param
• filed-of-view (fov)
• Constraints
- same cop:
- same fov:
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
ψ 0 =ψ 1
d0 = d1
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Analytic Solution
33
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
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• Constraint 1: cop
d0 =cosθ0α0
=cosθ1α1
=d1
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Analytic Solution
33
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
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• Constraint 1: cop
• Constraint 2: fov
d0 =cosθ0α0
=cosθ1α1
=d1
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Analytic Solution
33
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
tanψ 0 =tanθ0β0
=tanθ1β1
= tanψ 1
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• Constraint 1: cop
• Constraint 2: fov
• 2 Eqs and 2 Unknowns
d0 =cosθ0α0
=cosθ1α1
=d1
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Analytic Solution
33
m
pc
v0
v1
v2
v3q0
q1
y0
y0y1
y1Qs
ms
tanψ 0 =tanθ0β0
=tanθ1β1
= tanψ 1
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• Constraint 1: cop
• Constraint 2: fov
• 2 Eqs and 2 Unknowns
- Existence of solution?
- Geometric meaning?
d0 =cosθ0α0
=cosθ1α1
=d1
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Analytic Solution
34
tanψ 0 =tanθ0β0
=tanθ1β1
= tanψ 1
cosθ0 = ±C 2 −1
A B 2 −1
A =α1α0
B =β1β0
C =γ 1γ 0
Coefficients
Equation
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Analytic Solution
35
A2 ≥1, B 2 ≤1,C 2 ≤1OR
A2 ≤1, B 2 ≥1,C 2 ≥1
cosθ0 = ±C 2 −1
A B 2 −1
A =α1α0
B =β1β0
C =γ 1γ 0
Coefficients
EquationCoefficientConditions
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric MeaningSteps
1. Get a diagonal parameterization of a convex quad
2. Find two solution spheres from inverse line projection for each diagonal
3. Find an intersection circle of above two spheres
4. Find a point as center-of-projection where two line projections have the same field-of-view
36
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric MeaningStep 1. Get a diagonal parameterization of a convex quad
37
m
pc
v0
v1
v2
v3q0
y0
y0
m
pc
v0
v1
v2
v3
q1
y1
y1
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric MeaningStep 2. Find two solution spheres for each diagonal
38
m
pc
v0
v1
v2
v3
S0
m
pc
v0
v1
v2
v3 S1
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Step 3. Find an intersection of two solution spheres
m
pc
v0
v1
v2
v3
S0
S1
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric Meaning
39
m
pc
v0
v1
v2
v3
S0
S1m
pc
v0
v1
v2
v3
S0
S1
copconstraint
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Step 3. Find an intersection of two solution spheres
m
pc
v0
v1
v2
v3
S0
S1
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric Meaning
39
copconstraint
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Step 3. Find an intersection of two solution spheres
m
pc
v0
v1
v2
v3
S0
S1
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric Meaning
40
copconstraint
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Step 4. Find a center-of-projection where two line projections have the same field-of-view:
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric Meaning
41
pcHf,yL
0.0 0.5 1.0 1.5 2.0 2.5 3.0f
0.2
0.4
0.6
0.8
1.0
1.2
1.4
yif and y
m
pc
v0
v1
v2
v3
m
pc
v0
v1
v2
v3
fov constraint
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Step 4. Find a center-of-projection where two line projections have the same field-of-view:
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric Meaning
42
pcHf,yL
0.0 0.5 1.0 1.5 2.0 2.5 3.0f
0.2
0.4
0.6
0.8
1.0
1.2
1.4
yif and y
m
pc
v0
v1
v2
v3
ψ 0 =ψ 1
fov constraint
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m
pc
v0
v1
v2
v3
pcHf,yL
0.0 0.5 1.0 1.5 2.0 2.5 3.0f
0.2
0.4
0.6
0.8
1.0
1.2
1.4
yif and y
Different field-of-views:
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quad: Geometric Meaning
43
ψ 0 ≠ ψ 1
fov constraintis not satisfied!
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Type of Quads
44
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TypesDiag Param
Projectability Remarks
square always
rectangle always
rhombus never no int. param
parallelogram never no int. param
kite conditionally remark 1
iso. trapezoid always
trapezoid never no ext. param
quad conditionally remark 2
(d2 , ρ, t1, t 2 )
(1, ρ, 0.5, 0.5)
(1, π / 2, 0.5, 0.5)
(d2 , π / 2, 0.5, 0.5)
(d2 , ρ, 0.5, 0.5)
(d2 , π / 2, t1, 0.5)
(1, π / 2, t1, t1)
(d2 , π / 2, t1, t1)
(d2 , ρ, t1, t 2 )
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Kite
46
m
pc
v0
v1
v2
v3
pcHf,yL
0.0 0.5 1.0 1.5 2.0 2.5 3.0f
0.2
0.4
0.6
0.8
1.0
1.2
1.4
yif and y
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0.0 0.5 1.0 1.5 2.0 2.5 3.0f
0.2
0.4
0.6
0.8
1.0
1.2
1.4
yif and y
Joo-Haeng Lee (joohaeng at etri.re.kr)
Kite
47
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0.0 0.5 1.0 1.5 2.0 2.5 3.0f
0.2
0.4
0.6
0.8
1.0
1.2
1.4
yif and y
Joo-Haeng Lee (joohaeng at etri.re.kr)
Isosceles Trapezoid
48
m
pc
v0
v1
v2v3
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m
pc
v0
v1v2
v3pcHf,yL
0.0 0.5 1.0 1.5 2.0 2.5 3.0f
0.2
0.4
0.6
0.8
1.0
1.2
1.4
yif and y
Joo-Haeng Lee (joohaeng at etri.re.kr)
General Quad
49
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(a) (b)
(c) (d)
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #2
50
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(a) (b)
(c) (d)
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #2
51
(1.3, π / 2, 0.75, 0.3) (1.3, π / 2, 0.6, 0.2)
(1.3, 0.7, 0.6, 0.2) (1.3, π / 2, 0.6, 0.3)
Diagonal Parameters: (d2 , ρ, t1, t 2 )
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(a) (b)
(c) (d)
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #2
52
Diagonal Parameters:
(1.3, π / 2, 0.75, 0.3) (1.3, π / 2, 0.6, 0.2)
(1.3, 0.7, 0.6, 0.2) (1.3, π / 2, 0.6, 0.3)
Solution Coefficients: !A2 , B 2 ,C 2 '(d2 , ρ, t1, t 2 )
(0.3, 1.5, 0.4) (12.0, 0.11, 1.33)
(12.0, 0.11, 1.33)
(12.0, 0.11, 1.33)
(3.1, 0.3, 0.8)
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(a) (b)
(c) (d)
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #2
53
Diagonal Parameters:
(1.3, π / 2, 0.75, 0.3) (1.3, π / 2, 0.6, 0.2)
(1.3, 0.7, 0.6, 0.2) (1.3, π / 2, 0.6, 0.3)
Solution Coefficients:
A2 ≥1, B 2 ≤1,C 2 ≤1OR
A2 ≤1, B 2 ≥1,C 2 ≥1 !A2 , B 2 ,C 2 '(d2 , ρ, t1, t 2 )
(0.3, 1.5, 0.4) (12.0, 0.11, 1.33)
(12.0, 0.11, 1.33)
(12.0, 0.11, 1.33)
(3.1, 0.3, 0.8)
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(a) (b)
(c) (d)
Joo-Haeng Lee (joohaeng at etri.re.kr)
Quiz #2
54
Diagonal Parameters:
(1.3, π / 2, 0.75, 0.3) (1.3, π / 2, 0.6, 0.2)
(1.3, 0.7, 0.6, 0.2) (1.3, π / 2, 0.6, 0.3)
Solution Coefficients:
A2 ≥1, B 2 ≤1,C 2 ≤1OR
A2 ≤1, B 2 ≥1,C 2 ≥1 !A2 , B 2 ,C 2 '(d2 , ρ, t1, t 2 )
(0.3, 1.5, 0.4) (12.0, 0.11, 1.33)
(12.0, 0.11, 1.33)
(12.0, 0.11, 1.33)
(3.1, 0.3, 0.8)
Projectable
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Summary
• Geometric Projectability of a Convex Quad
- Given an arbitrary convex quadrilateral, we can find projector parameters analytically with a geometric interpretation.
• Future Works
- How to modify an un-projectable quad to be projectable? Note that a projectable bounding quad is important in RSAR application
- Can it be applied to a triangle or other polygons?
- Comparison with PnP (perspective-n-point) problem in computer vision
55
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Joo-Haeng Lee (joohaeng at etri.re.kr)
Q & A
Contact:
Joo-Haneg Lee
joohaeng at gmail dot com
56
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Thank You!
5711년 8월 28일 일요일