an evaluation methodology for stereo correspondence algorithms
TRANSCRIPT
An Evaluation Methodology for Stereo Correspondence Algorithms
Ivan Cabezas, Maria Trujillo and Margaret [email protected]
February 25th 2012International Conference on Computer Vision Theory and Applications, VISAPP 2012, Rome - Italy
Slide 2
Multimedia and Vision Laboratory
MMV is a research group of the Universidad del Valle in Cali, Colombia
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Ivan Maria et al.
Slide 3
Ayax Inc.
Ayax Inc. offers informatics solutions for decision analysis
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Margaret
Slide 4
Content
Stereo Vision Canonical Stereo Geometry and Disparity Ground-truth Based Evaluation
Quantitative Evaluation Methodologies Middlebury’s Methodology A* Methodology
A* Groups Methodology Experimental Results Final Remarks
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Slide 5
Stereo Vision
The stereo vision problem is to recover the 3D structure of the scene using two or more images
3D ModelStereo Images
Disparity Map
Left RightCorrespondence
Algorithm
ReconstructionAlgorithm
CameraSystem
3D World
2D Images
InverseProblem
OpticsProblem
Yang Q. et al., Stereo Matching with Colour-Weighted Correlation, Hierarchical Belief Propagation, and Occlusion Handling, IEEE PAMI 2009
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Slide 6
Canonical Stereo Geometry and Disparity
Disparity is the distance between corresponding points
Trucco, E. and Verri A., Introductory Techniques for 3D Computer Vision, Prentice Hall 1998
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Accurate Estimation Inaccurate Estimation
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Slide 7
Ground-truth Based Evaluation
Ground-truth based evaluation is based on the comparison using disparity ground-truth data
Scharstein, D. and Szeliski, R., High-accuracy Stereo Depth Maps using Structured Light, CVPR 2003Tola, E., Lepetit, V. and Fua, P., A Fast Local Descriptor for Dense Matching, CVPR 2008Strecha, C., et al. On Benchmarking Camera Calibration and Multi-View Stereo for High Resolution Imagery, CVPR 2008http://www.zf-usa.com/products/3d-laser-scanners/
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Slide 8
Quantitative Evaluation Methodologies
Szeliski, R., Prediction Error as a Quality Metric for Motion and Stereo, ICCV 2000Kostliva, J., Cech, J., and Sara, R., Feasibility Boundary in Dense and Semi-Dense Stereo Matching, CVPR 2007Tomabari, F., Mattoccia, S., and Di Stefano, L., Stereo for robots: Quantitative Evaluation of Efficient and Low-memory Dense Stereo Algorithms, ICCARV 2010Cabezas, I. and Trujillo M., A Non-Linear Quantitative Evaluation Approach for Disparity Estimation, VISAPP 2011
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
The use of a methodology allows to:
Assert specific components and procedures
Tune algorithm's parameters
Support decision for researchers and practitioners
Measure the progress on the field
Slide 9
Middlebury’s Methodology
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Select Test Bed Images Select Error Criteria
Select Error Measures
nonocc all disc
Select and Apply Stereo Algorithms
Compute Error Measures
ObjectStereo GC+SegmBorder PUTv3
PatchMatch ImproveSubPix OverSegmBP
Scharstein, D. and Szeliski, R., High-accuracy Stereo Depth Maps using Structured Light, CVPR 2003Scharstein, D. and Szeliski, R., http://vision.middlebury.edu/stereo/eval/, 2012
Slide 10
Middlebury’s Methodology (ii)
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Select and Apply Stereo Algorithms
Compute Error Measures
Algorithm nonocc all discObjectStereo 2.20 1 6.99 2 6.36 1
GC+SegmBorder 4.99 6 5.78 1 8.66 5PUTv3 2.40 2 9.11 6 6.56 2
PatchMatch 2.47 3 7.80 3 7.11 3ImproveSubPix 2.96 4 8.22 4 8.55 4OverSegmBP 3.19 5 8.81 5 8.89 6
Algorithm Average Rank
FinalRanking
ObjectStereo 1.33 1
PatchMatch 3.00 2PUTv3 3.33 3
GC+SegmBorder 4.00 4ImproveSubPix 4.00 5OverSegmBP 5.33 6
Apply Evaluation Model
Algorithm nonocc all discObjectStereo 2.20 6.99 6.36
GC+SegmBorder 4.99 5.78 8.66PUTv3 2.40 9.11 6.56
PatchMatch 2.47 7.80 7.11ImproveSubPix 2.96 8.22 8.55 OverSegmBP 3.19 8.81 8.89
Scharstein, D. and Szeliski, R., http://vision.middlebury.edu/stereo/eval/, 2012
Slide 11
Middlebury’s Methodology (iii)
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Scharstein, D. and Szeliski, R., A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms, IJCV 2002Scharstein, D. and Szeliski, R., http://vision.middlebury.edu/stereo/eval/, 2012
Apply Evaluation Model Interpret Results
The ObjectStereo algorithm produces accurate resultsMiddlebury’s
Evaluation Model
Algorithm Average Rank
FinalRanking
ObjectStereo 1.33 1
PatchMatch 3.00 2
PUTv3 3.33 3
GC+SegmBorder 4.00 4
ImproveSubPix 4.00 5
OverSegmBP 5.33 6
Slide 12
Middlebury’s Methodology (iv): Weaknesses
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
The Middlebury’s evaluation model have some shortcomings
In some cases, the ranks are assigned arbitrarily
The same average ranking does not imply the same performance (and vice versa)
The cardinality of the set of top-performer algorithms is a free parameter
It operates values related to incommensurable measures
Slide 13
Middlebury’s Methodology (v): Weaknesses
The BMP percentage measures the quantity of disparity estimation errors exceeding a threshold
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
The BMP measure have some shortcomings:
It is sensitive to the threshold selection
It ignores the error magnitude
It ignores the inverse relation between depth and disparity
It may conceal estimation errors of a large magnitude, and, also it may penalise errors of small impact in the final 3D reconstruction
Cabezas, I., Padilla, V., and Trujillo M., A Measure for Accuracy Disparity Maps Evaluation, CIARP 2011Gallup, D., et al. Variable Baseline/Resolution Stereo, CVPR, 2008
Slide 14
The A* evaluation methodology brings a theoretical background for the comparison of stereo correspondence algorithms The set of algorithms under evaluation
The set of estimated maps to be compared
The function that produces a vector of error measures
The set of vectors of error measures
A* Methodology
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Cabezas, I. and Trujillo M., A Non-Linear Quantitative Evaluation Approach for Disparity Estimation, VISAPP 2011
Slide 15
A* Methodology (ii)
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Cabezas, I. and Trujillo M., A Non-Linear Quantitative Evaluation Approach for Disparity Estimation, VISAPP 2011
The evaluation model of the A* methodology addresses the comparison of stereo correspondence algorithms as a multi-objective optimisation problem It defines a partition over the set A (the decision space)
Subject to:
where ≺ denotes the Pareto Dominance relation: Let p and q be two algorithms
Let Vp and Vq be a pair of vectors belonging to the objective space
Thus, three possible relations are considered
Slide 16
A* Methodology (iii): Pareto Dominance
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Van Veldhuizen, D., et al., Considerations in Engineering Parallel Multi-objective Evolutionary Algorithms, Trans in Evolutionary Computing 2003
The Pareto Dominance defines a partial order relation
VGC+SegmBorder = < 4.99, 5.78, 8.66 >VPatchMatch = < 2.47, 7.80, 7.11 >VImproveSubPix = < 2.96, 8.22, 8.55 >
VGC+SegmBorder VPatchMatch < 4.99, 5.78, 8.66 > < 2.47, 7.80, 7.11 >
GC+SegmBorder ~ PatchMatch
VPatchMatch VImproveSubPix
< 2.47, 7.80, 7.11 > < 2.96, 8.22, 8.55 >
Patchmatch ≺ ImproveSubPix
Slide 17
A* Methodology (iv): Illustration
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Select Test Bed Images Select Error Criteria
Select Error Measures
nonocc all disc
Select and Apply Stereo Algorithms
Compute Error Measures
ObjectStereo GC+SegmBorder PUTv3
PatchMatch ImproveSubPix OverSegmBP
Scharstein, D. and Szeliski, R., High-accuracy Stereo Depth Maps using Structured Light, CVPR 2003Scharstein, D. and Szeliski, R., http://vision.middlebury.edu/stereo/eval/, 2012
Slide 18
A* Methodology (v): Illustration
The evaluation model performs the partitioning and the grouping of stereo algorithms under evaluation, based on the Pareto Dominance relation
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Compute Error Measures
Algorithm nonocc all discObjectStereo 2.20 6.99 6.36
GC+SegmBorder 4.99 5.78 8.66PUTv3 2.40 9.11 6.56
PatchMatch 2.47 7.80 7.11ImproveSubPix 2.96 8.22 8.55 OverSegmBP 3.19 8.81 8.89
Algorithm nonocc all disc SetObjectStereo 2.20 6.99 6.36 A*
GC+SegmBorder 4.99 5.78 8.66 A*PUTv3 2.40 9.11 6.56 A’
PatchMatch 2.47 7.80 7.11 A’ImproveSubPix 2.96 8.22 8.55 A’OverSegmBP 3.19 8.81 8.89 A’
Apply Evaluation Model
, GC+SegmBorder
PatchMatch
ObjectStereo
PUTv3 ImproveSubPix OverSegmBP,, ,
Slide 19
A* Methodology (vi): Illustration
Interpretation of results is based on the cardinality of the set A*
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Apply Evaluation Model Interpret Results
The Objectstereo and the GC+SegmBorder algorithms are,
comparable among them, and have a superior performance to the rest of
algorithms
A* Evaluation Model
Algorithm nonocc all disc SetObjectStereo 2.20 6.99 6.36 A*
GC+SegmBorder 4.99 5.78 8.66 A*PUTv3 2.40 9.11 6.56 A’
PatchMatch 2.47 7.80 7.11 A’ImproveSubPix 2.96 8.22 8.55 A’OverSegmBP 3.19 8.81 8.89 A’
Slide 20
A* Methodology (vii): Strength and Weakness
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - ItalyCabezas, I. and Trujillo M., A Non-Linear Quantitative Evaluation Approach for Disparity Estimation, VISAPP 2011
Strength: It allows a formal interpretation of results, based on the cardinality of the set A*, and in regard to considered imagery test-bed
Weakness: It does not allow an exhaustive evaluation of the entire set of algorithms under evaluation It computes the set A* just once, and does not bring information about A’
Slide 21
A* Groups Methodology
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
It extends the evaluation model of the A* methodology, incorporating the capability of performing an exhaustive evaluation
It introduces the partitioningAndGrouping algorithmA = Set ( { } );A.load( “Algorithms.dat” );A* = Set ( { } );A’ = Set ( { } );group = 1;do { computePartition( A, A*, A’, g, ≺ ); A*.save ( “A*_group_”+group ); group++; A.update ( A’ ); // A = A / A* A*.removeAll ( ); // A* = { } A’.removeAll ( ); // A’ = { } }while ( ! A.isEmpty ( ) );
subject to:
Slide 22
The A* Groups methodology uses the Sigma-Z-Error (SZE) measure
The SZE measure has the following properties:
It is inherently related to depth reconstruction in a stereo system
It is based on the inverse relation between depth and disparity
It considers the magnitude of the estimation error
It is threshold free
A* Groups Methodology (ii): Sigma-Z-Error
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - ItalyCabezas, I., Padilla, V., and Trujillo M., A Measure for Accuracy Disparity Maps Evaluation, CIARP 2011
Slide 23
A* Groups Methodology (iii): Illustration
The evaluation process of selected algorithms by using the proposal
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Select Test Bed Images Select Error Criteria
Select Error Measures
nonocc all disc
Select and Apply Stereo Algorithms
Compute Error Measures
ObjectStereo GC+SegmBorder PUTv3
PatchMatch ImproveSubPix OverSegmBP
Slide 24
A* Groups Methodology (iv): Illustration
The evaluation model performs the partitioning and the grouping of stereo algorithms under evaluation, based on the Pareto Dominance relation
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Compute Error Measures
Algorithm nonocc all discObjectStereo 73.88 117.90 36.25
GC+SegmBorder 50.48 64.90 24.33PUTv3 99.67 333.37 53.79
PatchMatch 49.95 261.84 32.85ImproveSubPix 50.66 97.94 32.01OverSegmBP 58.65 108.60 34.58
,GC+SegmBorder PatchMatch
ObjectStereo PUTv3 ImproveSubPix OverSegmBP,, ,
Algorithm nonocc all disc GroupGC+SegmBorder 50.48 64.90 24.33 1
PatchMatch 49.95 261.84 32.85 1PUTv3 99.67 333.37 53.79
ImproveSubPix 50.66 97.94 32.01
OverSegmBP 58.65 108.60 34.58
ObjectStereo 73.88 117.90 36.25
Apply Evaluation Model
,
Slide 25
A* Groups Methodology (v): Illustration
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
ObjectStereo PUTv3 ImproveSubPix OverSegmBP,, ,
Algorithm nonocc all discPUTv3 99.67 333.37 53.79
ImproveSubPix 50.66 97.94 32.01
OverSegmBP 58.65 108.60 34.58
ObjectStereo 73.88 117.90 36.25
Apply Evaluation Model
Algorithm nonocc all disc GroupImproveSubPix 50.66 97.94 32.01 2
PUTv3 99.67 333.37 53.79
ObjectStereo 73.88 117.90 36.25
OverSegmBP 58.65 108.60 34.58
ImproveSubPix
ObjectStereo PUTv3 OverSegmBP, ,
ObjectStereo PUTv3 OverSegmBP, ,Algorithm nonocc all disc
PUTv3 99.67 333.37 53.79
OverSegmBP 58.65 108.60 34.58
ObjectStereo 73.88 117.90 36.25
ObjectStereo
OverSegmBP
,PUTv3
Algorithm nonocc all disc GroupOverSegmBP 58.65 108.60 34.58 3
PUTv3 99.67 333.37 53.79
ObjectStereo 73.88 117.90 36.25
And so on …
Slide 26
A* Groups Methodology (vi): Illustration
Interpretation of results is based on the cardinality of each group
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Apply Evaluation Model Interpret Results
There are 5 groups of different performance
The GC+SegmBorder and the PatchMatch algorithms are, comparable among them,
and have a superior performance to the rest of algorithms
The ImproveSubPix algorithm is superior to the OverSegmBP, the ObjectStereo, and
the PUTv3 algorithms
…
The PUTv3 algorithm has the lowest performance
A* GroupsEvaluation Model
Algorithm nonocc all disc GroupGC+SegmBorder 50.48 64.90 24.33 1
PatchMatch 49.95 261.84 32.85 1ImproveSubPix 50.66 97.94 32.01 2OverSegmBP 58.65 108.60 34.58 3ObjectStereo 73.88 117.90 36.25 4
PUTv3 99.67 333.37 53.79 5
Slide 27
Experimental Results
The conducted evaluation involves the following elements:
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Test Bed Images
Error Criteria
Evaluation Models
Error Measures
A* Groups Middlebury
SZE , BMP
nonocc , all , disc
Scharstein, D. and Szeliski, R., http://vision.middlebury.edu/stereo/eval/, 2012
Stereo Algorithms 112 algorithms from the Middlebury’s repository
Slide 28
Experimental Results (ii)
An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
Algorithm Strategy Group Middlebury’s Ranking
DoubleBP Global 1 4
PatchMatch Local 1 11GC+SegmBorder Global 1 13
FeatureGC Global 1 18Segm+Visib Global 1 29MultiresGC Global 1 30DistinctSM Local 1 34
GC+occ Global 1 67MultiCamGC Global 1 68
Algorithm Group Middlebury’s Ranking
ADCensus 2 1
AdaptingBP 2 2CoopRegion 2 3DoubleBP 1 4
RDP 2 5OutlierConf 2 6
SubPixDoubleBP 2 7SurfaceStereo 2 8
WarpMat 2 9ObjectStereo 2 10PatchMatch 1 11
Undr+OverSeg 2 12GC+SegmBorder 1 13
InfoPermeable 2 14CostFilter 2 15
Slide 29
Final Remarks
The use of the A* Groups methodology allows to perform an exhaustive evaluation, as well as an objective interpretation of results
Innovative results in regard to the comparison of stereo correspondence algorithms were obtained using proposed methodology and the SZE error measure
The introduced methodology offers advantages over the conventional approaches to compare stereo correspondence algorithms
Authors are already working in order to provide to the research community an accessible way to use the introduced methodology
Thanks!An Evaluation Methodology for Stereo Correspondence Algorithms, VISAPP 2012, Rome - Italy
An Evaluation Methodology for Stereo Correspondence Algorithms
Ivan Cabezas, Maria Trujillo and Margaret [email protected]
February 25th 2012International Conference on Computer Vision Theory and Applications, VISAPP 2012, Rome, Italy