Method

Variational Scene Flow [VSF]
http://devernay.free.fr/vision/varsceneflow/

Submitted on 29 Jul. 2015 11:27 by
Andreas Geiger (MPI Tübingen)

Running time:125 min
Environment:1 core @ 2.5 Ghz (C/C++)

Method Description:
We present a method for scene flow estimation from a calibrated stereo image sequence. The scene flow contains the 3-D displacement field of scene points, so that the 2-D optical flow can be seen as a projection of the scene flow onto the images. We propose to recover the scene flow by coupling the optical flow estimation in both cameras with dense stereo matching between the images, thus reducing the number of unknowns per image point. The use of a variational framework allows us to properly handle discontinuities in the observed surfaces and in the 3-D displacement field. Moreover our approach handles occlusions both for the optical flow and the stereo. We obtain a partial differential equations system coupling both the optical flow and the stereo, which is numerically solved using an original multi-resolution algorithm. Whereas previous variational methods were estimating the 3-D reconstruction at time t and the scene flow separately, our method jointly estimates both in a single optimization. We present numerical results on synthetic data with ground truth information, and we also compare the accuracy of the scene flow projected in one camera with a state-of-the-art single-camera optical flow computation method. Results are also presented on a real stereo sequence with large motion and stereo discontinuities.
Parameters:
See paper.
Latex Bibtex:
@InProceedings{Huguet2007ICCV,
Title = {A Variational Method for Scene Flow Estimation from Stereo Sequences},
Author = {Huguet, Frederic and Devernay, Frederic},
Booktitle = {ICCV},
Year = {2007}
}

Detailed Results

This page provides detailed results for the method(s) selected. For the first 20 test images, the percentage of erroneous pixels is depicted in the table. We use the error metric described in Object Scene Flow for Autonomous Vehicles (CVPR 2015), which considers a pixel to be correctly estimated if the disparity or flow end-point error is <3px or <5% (for scene flow this criterion needs to be fulfilled for both disparity maps and the flow map). Underneath, the left input image, the estimated results and the error maps are shown (for disp_0/disp_1/flow/scene_flow, respectively). The error map uses the log-color scale described in Object Scene Flow for Autonomous Vehicles (CVPR 2015), depicting correct estimates (<3px or <5% error) in blue and wrong estimates in red color tones. Dark regions in the error images denote the occluded pixels which fall outside the image boundaries. The false color maps of the results are scaled to the largest ground truth disparity values / flow magnitudes.

Test Set Average

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 27.31 21.72 26.38 59.51 44.93 57.08 50.06 45.40 49.28 67.69 62.93 66.90
All / Est 27.31 21.72 26.38 59.51 44.93 57.08 50.06 45.40 49.28 67.69 62.93 66.90
Noc / All 26.38 19.88 25.31 52.30 40.83 50.24 41.15 41.85 41.28 61.14 59.17 60.78
Noc / Est 26.38 19.88 25.31 52.30 40.83 50.24 41.15 41.85 41.28 61.14 59.17 60.78
This table as LaTeX

Test Image 0

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 30.82 2.74 26.97 57.17 20.75 52.17 33.67 97.67 42.46 62.66 100.00 67.78
All / Est 30.82 2.74 26.97 57.17 20.75 52.17 33.67 97.67 42.46 62.66 100.00 67.78
Noc / All 29.84 2.74 26.06 51.24 20.75 46.52 25.61 97.67 36.54 57.03 100.00 63.68
Noc / Est 29.84 2.74 26.06 51.24 20.75 46.52 25.61 97.67 36.54 57.03 100.00 63.68
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 1

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 22.33 15.55 21.57 53.14 31.77 50.75 31.59 85.04 37.56 58.69 86.82 61.83
All / Est 22.33 15.55 21.57 53.14 31.77 50.75 31.59 85.04 37.56 58.69 86.82 61.83
Noc / All 21.33 15.55 20.67 46.19 31.77 44.37 23.41 85.04 31.02 52.52 86.82 56.85
Noc / Est 21.33 15.55 20.67 46.19 31.77 44.37 23.41 85.04 31.02 52.52 86.82 56.85
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 2

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 33.25 2.36 31.74 66.06 55.29 65.54 52.87 18.45 51.19 72.54 65.09 72.17
All / Est 33.25 2.36 31.74 66.06 55.29 65.54 52.87 18.45 51.19 72.54 65.09 72.17
Noc / All 32.37 2.36 30.89 58.51 55.29 58.32 43.02 18.45 41.59 66.04 65.09 65.98
Noc / Est 32.37 2.36 30.89 58.51 55.29 58.32 43.02 18.45 41.59 66.04 65.09 65.98
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 3

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 45.75 30.44 44.34 68.30 94.69 70.74 74.36 96.77 76.43 78.79 97.15 80.48
All / Est 45.75 30.44 44.34 68.30 94.69 70.74 74.36 96.77 76.43 78.79 97.15 80.48
Noc / All 45.08 30.44 43.71 60.66 94.49 63.04 68.32 95.69 70.68 73.33 95.18 74.87
Noc / Est 45.08 30.44 43.71 60.66 94.49 63.04 68.32 95.69 70.68 73.33 95.18 74.87
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 4

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 22.02 17.47 21.26 67.74 68.51 67.87 52.46 93.97 59.34 75.62 95.29 78.88
All / Est 22.02 17.47 21.26 67.74 68.51 67.87 52.46 93.97 59.34 75.62 95.29 78.88
Noc / All 20.58 17.47 20.05 61.76 73.99 63.87 43.06 93.75 52.54 70.36 94.53 74.53
Noc / Est 20.58 17.47 20.05 61.76 73.99 63.87 43.06 93.75 52.54 70.36 94.53 74.53
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 5

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 39.59 5.39 36.51 59.64 5.97 54.82 45.63 0.06 41.53 65.95 6.40 60.59
All / Est 39.59 5.39 36.51 59.64 5.97 54.82 45.63 0.06 41.53 65.95 6.40 60.59
Noc / All 38.10 5.39 35.09 53.23 5.97 48.22 36.90 0.06 33.11 59.12 6.40 53.53
Noc / Est 38.10 5.39 35.09 53.23 5.97 48.22 36.90 0.06 33.11 59.12 6.40 53.53
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 6

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 42.29 6.43 38.51 57.72 16.93 53.42 50.74 0.80 45.48 67.72 18.10 62.49
All / Est 42.29 6.43 38.51 57.72 16.93 53.42 50.74 0.80 45.48 67.72 18.10 62.49
Noc / All 41.26 6.43 37.52 52.21 16.93 47.91 43.60 0.80 38.51 62.00 18.10 56.65
Noc / Est 41.26 6.43 37.52 52.21 16.93 47.91 43.60 0.80 38.51 62.00 18.10 56.65
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 7

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 42.00 65.87 46.67 42.26 68.95 47.48 1.66 100.00 20.91 43.31 100.00 54.40
All / Est 42.00 65.87 46.67 42.26 68.95 47.48 1.66 100.00 20.91 43.31 100.00 54.40
Noc / All 41.30 65.87 46.18 41.51 67.14 46.37 1.66 100.00 20.05 42.52 100.00 53.41
Noc / Est 41.30 65.87 46.18 41.51 67.14 46.37 1.66 100.00 20.05 42.52 100.00 53.41
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 8

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 33.51 5.76 28.38 33.19 8.54 28.64 2.40 100.00 20.43 35.31 100.00 47.25
All / Est 33.51 5.76 28.38 33.19 8.54 28.64 2.40 100.00 20.43 35.31 100.00 47.25
Noc / All 33.48 5.76 28.36 33.16 8.54 28.61 2.40 100.00 20.43 35.26 100.00 47.22
Noc / Est 33.48 5.76 28.36 33.16 8.54 28.61 2.40 100.00 20.43 35.26 100.00 47.22
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 9

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 30.73 41.68 33.53 30.36 44.21 33.90 1.21 100.00 26.45 31.72 100.00 49.16
All / Est 30.73 41.68 33.53 30.36 44.21 33.90 1.21 100.00 26.45 31.72 100.00 49.16
Noc / All 30.01 38.85 32.21 29.63 41.44 32.57 1.21 100.00 26.45 30.92 100.00 48.12
Noc / Est 30.01 38.85 32.21 29.63 41.44 32.57 1.21 100.00 26.45 30.92 100.00 48.12
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 10

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 25.96 11.63 22.69 74.09 61.67 71.26 47.28 71.28 52.76 78.13 80.91 78.77
All / Est 25.96 11.63 22.69 74.09 61.67 71.26 47.28 71.28 52.76 78.13 80.91 78.77
Noc / All 25.04 11.63 21.94 69.44 63.60 67.96 37.40 71.28 46.21 73.54 79.91 75.16
Noc / Est 25.04 11.63 21.94 69.44 63.60 67.96 37.40 71.28 46.21 73.54 79.91 75.16
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 11

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 13.75 4.35 12.06 47.89 47.29 47.79 47.30 47.82 47.39 57.94 75.80 61.15
All / Est 13.75 4.35 12.06 47.89 47.29 47.79 47.30 47.82 47.39 57.94 75.80 61.15
Noc / All 13.07 4.35 11.49 40.32 51.40 42.43 39.25 47.77 40.96 50.80 73.70 55.17
Noc / Est 13.07 4.35 11.49 40.32 51.40 42.43 39.25 47.77 40.96 50.80 73.70 55.17
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 12

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 11.03 3.82 10.55 60.24 44.71 59.19 55.93 14.43 53.14 67.46 55.84 66.68
All / Est 11.03 3.82 10.55 60.24 44.71 59.19 55.93 14.43 53.14 67.46 55.84 66.68
Noc / All 10.22 3.82 9.78 53.02 44.71 52.34 47.33 14.43 44.71 60.61 55.84 60.22
Noc / Est 10.22 3.82 9.78 53.02 44.71 52.34 47.33 14.43 44.71 60.61 55.84 60.22
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 13

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 20.03 7.61 18.51 52.43 95.97 57.77 51.75 100.00 57.67 59.39 100.00 64.38
All / Est 20.03 7.61 18.51 52.43 95.97 57.77 51.75 100.00 57.67 59.39 100.00 64.38
Noc / All 19.20 7.61 17.76 43.25 99.61 48.71 41.73 100.00 48.50 50.32 100.00 55.12
Noc / Est 19.20 7.61 17.76 43.25 99.61 48.71 41.73 100.00 48.50 50.32 100.00 55.12
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 14

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 12.45 10.34 12.41 57.83 42.50 57.56 53.79 14.62 53.11 66.99 45.53 66.62
All / Est 12.45 10.34 12.41 57.83 42.50 57.56 53.79 14.62 53.11 66.99 45.53 66.62
Noc / All 11.72 10.34 11.70 49.89 42.50 49.73 44.54 14.62 43.92 60.04 45.53 59.74
Noc / Est 11.72 10.34 11.70 49.89 42.50 49.73 44.54 14.62 43.92 60.04 45.53 59.74
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 15

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 28.83 7.20 26.87 78.51 63.45 77.14 73.27 45.29 70.73 85.21 78.54 84.60
All / Est 28.83 7.20 26.87 78.51 63.45 77.14 73.27 45.29 70.73 85.21 78.54 84.60
Noc / All 27.62 7.20 25.73 74.06 63.45 72.81 65.18 45.29 62.89 80.58 78.54 80.34
Noc / Est 27.62 7.20 25.73 74.06 63.45 72.81 65.18 45.29 62.89 80.58 78.54 80.34
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 16

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 17.16 11.11 16.27 75.97 91.83 78.31 57.97 99.89 64.14 78.52 100.00 81.68
All / Est 17.16 11.11 16.27 75.97 91.83 78.31 57.97 99.89 64.14 78.52 100.00 81.68
Noc / All 16.52 11.11 15.72 68.71 91.83 72.99 46.61 99.89 56.19 71.74 100.00 76.97
Noc / Est 16.52 11.11 15.72 68.71 91.83 72.99 46.61 99.89 56.19 71.74 100.00 76.97
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 17

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 23.32 6.66 21.59 66.63 74.72 67.47 66.56 33.84 63.15 78.95 86.38 79.72
All / Est 23.32 6.66 21.59 66.63 74.72 67.47 66.56 33.84 63.15 78.95 86.38 79.72
Noc / All 22.18 6.66 20.53 58.13 74.72 60.32 57.23 33.84 54.20 72.50 86.38 74.33
Noc / Est 22.18 6.66 20.53 58.13 74.72 60.32 57.23 33.84 54.20 72.50 86.38 74.33
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 18

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 26.40 27.36 26.85 69.87 100.00 84.19 61.83 100.00 79.97 76.42 100.00 87.62
All / Est 26.40 27.36 26.85 69.87 100.00 84.19 61.83 100.00 79.97 76.42 100.00 87.62
Noc / All 25.36 27.36 26.32 61.00 100.00 69.21 48.78 100.00 62.90 67.88 100.00 74.63
Noc / Est 25.36 27.36 26.32 61.00 100.00 69.21 48.78 100.00 62.90 67.88 100.00 74.63
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error


Test Image 19

Error D1-bg D1-fg D1-all D2-bg D2-fg D2-all Fl-bg Fl-fg Fl-all SF-bg SF-fg SF-all
All / All 11.83 18.96 12.63 68.65 80.28 69.97 69.38 87.87 71.47 76.19 91.37 77.91
All / Est 11.83 18.96 12.63 68.65 80.28 69.97 69.38 87.87 71.47 76.19 91.37 77.91
Noc / All 10.53 18.96 11.50 58.55 80.28 61.75 59.37 87.87 63.50 67.79 91.37 71.26
Noc / Est 10.53 18.96 11.50 58.55 80.28 61.75 59.37 87.87 63.50 67.79 91.37 71.26
This table as LaTeX

Input Image

D1 Result

D1 Error

D2 Result

D2 Error

Flow Result

Flow Error

Scene Flow Error




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