1. 100+ Times Faster Weighted Median Filter [cvpr ‘14]
Presenter: Chang-Ryeol Lee

2. Introduction Typical problems in stereo matching
Wrong disparity estimates in depth discontinuity regions
Disparity image estimated by our active stereo system [samsung project ’14]

3. Introduction One of the ways to get better disparity image
Post-processing of estimated disparity image
Initial disparity image
Improved disparity map

4. Introduction
Post processing by using color image is popular and powerful
Weighted Median Filtering (WMF)
Weighted Bilateral Filtering (WBF)
Weighted Mode Filtering (WDF)
Initial disparity image
Color image
Improved disparity map

5. Introduction
Post processing by using color image is popular and powerful
Weighted Median Filtering (WMF)
Effective to salt and pepper noises
Edge-preserving filter
Initial disparity image
Color image
Improved disparity map

6. What is WMF?
Based on sliding window strategies
Disparity image

7. The number of disparity
What is WMF?
Based on sliding window strategies
Median filtering
Select median value within a window 5 1 3 4 1 1 5 3 8 7
Disparity image 3 6 2 1 9
disparity
The number of disparity 5 8 3 9 3 1 3 7 4 6
Median value
Disparity image

8. What is WMF? Based on sliding window strategies
Weighted median filtering
Select color weighted median value within a window
Weight
Color similarity between center point pixel and neighborhood pixel
disparity
Color weight
I(p)
I(q)
D(q)
Disparity image
Color image 5
Weighted 히스토그램

9. What is WMF? Based on sliding window strategies
Weighted median filtering
Select color weighted median value within a window
Median value computation by cumulative histogram
Color weight k n
histogram
Cumulative histogram
Color weight
disparity
disparity

10. Limitation of WMF Nonlinearity Improvement strategies
⇒ histogram and cumulative histogram have to be computed within every window
Improvement strategies
Joint histogram to use box filtering technique
Median tracking to cut cumulative histogram procedure
Necklace table for fast access in sparse data structure
median{ window1 + window2 }  median{ window1 } + median{ window2 }

11. Fast WMF Joint histogram
2D histogram composed of disparity and color intensity
Color weighted histogram can be computed by multiplication of joint histogram and color similarity
disparity
Color intensity
255
100 d i
disparity
Color weight
Color weighted histogram
Joint histogram

12. Fast WMF Joint histogram
2D histogram composed of disparity and color intensity
Only count the number of disparities and corresponding color intensity
It means that we can use box filtering technique
disparity
255 i
Color intensity
I(q)
D(q) d
100
Color intensity
Disparity image
Joint histogram

13. Fast WMF Median tracking Insight
Colors in a window are similar to those in neighborhood window
So median value is not largely changed as a window moves
Tracking current median value by shifting of median value in previous window
* k is median value
Previous window
Current window
disparity
Color
weight
disparity
Color
weight

14. Fast WMF Median tracking Balance
Difference between left sum and right sum of histogram
disparity
Color
weight
Left sum
Right sum

15. Fast WMF .* Median tracking Fast balance computation + -
To compute balance, all values in joint histogram and corresponding color similarities should be multiplied
255 k i + - .*
Color intensity
Disparity
100
Joint histogram

16. Fast WMF .* Median tracking Fast balance computation + -
To compute balance, all values in joint histogram and corresponding color similarities should be multiplied
255 k i + - .*
Color intensity
Disparity
100
Joint histogram

17. Fast WMF Median tracking Fast balance computation + -
Balance Counting Box (BCB)
Row by Row computation of balance in joint histogram
Disparity
Color intensity
255
100 k i + -
Joint Histogram
Balance Counting Box (BCB)

18. Fast WMF .* Median tracking Fast balance computation
Balance Counting Box (BCB)
Multiplication of only BCB and corresponding color similarity .*
Balance Counting Box (BCB)

19. Fast WMF Experiments Resolution: 640 x 480
Environments: single core, C code
Comparison
About 6 times faster
Color image
time (s)
speed (fps)
WMF
0.574
1.74
Fast WMF
0.091
10.98
Initial disparity image
WMF
Fast WMF

20. Conclusion Practical issues show up in computer vision community
The main idea of this paper can be applied to other histogram- based application

21. Box filtering