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# 3D RECONSTRUCTION USING MULTIPLE IMAGES

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on 10 February 2016

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#### Transcript of 3D RECONSTRUCTION USING MULTIPLE IMAGES

3D RECONSTRUCTION FROM MULTIPLE IMAGES
INTRODUCTION
3D RECONSTRUCTION USING STRUCTURE FROM MOTION METHOD
3D RECONSTRUCTION USING MULTIPLE IMAGES
3D RECONSTRUCTION
Process of capturing the shape and appearance of the real objects
Human computer interaction
Face Recognition
Animation
Parts Inspection
TYPES OF 3D RECONSTRUCTION
Active method
Passive method
Single Vantage
Point
Multiple Vantage
Point
Single Vantage
Point
Multiple Vantage
Point
ACTIVE METHOD
Light Sources are controlled specially
PASSIVE METHOD
Light sources are not controlled specially
Works in any environment !!
SINGLE VANTAGE POINT
Reconstruction is done based on single view point
MULTIPLE VANTAGE POINT
Reconstruction is done based on multiple view point
SFM
Passive Multiple vantage method
Single Camera can be Used
Can be Used in any environment
Difference Between Calibrated Rigs & sfm
PIPELINE
POINT MATCHING
Using Feature Descriptor
Using Optical Flow
Finding the Fundamental Matrix F and Calibration Matrix K
Finding the Camera Matrices P and P' Using F and K
Triangulating to get the basic Scene Structure
Computing the position of other Cameras Using the Basic Scene Structure & Building the 3D Reconstruction
How is image formed in a camera ??
A ray of light from point in the world passes through the lens of the camera and impinges on a film or digital device producing an image of the point
Central projection
Mapping of 3D projection space to 2D projection plane
Mapping of 3D homogeneous coordinates is represented by 3 x 4 Matrix P (Camera matrix )
x = PX
x' = P'X
3D RECONSTRUCTION FROM TWO IMAGES
THE FUNDAMENTAL MATRIX F
Geometrical Relation between corresponding points of two images
Obtained by mapping epipolar point to line
3 X 3 matrix of Rank 2
Given x and x' the fundamental matrix satisfies the equation

(x')tFX = 0
FINDING THE CAMERA MATRICES P & P'
First camera
Second Camera
The Camera Matrices P and P' are found
For each correspondence x -- > x' , X should be found
We have the relation
x= PX ; x'=P'X
WKT x and x' will intersect at X
Thus X can be found by using
Linear

Triangulation method
Reconstructing 3D point
LINEAR TRIANGULATION METHOD
X = T(x,x',P,P')
The two equations are rewritten to obtain a system of linear equations to solve for X
Assume X = (X,Y,Z,1)t in homogenous coodinates
The inhomogenous equation will be in the form AX = B where we solve for X
3D points from two images
3D points from multiple images
TO FIND THE CAMERA MATRICES
P1',P2',P3',..............
Estimation of calibrated camera's position and orientation by using set of correspondence between observed 3D points and their corresponding 2D projections
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