CUDA: Hessian computation is not bit-exact

[tomoaki0705]

System information (version)

• OpenCV => recent 3.4 ( 49497d8 ) + contrib 3.4 branch ( d3ea23c )
• Operating System / Platform => Jetson (Aarch64)
• Compiler => GCC 5.4.0 (Jetson TX1, TX2), 7.5.0 (Jetson Nano, Xavier)

Detailed description

• Some combinations of test CUDA_Features2D/CUDA_SURF.Detector_Masked fail on Jetson

[  FAILED  ] 32 tests, listed below:
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/0, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/1, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/2, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/3, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/4, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/5, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/6, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/7, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/8, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/9, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/10, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/11, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/12, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/13, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/14, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/15, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/16, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/17, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/18, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/19, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/20, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/21, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/22, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/23, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(3), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/24, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/25, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/26, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/27, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(2), SURF_Extended(true), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/28, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/29, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(false), SURF_Upright(true))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/30, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(false))
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/31, where GetParam() = (SURF_HessianThreshold(500), SURF_Octaves(4), SURF_OctaveLayers(3), SURF_Extended(true), SURF_Upright(true))

• The detail of each single error is as following

[ RUN      ] CUDA_Features2D/CUDA_SURF.Detector_Masked/0, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(false))
/home/nvidia/opencv_contrib/modules/xfeatures2d/test/test_surf.cuda.cpp:133: Failure
Expected equality of these values:
  keypoints_gold.size()
    Which is: 696
  keypoints.size()
    Which is: 697
[  FAILED  ] CUDA_Features2D/CUDA_SURF.Detector_Masked/0, where GetParam() = (SURF_HessianThreshold(100), SURF_Octaves(3), SURF_OctaveLayers(2), SURF_Extended(false), SURF_Upright(false)) (31 ms)

• This error message indicates that the detected # of key points differs between CPU and GPU.
• Computation of Hessian has floating point operation and it's not bit-exact

opencv_contrib/modules/xfeatures2d/src/surf.cpp

Lines 202 to 209 in 8c09249

	{
	float dx = calcHaarPattern( sum_ptr, Dx , 3 );
	float dy = calcHaarPattern( sum_ptr, Dy , 3 );
	float dxy = calcHaarPattern( sum_ptr, Dxy, 4 );
	sum_ptr += sampleStep;
	det_ptr[j] = dx*dy - 0.81f*dxy*dxy;
	trace_ptr[j] = dx + dy;
	}

Steps to reproduce

cmake -DWITH_CUDA
make all
./bin/opencv_test_xfeatures2d --gtest_filter=CUDA_Features2D/CUDA_SURF.Detector_Masked*

How to fix

• Technically, it's not realistic to make Hessian computation bit-exact
• The other way round is to make the test to tolerate with rounding error
• This corresponds to increase the HessianThreshold here

opencv_contrib/modules/xfeatures2d/test/test_surf.cuda.cpp

Line 175 in 8c09249

testing::Values(SURF_HessianThreshold(100.0), SURF_HessianThreshold(500.0), SURF_HessianThreshold(1000.0)),

• The test has already hard-coded threshold 100, 500 and 1000
• Above error message indicates that threshold 100 and 500 requires bit-exactness of Hessian computation.
• I'd like to add an ifdef for this hard coded value, so it will keep bit-exact computation for Intel, but not for the other platforms (i.e. Jetson)
• I'll send a PR shortly

Issue submission checklist

• I report the issue, it's not a question
• I checked the problem with documentation, FAQ, open issues,
  answers.opencv.org, Stack Overflow, etc and have not found solution
• I updated to latest OpenCV version and the issue is still there
• There is reproducer code and related data files: videos, images, onnx, etc