/
Recursive Bilateral Filtering Recursive Bilateral Filtering

Recursive Bilateral Filtering - PowerPoint Presentation

phoebe-click
phoebe-click . @phoebe-click
Follow
729 views
Uploaded On 2015-10-27

Recursive Bilateral Filtering - PPT Presentation

F01943024 Reference Yang Qingxiong Recursive bilateral filtering  ECCV 2012 Deriche Rachid Recursively implementating the Gaussian and its derivatives ICIP 1993 2 ID: 173725

bilateral filter filtering recursive filter bilateral recursive filtering kernel gaussian implementation complexity spatial range cost recap recursively memory implemented proposed size applications

Share:

Link:

Embed:

Download Presentation from below link

Download Presentation The PPT/PDF document "Recursive Bilateral Filtering" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

Slide1

Recursive Bilateral Filtering

F01943024Slide2

Reference

Yang, Qingxiong. "Recursive bilateral filtering." 

ECCV

2012

.Deriche, Rachid. "Recursively implementating the Gaussian and its derivatives." ICIP 1993.

2Slide3

Outline

Recap of Bilateral FilteringWhy Recursive Filtering?Recursive Bilateral Filtering

Complexity Analysis

Applications

Conclusion3Slide4

Recap of Bilateral Filtering

Naïve image smoothing: Gaussian filteringNot edge-preserving

Bilateral filtering

4Slide5

Recap of Bilateral Filtering

The bilateral filter is a robust edge-preserving filter introduced by Tomasi and

Manduchi

in 1998.

5Slide6

Recap of Bilateral Filtering

Being non-linear, the brute force implementations of the bilateral filter are slow when kernel is large.Pham and

Vliet

implemented the BF as a separable operation.

The cost is still high for large kernels. (In ICME 2005)By constraining the spatial filter kernel to box filter, Weiss showed that the result depends only on the histogram of the neighborhood. However, this method works efficiently only on grascale image. (In Siggraph

2006)

Paris and Durand presented a volumetric data structure called

bilateral grid

. The BF corresponds to convolving a grid with a 3D/5D Gaussian. However, the memory cost maybe unacceptable when filter kernel is small. (In

Siggraph

2007)

6Slide7

Recap of Bilateral Filtering

Porikli is the first to remove the dependency of the filter(kernel) size by integral histogram. He also proposed a Taylor series based solution to remove the box filter constraint. (In CVPR 2008)

Yang showed that Durand’s method can be implemented using recursive Gaussian filter so that its complexity will be independent of the filter size. (In CVPR 2009)

The state-of-the-art implementation is proposed by Adams.

Gaussian KD-trees, complexity O(Nlog(N)D), memory cost O(ND)Permutohedral

lattice, complexity O(ND

2

), memory cost much higher

This paper:

implementing bilateral filter in a recursive

fasion

with complexity O(ND), memory cost O(ND)

7Slide8

Why Recursive Filtering?

FIR filterIIR filter

8Slide9

Why Recursive Filtering?

1st

-order recursive filtering

2

nd-order recursive filtering

Ex:

[

Deriche

1992] demonstrated that Gaussian filter

can be computed using 2

nd

-order recursive filtering.

9Slide10

Why Recursive Filtering?

Deriche, R. Recursively implementing the Gaussian and its derivatives. In ICIP. 1992

causal

anticausal

10Slide11

Why Recursive Filtering?

So why?Filter size dependencyRecursive implementation is linear in the number of pixels.

11Slide12

Recursive Bilateral Filtering

Bilateral filtering

Modified range kernel

The proposed method measures the range distance by accumulating the color difference between every two neighboring pixels on the path between

k and i.

12Slide13

Recursive Bilateral Filtering

Claim: For any bilateral filter containing

the new range filter kernel

and

any spatial filter kernel that can be recursively implemented, an exact recursive implementation can be obtained by simply altering the coefficients of the recursive system defined by the spatial filter kernel at each pixel location.Recursive implementation of the spatial filter

Recursive bilateral filter

Con be proved by math induction:

http://www.cs.cityu.edu.hk/~qiyang/publications/eccv-12

/

13Slide14

Complexity Analysis

Recursive implementation of the spatial filter

Recursive

bilateral

filterNew range kernel can be computed recursively.

2n multiplication operations and 2n-1 addition/subtraction operations

Only 3n-2 additional multiplication operations

14Slide15

Applications

Non-Photorealistic Rendering

15Slide16

Applications

Tone Mapping

16Slide17

Applications

Stereo Matching (average 10x

faster)

17Slide18

Conclusion

A recursive implementation of the bilateral filter is proposed in this paper. Witha new range filter kernel

any spatial filter kernel that can be recursively implemented.

It’s the first bilateral whose computational and memory complexity are linear in both input size and dimensionality.

18