2009. 3. 25 (Wed)

Young Ki Baik

Computer Vision Lab.

References

Inverse Depth parameterization for Monocular SLAM J. Civera, A. J. Davison, J. M. M. Montiel (IEEE Trans. On Robotics 2008)

Inverse Depth to Depth Convsrsion for Monocualr SLAM J. Civera, A. J. Davison, J. M. M. Montiel (ICRA 2007)

Unified Inverse Depth Parameterization for Monocular SLAM J. M. M. Montiel, J. Civera, A. J. Davison (RSS 2006)

Computer Vision Lab.

Outline

What is SLAM? What is Visual SLAM? Overall process of SLAM An issue of the Map Inverse depth parameterization Conclusion

Computer Vision Lab.

What is SLAM?

SLAM : Simultaneous Localization and Mapping is a technique used by robots and autonomous vehicles to build up

a map within an unknown environment while at the same time keeping track of their current position.

Where am I ?

Map building

Observation

Computer Vision Lab.

What is SLAM?

SLAM : Simultaneous Localization and Mapping basically uses some statistical techniques based on recursive basically uses some statistical techniques based on recursive

Bayesian estimation such as Bayesian estimation such as Kalman filters Kalman filters and and particle filters particle filters (aka. Monte Carlo methods).(aka. Monte Carlo methods).

^$#!@&%?^$#!@&%?Computer Vision Lab.

What is Visual SLAM?

SLAM : Simultaneous Localization and Mapping can use many different types of sensor to acquire observation

data used in building the map such as laser rangefinders, sonar sensors and cameras.

Visual SLAM - is to use cameras as a sensor.

Computer Vision Lab.

Why Visual SLAM? Vision data can inform us more meaningful

information (such as color, texture, shape…) relative to other sensors.

Computer Vision Lab.

Overall process of Visual SLAM

Mapmanagement

Measurement

InitializationPrediction

Update

Computer Vision Lab.

Visual SLAM

DEMOMono-slam

Computer Vision Lab.

Problems

Proposal Data association Filter Map management Real-time

Computer Vision Lab.

What is the map of visual SLAM?

Map (Landmarks:LM)

Li = (yi, Yi)T + Patch

y : 3D position of LM

Y : 3x3 covariance matrix of LM

Robot (or Camera)

r : 3D position

C = (r, q)T

q : 3D orientation

Computer Vision Lab.

Robot and maps

What is the map of visual SLAM?

Computer Vision Lab.

C6D = (r, q)T

L2 = (y2, Y2)T

L1 = (y1, Y1)T

Binocular camera case 3D landmarks are directly reconstructed from stereo

images since binocular camera retains parallax.

How can we obtain initial LM info.?

Computer Vision Lab.

C6D = (r, q)T

L = (y, Y)T Parallax : The measured angle between the captured rays from different view points

Monocular camera case Is it possible that 3D landmarks are directly reconstructed

by monocular camera?

How can we obtain initial LM info.?

Computer Vision Lab.

C6D = (r, q)T

L = (y, Y)T

??

How can we obtain initial LM info.?

Delayed Initialization of LM location A batch update [Dean 2000, Bailey 2003]

Computer Vision Lab.

- Large base line will assure high parallax !!!- We can’t always expect large base line !!! → Problem is distance from camera to LM.

How can we obtain initial LM info.?

Delayed Initialization of LM location Gaussian Sum Filter [Kwok 2005, Sola 2005]

Computer Vision Lab.

- Initializing predefined multiple hypothesis at various depths !!!

-Pruning those not re-observed in subsequent images !!! → It can cover the predefined depth only. → can not cover the distant depth. → can not cover low parallax cases.

How can we obtain initial LM info.?

Undelayed Initialization of LM Inverse Depth Parameterization [Montiel 2006~2008]

Computer Vision Lab.

- Initializing a ray !!!

- Updating uncertainty by inverse depth coding !!! → It can cover the infinity depth.

How can we obtain initial LM info.?

Undelayed Initialization of LM Inverse Depth Parameterization [Montiel 2006~2008]

• Contribution

Computer Vision Lab.

* Initializing LM immidiately !!!

* Covering the infinity depth of LM !!!

* Covering the Low parallax case !!!

Inverse Depth Parameterization

Overview

Computer Vision Lab.

W rwc C6D = (rwc, qwc)T

C

LXYZ = (X, Y, Z)T = (x,y,z)T + 1/ρ*m(θ,ф)

(x,y,z)T m

1/ρ = dα

Inverse Depth Parameterization

Definition (Point parameterization)X-Y-Z Point Parameterization

Inverse Depth Point Parameterization

Computer Vision Lab.

LIDP = (x, y, z, θ, ф, ρ)T

LXYZ = (X, Y, Z)T = (x,y,z)T + 1/ρ*m(θ, ф)m( cosфsinθ, -sinф, cosфsinθ)

Inverse Depth Parameterization

Definition (Measurement Equation)X-Y-Z system

Inverse Depth system

Computer Vision Lab.

LXYZ = (X, Y, Z)T = (x, y, z)T + 1/ρ*m(θ, ф)

hC = hXYZ = Rcw [ (X, Y, Z)T – rwc]

hC = hρ = Rcw [ρ((x, y, z)T – rwc) + m(θ, ф)]

It can be safely used even for points at infinity (ρ=0) !!!

(u, v)T = (u0 – fx hxC / hz

C , v0 - fy hyC / hz

C )

Inverse Depth Parameterization

Initialization of LM using IDP

Computer Vision Lab.

LIDP = (x, y, z, θ, ф, ρ)T

C = (r, q)T LIDP = (r, θ, ф, ρ)T

Inverse Depth Parameterization

Initialization of LM using IDP

Computer Vision Lab.

LIDP = (x, y, z, θ, ф, ρ)T

LIDP = (r, θ, ф, ρ)T

(u’, v’, 1)T

C = (r, q)T Hw = Rwc(u’, v’, 1)T

θ = arctan (hxw, hz

w)T

ф = arctan (-hyw, sqrt(hx

w ^2+hzw^2) )T

ρ = 0.1 (or arbitrary constant value)

Inverse Depth Parameterization

Initialization of LM using IDP Updating state covariance matrix

Computer Vision Lab.

State covariance

Measurement covariance

Inverse depth variance

Inverse Depth Parameterization

Switching from Inverse depth to XYZ

Computer Vision Lab.

LIDP

PIDP

LXYZ

PXYZ

L = (X, Y, Z)T = (x,y,z)T + 1/ρ*m(θ,ф)

Inverse Depth Parameterization

Demo Monocular SLAM based on EKF

Computer Vision Lab.

Inverse Depth Parameterization

Demo Monocular SLAM based on PF with OIF

Computer Vision Lab.

Conclusion

Pros. IDP is robust for monocular SLAM.

• Non-delayed LM initialization• Processing for any point in the scene, close or distant, or

even at “infinity”• Dealing simultaneously with low and high parallax case

Cons. IDP requires 6-D state vector → This doubles the map state vector size

Computer Vision Lab.

Q & A

Computer Vision Lab.