1. Visual feature selection for GP-based
localization using an omnidirectional camera
Huan N. Do, Jongeun Choi, and Chae Young Lim
American Control Conference, 1-3 July, 2015, Chicago, USA 1

2. Introduction
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Visual
features
𝑌
Locations
𝑋
𝐹 𝑋 = 𝑌
Problem: Given the learning data set {𝑋, 𝑌}, the
problem is to find the optimal subset of features
𝑌∗ that maximize the localization performance.

3. Introduction
Feature Selection
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𝑌∗ = 𝑎𝑟𝑔𝑚𝑖𝑛 𝑋 − 𝐹−1 𝑌
2
, 𝑌 ⊂ 𝑌
𝑌
𝑌 = 𝐹(𝑋)
𝑌∗ = 𝑎𝑟𝑔𝑚𝑖𝑛 𝑌 − 𝐹 𝑋
2
, 𝑌 ⊂ 𝑌
𝑌
1. H.N. Do, J. Choi, C. Lim, and T. Maiti, “Appearance-based localization using
Group LASSO regression with an indoor experiment,” Proceedings of
International Conference on Advanced Intelligent Mechatronic, 2015.
1. H. N. Do, M. Jadaliha, J. Choi, and C. Y. Lim, “Feature selection
for position estimation using an omnidirectional camera,” Image and
Vision Computing, 2015.

4. Timeline
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Features
extraction
GP
models
Features
selection
Localization

5. Visual features extraction
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Raw
image
Histogram
Fast
Fourier
Transform
Steerable
Pyramid

6. Visual features extraction
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Fast Fourier Transform Steerable Pyramid Histogram
SpatialdomainFrequencydomain
(4 orientations)x(3 scales)

7. Gaussian process (GP) model
7
𝑓1 𝑓2 𝑓∗
𝑦𝜌 = 𝑓 𝒙 + 𝜖
𝒙1
!
?
Known
Unknown
𝑦 𝜌,1
𝒙2
𝒚 𝝆,∗ ∼ 𝑁(𝜇 𝜌 𝑥∗ , 𝜎𝜌
2(𝑥∗))𝑦 𝜌,2
𝒙∗MLE
Visual feature 𝜌
Gaussian fields
Locations
x Algorithm
TRAIN TEST

8. Gaussian process (GP) model
Example of realization of one visual feature in the training phase
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…
t=1 t=2 t=N

9. Features selection
Backward sequential elimination
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Ω0 = 𝐺𝑃1, 𝐺𝑃2, … , 𝐺𝑃 𝑁 , Ω ⊂ Ω0
Ω0 Ω
Ω{GP1}
Ω{GPN}
…
MLE 𝑅𝑀𝑆𝐸1
MLE 𝑅𝑀𝑆𝐸 𝑁
𝐸𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑒
𝐺𝑃𝑖 = 𝑎𝑟𝑔𝑚𝑖𝑛{𝑅𝑀𝑆𝐸𝑖}
𝐺𝑃
…
…

10. Localization
Maximum Likelihood Estimator
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𝑥∗ = 𝑎𝑟𝑔𝑚𝑎𝑥 𝐿 𝜌(𝑥∗)
𝜌∈Ω
𝑥∗
𝐿 𝜌 𝑥∗ = −
1
2
|𝑦∗ − 𝜇 𝜌 𝑥∗ |2
𝜎 𝑜𝑏𝑠,𝜌
2
+ 𝜎𝜌
2
(𝑥∗)
+ log 𝜎 𝑜𝑏𝑠,𝜌
2
+ 𝜎𝜌
2
𝑥∗ + 𝑙𝑜𝑔2𝜋

11. Localization
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12. Experiment results
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13. Computation Time
(in seconds)
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Procedure FFT HIST SP
Learning GP fields 1057 1221 583
Backward Elimination 348 523 111
Localization 0.0362 0.0457 0.717

14. Localization result
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15. Conclusion
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Test Image
Visual Features
GP models
FFT
HIST
SP
…
Feature
Selection
Selected GP
models
Maximum Likelihood
Estimator
Estimated
locations
Train Images

16. 16
THANK YOU!