bilateral filter and applications · c. tomasi, r. manduchi, "bilateral filtering for gray and...
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Survey: Bilateral Filter and Applications
Presented by Jiangjian Xiao
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Related Papers
C. Tomasi, R. Manduchi, "Bilateral filtering for gray and color images", ICCV 1998.D. Comaniciu, P. Meer, "Mean Shift: A Robust Approach toward Feature Space Analysis", PAMI, 2002.F. Durand, J. Dorsey, "Fast Bilateral Filtering for the Display of High-Dynamic-Range Images", SIGGRAPH 2002.S. Fleishman, I. Drori, D. Cohen-Or, "Bilateral Mesh Denoising", SIGGRAPH 2003.T. Jones, F. Durand, M. Desbrun. "Non-Iterative, Feature-Preserving Mesh Smoothing", SIGGRAPH 2003.
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Gaussian Filter
Normal distribution
dtet 2
21
−∞
∞−∫=Φ σ
σπ
Gaussian kernal filter
dtetXYt 2
21)()(
−
−+
−∫=σµ
τµ
τµ σπµ
The filter’s width is 2τ, and center is at µ, bandwidth is σ.
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Bilateral Filter
For image I(u), at coordinate u=(x,y):
Two Gaussian filters:
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Bilateral Filter: 2D spatial +1D range
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Example: 1D spatial +1D range
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Example: 2D spatial +1D range
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Example: 2D spatial +1D range
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Early Mean-Shift (ICCV1997)
Kernel smooth on Probability Density Function (PDF).The feature space only includes color information (range data).
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Range Data (Multiple Colors)
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Recent Mean-Shift
xi is a multiple dimension (2+p) vector including 2D spatial and pD range feature.The mean of an initial vector y0 shift from y0 to yj if it is convergent.
∑
∑
=
=
+
−
−
=n
iij
n
iij
i
j
hxy
g
hxy
gx
y
1
2
1
2
1
=
22
2, )(r
r
s
s
prs
hh hxg
hxg
hhCxg
rs
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Algorithm of Mean-Shift
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2D Spatial +1D Range (Gray)
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My Results
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Comparison
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My Results
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3D Application
Using distance to tangent plane as range information.The normal of the tangent plane is mollified (smoothed).
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Result of Jones et al.
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Algorithm by Fleishman et al.
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Results Comparison
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Conclusion
An very efficient approach for smoothing.May be similar to human eyes response procedure.Can be easily to extend to many areas.