A Local Adaptive Approach for Dense Stereo Matching in Architectural Scene

Reconstruction

C. Stentoumis1, L. Grammatikopoulos2, I. Kalisperakis2, E. Petsa2, G. Karras1

1. Laboratory of Photogrammetry, Department of Surveying,National Technical University of Athens, GR-15780 Athens, Greece

2. Laboratory of Photogrammetry, Department of Surveying,Technological Educational Institute of Athens, GR-12210 Athens, Greece

5th International Workshop on 3D Virtual Reconstruction and Visualization of Complex Architectures (3D-ARCH '2013), 25-26 February 2013

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Outline• Introduction• Related Work• Proposed Algorithm • Experimental Results• Conclusion

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Introduction

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Objective• Present a method

• Combines pre-existing algorithms and novel considerations

• With good sub-pixel accuracy

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Related work

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Related Work

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Stereo Matching :

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5

Range: 0 - 16

(X,Y) (X-d,Y)

Related Work

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Matching cost computation• For every individual pixel• Cost is assigned to all possible disparities

Cost aggragation• Neighboring share the same disparity• A summation of pixel-wise costs (over a support region)

Disparity optimization • The disparity with the lowest aggregated cost is chosen.

Refinement• Correcting inaccurate disparity values

ProposedAlgorithm

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Census on intensity principal derivatives

• Census transformation based on gradients:• Less sensitive to radiometric differences and repetitive

patterns

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Intensity

Gradient

Census on Gradients

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1 1 0 0 0

1 1 0 0 0

1 1 X 0 0

0 0 0 1 1

1 1 1 1 1

0.7 0.8 0.3 0.2 0.3

0.6 0.6 0.4 0.3 0.2

0.6 0.7 0.5 0.4 0.1

0.4 0.4 0.3 0.6 0.6

0.6 0.7 0.6 0.7 0.7

1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1Census transform window :

Hamming Distance

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• Left image

• Right image

Hamming Distance = 3

1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1

1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1

XOR

0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Comparison• After aggregation step:

Default census Census on gradients

2.5% less erroneous pixels

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Comparison• After aggregation step[13]:

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[13]Mei X., Sun X., Zhou M., Jiao S., Wang H., Zhang X., 2011. On building an accurate stereo matching system on graphics hardware. ICCV Workshop on GPU in Computer Vision Applications.

Absolute Difference on Image Color and Gradients

•

•

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AD ( color ) :

AD ( Gradient ) :

Total Matching Cost

•

• normalized by λ

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AD (color)Census (gradient) AD (gradient)

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Census(gradient)

AD(color)

AD(gradient)

Combined

Support Region

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• Cross-based support region[25]:

• Threshold of cross-skeleton expansion:

[25]Zhang K., Lu J., Lafruit G., 2009. Cross-based local stereo matching using orthogonal integral images. IEEE Transactions on Circuits & Systems for Video Technology.

Support Region

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• Threshold of cross-skeleton expansion[16]:

• Lmax : largest semi-dimension of the window size• τmax : largest color dissimilarity between p and q

3X3 median filter

[16]Stentoumis C., Grammatikopoulos L., Kalisperakis I., Karras G., 2012. Implementing an adaptive approach for dense stereo matching. International Archives of Photogrammetry, Remote Sensing & Spatial Information Sciences,

P q

lq

Support Region

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Aggregation Step

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• A. Normalized by the number of pixels in the support region

• B. 3D Gaussian function is applied for smoothing the aggregated costs.

• C. Winner-take-all

Comparison• After aggregation step[13]:

21Run this step for 4 iterations to get stable cost values. For iteration 1 and 3, aggregated horizontally and then vertically. For iteration 2 and 4, aggregated vertically and then horizontally.

•

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[13] method

Proposed Method

Refinement

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• Left-right consistency check

• Pixel p is characterized as valid (inlier) if the following constraint holds:

Refinement

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• Outlier cross-based filtering

• The cross-based support regions provide a robust description of pixel neighborhoods

• The median value of inliers in the support region is selected and attributed to the mismatched pixel.

Refinement

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• Occlusion / mismatch labeling

• Remaining outliers are re-estimated

• Mismatches:

• The epipolar line of the mismatch pixel intersects with disparity function

• Use median interpolation in a small patch around them

• Occlusions

• Use the second lowest disparity value in the neighborhood

Refinement

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• Epipolar Line

Before After

Refinement

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• Sub-pixel estimation• Estimation at the sub-pixel level is made by interpolating a 2nd

order curve to the cost volume C(d).

• This curve is defined by the disparities of the preceding and following pixels and their corresponding cost values

• Choose minimum cost position through a closed form solution for the 3 curve points.

Refinement

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• Disparity map smoothing

• Median filter is applied.

The effect of overall post-processing refinement

ExperimentalResults

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Experimental Results• Evaluated on the Middlebury and EPFL multi-view datasets

• Parameter values were kept constant for all tests.

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Experimental Results• Middlebury evaluation

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Error Threshold = 1

Error Threshold = 0.75

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[13] method

Proposed Method

Experimental Results

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A Initial disparity map D Remaining occlusion/ mismatch handling

B Cost smoothing E Sub-pixel estimation

C Outlier filtering F Median smoothing

Threshold = 0.75 , % of wrong pixels

Experimental Results

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Herz-Jesu-K7 stereo pair

Experimental Results

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Herz-Jesu-K7 stereo pair

Conclusion

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Conclusion

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Initial Cost • AD (color / gradient)• Census (color / gradient)

Aggregation • Aggregation more times• Normalize → Smoothing

Refinement• Mismatch : Epipolar Line / Interpolation• Sub-pixel Estimation• Occlusion / Parameter adjustment