**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