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Mutual Information-based Stereo Matching Combined with SIFT Descriptor in Log-chromaticity Color Space
Yong Seok Heo, Kyoung Mu Lee, and Sang Uk LeeDepartment of EECS, ASRI, Seoul National University, 151-742, Seoul, Korea
IEEE Conference on Computer Vision and Pattern Recognition, 2009.
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Outline• Introduction• System Overview• Mutual Information as a Stereo Correspondence
Measure • Proposed Algorithm • Experiments• Conclusion
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Introduction• Radiometric variations (between two input images)
• Degrade the performance of stereo matching algorithms.
• Mutual Information :• Powerful measure which can find any global
relationship of intensities• Erroneous as regards local radiometric variations
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Introduction• Different camera exposures (global)
• Different light configurations (local) Conventional MI
Conventional MI
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Objective• To present a new method:• Based on mutual information combined with
SIFT descriptor• Superior to the state-of-the art algorithms
(conventional mutual information-based)
Mutual Informatio
nglobal radiometric variations
(camera exposure)
SIFT descriptor
local radiometric variations (light configuration)
+
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Proposed Alogorithm
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Mutual Information (as a Stereo Correspondence Measure)
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Energy Function• Energy Function:
• In MAP-MRF framework
• f: disparity map
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Mutual Information• Used as a data cost:
•Measures the mutual dependence of the two random variables
Disparity Map
Left / RightImage
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Mutual Information
• Entropy:
• Joint Entropy:
• P(i): marginal probability of intensity i
• P(iL,iR): joint probability of intensity iL and iR
Entropy Entropy Joint Entropy
1
0
1
0
1
0
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Mutual InformationSuppose you are reporting the result of rolling a
fair eight-sided die. What is the entropy?
→The probability distribution is f (x) = 1/8, for x =1··8 , Therefore entropy is:
= 8(1/8)log 8 = 3 bits
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Mutual Information
H( IL, IR )
H( IL ) H( IR )
H( IL | IR ) H( IR | IL )MI( IL; IR )
Entropy Entropy Joint Entropy
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Mutual Information
• Entropy:
• Joint Entropy:
• P(i): marginal probability of intensity i
• P(iL,iR): joint probability of intensity iL and iR
Entropy Entropy Joint Entropy
1
0
1
0
1
0
i1 i2
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Pixel-wise Mutual Information• Previous: Mutual Information of whole images• Difficult to use it as a data cost in an energy
minimization framework → Pixel-wise
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Pixel-wise Mutual Information
=
P(.) / P(., .) : marginal / joint probability
G(.) / G(., .) : 1D / 2D Gaussian function
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Left Image Intensity
Right Image Intensity
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Conventional MI• Cannot handle the local radiometric variations
caused by light configuration change
• Collect correspondences in the joint probability assuming that there is a global transformation
• The shape of the corresponding joint probability is very sparse.
• Do not encode spatial information
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Conventional MI• Different camera exposures (global)
• Different light configurations (local)Conventional MI
Conventional MI
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Proposed Algorithm
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Log-chromaticity Color Space• Transform the input color images to log-
chromaticity color space [5]
• To deal with local as well as global radiometric variations
• Used to establish a linear relationship between color values of input images
[5] Y. S. Heo, K.M. Lee, and S. U. Lee. Illumination and camera invariant stereo matching. In Proc. of CVPR, 2008
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SIFT Descriptor• Robust and accurately depicts local gradient
information
• Computed for every pixel in the log-chromaticity color space
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Energy Function• Data Cost:
• Mutual Information:
• SIFT descriptor distance:
( )constant
Log-chromaticity intensity
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Joint Probability Using SIFT DescriptorA joint probability is computed at each channel
by use of the estimated disparity map from the previous iteration.
Wrong disparity can induce an incorrect joint probability.
Incorporate the spatial information in the joint probability computation step
Adopt the SIFT descriptor
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Joint Probability Using SIFT Descriptor
• K-channel SIFT-weighted joint probability:
• : Euclidean distance• VL,K(P) / VR,K(P) : SIFT descriptors for the pixel P• l : SIFT descriptor size
T = 1 If TrueT = 0 If false
i1 i2
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Joint Probability Using SIFT Descriptor• A joint probability is computed at each channel • Use estimated disparity map from the previous
iteration.
• is governed by the constraint that corresponding pixels should have similar gradient structures.
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Energy Function• Data Cost:
• Smooth Cost:
MI SIFT
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Energy Minimization• The total energy is minimized by the Graph-cuts
expansion algorithm[3].
[3] Y. Boykov, O. Veksler, and R. Zabih. Fast approximate energy minimization via graph cuts. IEEE Trans. PAMI, 23(11):1222–1239, 2001.
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Energy Minimization
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Experimental Results• The std. dev σ of the Gaussian function is 10,
τ = 30, l = 4*4*8 = 128
• The window size of the SIFT descriptor : 9X9
• λ = 0.1, μ = 1.1, VMAX=5
• The total running time of our method for most images does not exceed 8 minutes.
• Aloe image (size : 427 X 370 / disparity range : 0-70) is about 6 minutes on a PC with PENTIUM-4 2.4GHz CPU.
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MI vs. SIFT
MI SIFT MI + SIFT
17.6% 11.97 % 9.27 %
26.45% 17.87 % 11.83 %
L: illum(1)-exp(1) / R: illum(3)-exp(1)
MI SIFT MI + SIFT
Error Rate
Error Rate
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L: illum(1)-exp(1) / R: illum(3)-exp(1)
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Different ExposureLeft Image Right Image Ground Truth Proposed
Rank/BT NCC ANCC MI
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Different Light Source ConfigurationsLeft Image Right Image Ground Truth Proposed
111
Rank/BT NCC ANCC MI
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Different ExposureLeft Image Right Image Ground Truth Proposed
111
Rank/BT NCC ANCC MI
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Different Light Source ConfigurationsLeft Image Right Image Ground Truth Proposed
111
Rank/BT NCC ANCC MI
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Different ExposureLeft Image Right Image Ground Truth Proposed
111
Rank/BT NCC ANCC MI
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Different Light Source ConfigurationsLeft Image Right Image Ground Truth Proposed
111
Rank/BT NCC ANCC MI
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Exposure Exposure
Light Configuration Light Configuration
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Exposure Exposure
Light Configuration Light Configuration
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Conclusion• Propose a new stereo matching algorithm
based on :• mutual information (MI) combined with• SIFT descriptor
• Quite robust and accurate to local as well as global radiometric variations