cheirality invariant young ki baik computer vision lab
TRANSCRIPT
![Page 1: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/1.jpg)
Cheirality InvariantCheirality Invariant
Young Ki Baik
Computer Vision Lab.
![Page 2: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/2.jpg)
ContentsContents
Introduce Cheirality Quasi-affine reconstruction
Cheirality invariant property 2D / 3D case
Cheiral inequalities Algorithm Conclusion and Future work
![Page 3: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/3.jpg)
IntroduceIntroduce Convex, Convex hull
A subset B of R is called convex if the line segment joining any two points in B also lies entirely within B.
Convex hull of B is the smallest convex set containing B.
R
BA
C
Convex hull
Convex
![Page 4: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/4.jpg)
IntroduceIntroduce
What is Cheirality? Phenomenon of breaking the Convex property by
transformation.
H
![Page 5: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/5.jpg)
IntroduceIntroduce
Why cheirality is occurred? Plane at infinity segments convex by H.
Hπ
![Page 6: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/6.jpg)
IntroduceIntroduce
Quasi-affine transformation
Euclidean
Similarity
Affine
Projective
Euclidean
Similarity
Affine
Projective
Quasi-affine
![Page 7: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/7.jpg)
IntroduceIntroduce
Quasi-affine transformation
R t 0 1λR t 0
1
KR t
L
KR t 0 1
λ
K
L
Euclidean
Similarity
Affine
Quasi-affine
Projective
![Page 8: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/8.jpg)
IntroduceIntroduce
Quasi-affine transformation
Quasi-affine
Projective
L
L
KR t
L
![Page 9: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/9.jpg)
IntroduceIntroduce
Quasi-affine reconstruction (QUARC) We have to perform QUARC before Metric
reconstruction.
Quasi-affine
Metric
![Page 10: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/10.jpg)
IntroduceIntroduce
Quasi-affine reconstruction (QUARC) Search for safe region and transform plane at
infinity.
Quasi-affine
LL’
L’
I 0 L’
![Page 11: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/11.jpg)
Cheirality invariant propertyCheirality invariant property
2D case Suppose that {xi} and {yi} are corresponding
points in two view and h representing a planar projectivity such that h( xi ) = wi yi .
To ensure convex hull, all wi have the same sign.
h (L) = L∞
h (B) ∩ L∞ = 0
![Page 12: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/12.jpg)
Cheirality invariant propertyCheirality invariant property
2D case To ensure convex hull, all wi have the same sign.
x∞ = [ a, b, c, 0 ]T
L
x = [ a, b, c, +w ]T x = [ a, b, c, -w ]T
![Page 13: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/13.jpg)
Cheirality invariant propertyCheirality invariant property
3D case ( Depth of points )
3d point
2d point
Camera center
3
det );(
m
MPX
T
wsigndepth
C
X
3m
3mX
]|[ 4pMP
X ofcomponent Last :T
x
xPX w
![Page 14: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/14.jpg)
Cheirality invariant propertyCheirality invariant property
3D case ( Sign of depth ) Positive
Negative
Zero or infinite
,0);( PXdepth
3d point
2d point
Camera center
CX
0);( PXdepth
X
X
L
C
CX
0);( PXdepth
3)0(
det );(
m
MPX
T
wsigndepth
![Page 15: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/15.jpg)
Cheirality invariant propertyCheirality invariant property
3D case ( Sign of depth ) We only concern with the sign of depth.
3
det );(
m
MPX
T
wsignsigndepthsign
]|[ 4pMP
X ofcomponent Last :T
xPX w Mdet wTsign
![Page 16: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/16.jpg)
Cheirality invariant propertyCheirality invariant property
3D case ( Sign of depth with transformation )
MPX det);( wTsigndepthsign
]1 0, 0, 0,[TE CEXE TTwsign TT XE
4det CM
![Page 17: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/17.jpg)
Cheirality invariant propertyCheirality invariant property
3D case ( Sign of depth with transformation )
CEXEPX TTwsigndepthsign );(
1);( PH
1 CEHXEPHHX TTwsigndepthsign
1det);( HHCEHXEPHHX P1 TTwsigndepthsign
![Page 18: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/18.jpg)
Cheirality invariant propertyCheirality invariant property
3D case ( Sign of depth with transformation )
1det);( HHCEHXEPHHX P1 TTwsigndepthsign
PCπXπ TTwsign
]1 0, 0, 0,[TETTπHE
Hdetsign
![Page 19: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/19.jpg)
Cheiral inequalitiesCheiral inequalities
Solving the cheiral inequalities
0);( PCvXvPX TTwsigndepthsign
0);( PCvXvPX TTsigndepthsign
j
ijT
Ti
allfor 0
allfor 0
vC
vX
suppose that w > 0
![Page 20: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/20.jpg)
Cheiral inequalitiesCheiral inequalities
Solving the cheiral inequalities We can solve inequalities using linear programming
(such as the simplex method).
We can perform QUARC using v.
j
ijT
Ti
allfor 0
allfor 0
vC
vX
Quasi-affine
I 0 vT
![Page 21: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/21.jpg)
AlgorithmAlgorithm
Summary of algorithm Obtain set ( X, P ) For each pair, search w from PX = wx Replace sign of P or X to ensure that each w > 0 Form the cheiral inequalities : For each of value δ = ±1, choose a solution with
maximum d (Av > d >0) using linear programming (Simplex method)
Define H having last row equal to v and sign of det(H) = δ
Implement QUARC using H
0 , 0 vCvX jTTi
![Page 22: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/22.jpg)
Conclusion and Future workConclusion and Future work
Conclusion QUARC using cheiral inequalities Untwisted 3D object reconstruction with QUARC
Future work Linear programming problem (Simplex method) Implementation of QUARC algorithm
![Page 23: Cheirality Invariant Young Ki Baik Computer Vision Lab](https://reader034.vdocuments.mx/reader034/viewer/2022051820/5697bf791a28abf838c827f9/html5/thumbnails/23.jpg)
The End