RANSAC

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RANSAC
David Nistér
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Outline

• Fruits of RANSAC (camera tracking)
• Hypothesis Generation (minimal cases)
• Preemptive RANSAC
• Millisecond RANSAC
• Hough vs RANSAC, RUDR
• RANSAC as an extended search technique

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Fruits of RANSAC
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Visual Odometrywork with Oleg Naroditsky and Jim
Bergen

• 365 m without loss of tracking
• 350 m ( 3.5 minutes) without GPS
• Error in distance traveled 1
• Accumulated error in position 3-5
• e.g. 10m over 350m

North
East
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Visual Odometrywork with Oleg Naroditsky and Jim
Bergen
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Visual Odometrywork with Oleg Naroditsky and Jim
Bergen
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RANSAC as Object-Oriented Programming
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Estimate or posterior likelihood output
Hypothesis Generator
Probabilistic Formulation
Precise Formulation
Data Input
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(No Transcript)
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Geometry Tools
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Hypothesis Generation
The 5-Point Relative Pose Problem
Unknown Focal Relative Pose
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15
2048
The Generalized 3-Point Problem
Microphone-Speaker Relative Orientation
8(4)
The 3 View 4-Point Problem
0 (or thousands)
8-38-150-344-??
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Relative Orientation
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2 Views
3 Views
6p Quan, 1994
8p von Sanden, 1908 Longuet-Higgins, 1981
4p Nister, Schaffalitzky, 2004
7p R. Sturm, 1869
5p Nister, 2003
6p Philip, 1996
5p Kruppa 1913 Nister 2003
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The Five Point Problem
Given five point correspondences,
What is R,t ?
E. Kruppa, Zur Ermittlung eines Objektes aus zwei
Perspektiven mit Innerer Orientierung, 1913.
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The 5-point algorithm (Nistér CVPR 03)
E
R,t
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The 5-point algorithm (Nistér PAMI 04)
R,t
E
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The 5-point algorithm (Stewénius et al)
10 x 10 Action Matrix
Eigen-Decomposition
R,t
E
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The Generalized 3-Point Problem
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The Generalized 3-Point Problem
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The 3-View 4-Point Problem, Nister,
Schaffalitzky, 2004
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The 3-View 4-Point Problem, Nister,
Schaffalitzky, 2004
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Line Hypotheses
Points
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RANSAC
?
Hypotheses
500
Observations
1000
500 x 1000 500.000
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Preemptive RANSAC
Depth-first Preemption
Hypotheses
500
Observations
1000
500 x ???? ???????
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Preemptive RANSAC
Breadth-first Preemption
Hypotheses
500
Chunksize
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Observations
1000
500 x 200 100.000
Overhead 100 microseconds
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Preemptive RANSAC
Observed Tracks
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Preemptive RANSAC
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Preemptive RANSAC
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ms RANSAC (for Recognition)

• Rotation

• Viewpoint Change

• Lighting Variation

• Scale Change

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(No Transcript)
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(Generalized) Hough vs RANSAC

• Minimal or sub-minimal hypothesis generation
  (both, although sub-minimal for classical Hough)

Sub-Minimal
Minimal
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(Generalized) Hough vs RANSAC

• Comparing hypotheses to hypotheses (Hough), or
  hypotheses to data (RANSAC)

Hypotheses to Hypotheses
Hypotheses to Data
Fit?
?
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RUDR (Olson, 1998)

• Hypothesis generation is sub-minimal by one,
  followed by all possible final points
• Scoring is hypothesis-hypothesis

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Comment on the Standard Stopping Criterion
Remember that it works only with

• Strong geometry and
• No degeneracies

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Uncertainty in Epipolar Geometry work with Chris
Engels
Single Estimate often ill posed
Representation of posterior likelihood well
posed, but computationally challenging
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Uncertainty in Epipolar Geometry work with Chris
Engels
Single Estimate often ill posed
Representation of posterior likelihood well
posed, but computationally challenging
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Epipoloscope
Calibrated
Uncalibrated