ransac presentation

7/27/2019 RANSAC Presentation

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Motivation - I

Estimation of model parameters in presence of noise andoutliers is a crucial task in image processing, computervision, patter recognition. . .

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1

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0

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1

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y

x

Inliers

Outliers

Unbiased estimate(RANSAC)

Biased estimate(least squares) Least squares produce

biased estimates in

presence of outliers

Robust statistic can toler-

ate up to 50% outliers

The multiRANSAC Algorithm And Its Application to Detect Planar Homographies p. 2/22


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Motivation - I

Estimation of model parameters in presence of noise andoutliers is a crucial task in image processing, computervision, patter recognition. . .

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1

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y

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Affine model

Outliers

Inliers

RANSAC algorithm

[Fischler 1981]

RANdom SAmple Con-

sensus



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Motivation - II

What happens if there are multiple models?

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(a) (b)(a) Multiple segments, (b) Multiple planes



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Motivation - II

Traditional RANSAC-based approaches:

1. apply standard RANSAC

2. remove the detected set of inliers

3. go back to 1



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Motivation - II




3. go back to 1



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Motivation - II




3. go back to 1



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Motivation - II




3. go back to 1



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Motivation - II




3. go back to 1



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Motivation - II




3. go back to 1



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Motivation - III

Inaccurate inlier detection for the initial (or subsequent) pa-rameter estimation contributes heavily to the instability of theestimates of the parameters for the remaining models.

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Goals

Extend RANSAC to multiRANSAC

Present a theoretical analysis of multiRANSAC

Show its effectiveness on synthetic and real data sets



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Presentation Overview

Description of multiRANSAC algorithm

Experimental Results

Conclusions and Future Work



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From RANSAC to multiRANSAC - I

RANSAC key ideas:Estimate the model parameters using the minimum number of data possible

Check which of the remaining data points fit the model instantiated with the

estimated parameters.

Do this a sufficiently large number of times (more to come. . . )

RANSAC iteration:



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From RANSAC to multiRANSAC - II

multiRANSAC key ideas:At each iteration instantiate

models and find the corresponding CSs

Fuse the new CSs with the previously detected ones in a sensible way.

multiRANSAC iteration:



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From RANSAC to multiRANSAC - II

multiRANSAC key ideas:At each iteration instantiate

models and find the corresponding CSs

Fuse the new CSs with the previously detected ones in a sensible way.

multiRANSAC iteration:


H M It ti ? I


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How Many Iterations? - I

What is the probability that we draw MSSs onlycomposed by inliers?


H M It ti ? I


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It can be shown that:

where:

is the number of models

is the total number of data points

is the number of inliers for the

model

is the cardinality of the MSS for the

model


H M It ti ? II


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How Many Iterations? - II

The probability that MSSs are not entirely composedby inliers is


Ho Man Iterations? II


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The probability that this happens for trials is


How Many Iterations? II


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Goal: make sure that




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Then:




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Then:

Problem: a priori we dont know

!




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Then:

Problem: a priori we dont know

!

Solution: the estimate for is the cardinality oflargest CS found so far.


Fusing the CSs


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Fusing the CSs

Observation: the CSs obtained in current iteration canbe fused with the CSs obtained in the previousiterations to produce better CSs.

More specifically:Better is quantified in terms of a fitness function

Cardinality

MSE

Simplification: just look at the previous iteration

Greedy algorithm


Fusing the CSs


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Fusing the CSs

Observation: the CSs obtained in current iteration canbe fused with the CSs obtained in the previousiterations to produce better CSs.




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Experiments: Detecting Lines - I


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Experiments: Detecting Lines I

Toy problem: Identify the lines containing the segments.

The stair data set

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Wrong estimate


Experiments: Detecting Lines - I


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Experiments: Detecting Lines I

Toy problem: Identify the lines containing the segments.

The stair data set

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Correct estimate


Experiments: Detecting Lines - II


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Experiments: Detecting Lines II

Definitions:Set of correctly detected inliers for the model

:

where

is

the detected set of inliers

Percentage of correctly detected inliers:

is the averaged value of

over 50 trials and

models


Experiments: Detecting Lines - II


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Experiments: Detecting Lines II

Definitions:Set of correctly detected inliers for the model

:

where

is

the detected set of inliers

Percentage of correctly detected inliers:

is the averaged value of

over 50 trials and

models

Noise std multiRANSAC sequential RANSAC

5.5

95.96% 7499 93.80% 2016

6.0

95.22% 7626 86.00% 2049

6.5

90.08% 8194 67.14% 20807.0

90.13% 8699 47.92% 2103

7.5

86.01% 8110 37.29% 2103


Experiments: Detecting Homographies


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,




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p g g ap

, ,

,

multiRANSAC




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p g g p

, ,

,

sequential RANSAC




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p g g p

,




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p g g p

, ,

,

multiRANSAC




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p g g p

, ,

,

sequential RANSAC




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p g g p

,




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, ,

,

multiRANSAC




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, ,

,

sequential RANSAC




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Conclusion & Future Work


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We presented the multiRANSAC algorithm

On average, better performance than sequentialRANSAC

Synthetic data (quantitative results)Real data

Future Work

Quantitative experiments on real imagery

Improved CSs fusion strategy

Can we detect the number of models?

Explore waiting time between updates of the CSs


The End


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Thanks for your attention.

Special thanks to Dr. M. Bober, E. Drelie, D. Fedorov and prof. K. Rose for the helpful

discussion




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Think in terms of ratio of number of favorable to number

of possible




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The chance of drawing only inliers is given by:




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The chance of having the inliers belonging to the

correct model:




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Putting things together we have:




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Putting things together we have:


RANSAC vs. multiRANSAC iterations


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How big is

in a typical problem?

Number of data

Number of models

Cardinality of a MSS

Probability threshold

Total percentage of inliers

Inliers for each class

,


RANSAC vs. multiRANSAC iterations


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How big is

in a typical problem?

0.6 0.65 0.7 0.75 0.8 0.85 0.9

102

104

106

rI

Titer

N=250

W = 4

W = 3

W = 2

W = 1

W = 3

W = 2

W = 1

RANSAC

multiRANSAC

W = 4


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