Gaussian KD-Tree for Fast High-Dimensional Filtering A. Adams,
N. Gelfand, J. Dolson, and M. Levoy, Stanford University, SIGGRAPH
2009.
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Edge-Preserving Filtering Noise Suppression Detail Enhancement
High Dynamic Range Imaging
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Edge-Preserving Filtering for Image Analysis Input Image Base
ImageDetail Image
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Edge-Preserving Vs. Edge-Blurring Input Image Edge-Preserving
Base ImageEdge-Blurring Base Image
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Edge-Preserving Vs. Edge-Blurring Edge-Preserving Enhanced
ImageEdge-Blurring Enhanced Image Halo Artifacts
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Gaussian Filtering
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Bilateral Filtering Output Input Space WeightRange Weight Space
WeightRange Weight x y Intensity
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Bilateral Filtering Output Input Bilateral Weight Space
WeightRange Weight x y Intensity
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Bilateral Filtering Input ImageGaussian: p = 12 Bilateral: p =
12, c = 0.15
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Computational Complexity of Bilateral Filtering O(n 2 d) Image
Size: n Maximum Filter Size: n Dimension: d High Computational
Complexity Input x y Intensity
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Novel Methods Bilateral Grid J. Chen, S. Paris, and F. Durand,
Real-time edgeaware image processing with the bilateral grid, ACM
Transactions on Graphics (Proc. SIGGRAPH 07). Gaussian KD-Tree A.
Adams, N. Gelfand, J. Dolson, and M. Levoy, Gaussian KD-Trees for
Fast High-Dimensional Filtering, ACM Transactions on Graphics
(Proc. SIGGRAPH 09).
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High-Dimensional Filtering x y Intensity
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A Two-Dimensional Example x I Space Range Signal Kernel x I
Output Signal Kernel Gaussian Filtering x I Space SignalOutput
Signal Bilateral Filtering Large Kernel Size High Computational
Complexity!
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Bilateral Grid Downsampling x I Signal Bilateral Grid x I
Signal Spatial Grid Traditional Spatial Downsampling x I Signal
Bilateral Grid Bilateral Grid Downsampling x I Bilateral Grid
Kernel
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Bilateral Filter on the Bilateral Grid Image scanline space
intensity Bilateral Grid
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space intensity Bilateral Filter on the Bilateral Grid Image
scanline Filtered scanline Slice: query grid with input image
Bilateral Grid Gaussian blur grid values space intensity
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Bilateral Filtering for Color Image Bilateral Filtering Based
on LuminanceBilateral Filtering Based on Color
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Bilateral Grid for Color Image Image High-Dimensional Grid (5d
grid) High Memory Usage Cost
Complexity and Performance Analysis Filter Size Large Small 5D
Grid Gaussian KD-Tree Nave
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Applications Non-local Mean Filtering Input ImageOutput
Image
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Non-local Mean Filtering Target Patch Searching Patches ..
Patch
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Non-local Mean Filtering with PCA Patch Examples 16 Leading
Eigenvectors
http://www.ceremade.dauphine.fr/~peyre/numerical-tour/tours/denoising_nl_means/
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Non-local Mean Filtering Target Patch Searching Patches ..
Patch High-Dimensional Space
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Non-local Mean Filtering with Gaussian KD-Tree Gaussian KD Tree
Inner Node Leaf Node Image Pixel Different Weighting to Leaf Nodes
High-Dimensional Space
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Applications Non-local Mean Filtering Input ImageOutput
Image
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Applications Geometry Filtering Input ModelOutput Model with
Gaussian Filtering Output Model with Non-local Mean