Optical flow evaluation results Statistics:     Average   SD   R0.5   R1.0   R2.0   A50   A75   A95  
Error type:   endpoint   angle   interpolation   normalized interpolation  
Show images: below table   above table        
R1.0
endpoint
error
avg. Army
(Hidden texture)
GT   im0   im1
Mequon
(Hidden texture)
GT   im0   im1
Schefflera
(Hidden texture)
GT   im0   im1
Wooden
(Hidden texture)
GT   im0   im1
Grove
(Synthetic)
GT   im0   im1
Urban
(Synthetic)
GT   im0   im1
Yosemite
(Synthetic)
GT   im0   im1
Teddy
(Stereo)
GT   im0   im1
rank all disc untext all disc untext all disc untext all disc untext all disc untext all disc untext all disc untext all disc untext
NNF-Local [87]6.7 0.82 12 4.87 13 0.37 16 1.75 7 12.1 8 0.53 6 2.22 2 7.90 2 0.57 7 1.07 3 9.10 5 0.17 2 9.77 1 16.5 1 2.56 2 4.53 3 15.6 2 3.00 3 0.00 1 0.02 30 0.00 1 5.99 9 19.5 22 3.94 2
OFLAF [77]8.5 0.82 12 4.86 12 0.38 18 1.74 5 11.1 5 0.62 12 2.08 1 7.42 1 0.57 7 1.61 10 12.0 10 0.48 12 11.2 6 19.0 6 3.96 6 6.81 21 19.8 11 4.79 21 0.00 1 0.00 1 0.00 1 5.80 6 15.6 3 9.76 15
PMMST [114]8.9 0.65 2 3.86 2 0.05 1 2.23 18 13.5 16 1.21 33 2.81 8 9.66 8 0.83 13 1.29 5 6.70 2 0.42 10 11.7 7 19.1 7 5.55 10 5.50 8 17.8 6 4.52 13 0.00 1 0.02 30 0.00 1 5.44 3 15.8 4 5.70 5
NN-field [71]11.4 0.89 25 5.29 27 0.40 25 2.06 13 14.1 21 0.62 12 2.49 4 8.79 5 0.68 10 0.99 2 8.66 4 0.09 1 9.99 2 16.8 2 2.51 1 6.53 19 11.2 1 2.42 2 0.01 36 0.02 30 0.00 1 5.86 7 19.6 23 2.84 1
MDP-Flow2 [68]12.6 0.77 6 4.59 6 0.31 4 1.46 2 9.56 1 0.39 1 2.59 5 9.00 6 0.91 18 2.48 45 17.7 51 0.70 44 14.1 20 23.0 19 8.20 23 5.27 5 18.2 7 4.66 16 0.00 1 0.00 1 0.00 1 5.91 8 16.7 6 8.80 7
Correlation Flow [75]16.1 0.81 9 4.81 10 0.22 2 2.03 10 13.0 11 0.42 2 5.14 49 15.7 47 0.55 6 1.09 4 8.36 3 0.28 6 16.6 38 26.1 38 10.8 41 7.92 30 22.7 23 4.18 10 0.00 1 0.02 30 0.00 1 5.54 4 17.2 7 5.00 4
WLIF-Flow [93]16.6 0.84 17 4.97 18 0.34 10 2.03 10 13.3 14 0.76 19 3.64 18 12.0 17 1.41 30 2.23 33 14.4 24 0.55 18 13.1 13 21.6 13 7.54 16 8.23 36 20.9 15 5.39 28 0.00 1 0.00 1 0.00 1 6.94 15 18.0 11 10.4 20
NNF-EAC [103]21.6 0.81 9 4.82 11 0.39 23 1.95 9 12.0 7 0.83 22 3.16 11 10.6 11 1.00 20 2.60 49 18.5 54 0.77 49 13.9 17 22.8 18 7.86 18 6.67 20 19.3 9 5.14 26 0.10 49 0.02 30 0.00 1 7.08 18 19.2 17 10.5 21
ComponentFusion [96]22.7 0.98 47 5.81 54 0.37 16 1.59 4 10.7 4 0.53 6 2.84 9 9.86 9 0.85 16 1.94 17 13.3 13 0.54 17 15.3 32 24.9 32 10.5 40 6.83 22 26.2 46 5.50 31 0.03 42 0.00 1 0.32 52 6.69 11 18.5 13 9.59 11
TC/T-Flow [76]23.4 0.71 3 4.20 3 0.40 25 2.67 32 15.4 28 0.77 20 3.30 14 11.2 12 0.44 3 2.33 37 15.9 39 0.60 27 14.8 25 23.6 24 8.02 19 3.70 1 15.8 3 2.27 1 0.13 52 0.02 30 1.23 70 7.85 31 21.7 34 10.9 29
Layers++ [37]23.9 0.91 31 5.39 33 0.43 39 2.18 17 13.9 20 0.96 24 2.73 7 9.43 7 1.40 29 1.70 12 10.5 7 0.56 19 10.2 3 16.8 2 6.50 13 9.09 48 22.7 23 5.92 42 0.21 59 0.02 30 0.69 56 6.88 13 17.6 10 10.9 29
FC-2Layers-FF [74]24.7 0.87 22 5.16 23 0.42 34 2.70 34 17.8 39 1.20 31 2.59 5 8.73 4 1.39 28 1.88 15 13.3 13 0.50 13 11.1 5 18.0 5 6.07 11 9.16 51 21.3 17 5.89 40 0.04 45 0.02 30 0.22 50 7.48 24 19.4 20 11.1 34
AGIF+OF [85]25.2 0.90 27 5.34 29 0.42 34 3.13 45 19.3 48 1.37 38 3.87 22 12.8 19 1.80 43 2.19 30 14.3 22 0.64 32 12.4 9 20.6 9 7.20 15 9.27 53 22.4 20 5.97 46 0.00 1 0.00 1 0.00 1 7.26 20 18.8 15 10.7 26
LME [70]27.4 0.95 43 5.67 48 0.38 18 1.45 1 9.68 2 0.43 3 5.19 50 13.3 27 6.57 91 2.44 43 18.3 52 0.68 38 15.2 30 24.4 28 10.2 37 6.17 17 21.9 18 5.18 27 0.00 1 0.02 30 0.00 1 7.05 16 19.3 18 10.2 18
ALD-Flow [66]28.7 0.79 7 4.72 9 0.38 18 2.44 28 13.5 16 0.80 21 4.33 37 14.7 40 0.88 17 2.92 64 19.4 58 0.82 53 17.5 41 28.1 42 10.0 35 5.61 10 24.7 39 3.10 4 0.00 1 0.00 1 0.00 1 9.09 45 26.3 51 11.9 50
nLayers [57]28.8 0.88 23 5.25 25 0.44 43 2.79 36 15.6 32 1.47 43 4.34 38 14.4 36 2.33 57 1.54 8 11.6 9 0.52 16 10.4 4 17.1 4 5.51 9 8.89 42 19.3 9 5.79 39 0.31 70 0.00 1 1.16 68 7.27 21 19.3 18 11.3 40
MLDP_OF [89]29.2 0.94 40 5.51 43 0.36 14 1.74 5 11.7 6 0.44 5 4.05 28 13.1 24 0.50 5 1.48 7 12.3 11 0.29 7 15.4 33 24.7 31 9.15 28 5.54 9 18.2 7 3.11 5 1.54 108 0.05 89 9.31 115 8.33 37 21.4 33 9.39 10
PH-Flow [101]30.3 0.93 38 5.49 41 0.42 34 2.87 37 17.6 38 1.33 37 2.99 10 10.1 10 1.76 42 2.27 35 14.6 29 0.68 38 12.5 10 20.8 10 6.28 12 7.79 27 20.9 15 5.39 28 0.39 78 0.02 30 1.63 81 6.88 13 19.0 16 10.3 19
RNLOD-Flow [121]30.4 0.79 7 4.69 7 0.34 10 2.67 32 17.2 36 1.09 28 4.46 42 14.5 38 1.53 34 2.01 20 14.3 22 0.60 27 14.2 22 23.1 21 8.72 26 8.21 34 19.9 12 5.90 41 0.35 74 0.03 85 1.48 79 6.51 10 17.2 7 9.80 16
HAST [109]31.2 0.92 37 5.41 35 0.35 12 3.21 48 13.6 18 1.99 68 2.45 3 8.47 3 0.29 1 2.24 34 14.5 27 0.40 9 11.7 7 19.4 8 3.63 3 11.0 83 24.2 35 6.87 77 2.75 117 0.00 1 11.6 118 4.05 1 13.1 1 4.43 3
ProbFlowFields [128]32.6 1.16 69 6.86 77 0.85 90 2.32 20 14.6 23 1.45 41 4.28 35 14.9 42 2.43 60 1.56 9 9.89 6 0.50 13 18.1 45 29.1 47 11.5 45 4.44 2 20.6 13 4.20 11 0.00 1 0.02 30 0.00 1 8.97 43 25.7 46 9.75 13
IROF++ [58]33.0 0.96 44 5.70 52 0.44 43 3.00 42 19.4 49 1.37 38 3.90 24 12.8 19 1.96 48 2.36 40 15.8 38 0.69 42 14.1 20 23.0 19 8.22 24 9.14 50 25.0 40 6.07 52 0.00 1 0.02 30 0.00 1 7.35 22 20.3 26 10.8 27
TC-Flow [46]33.3 0.75 5 4.45 5 0.38 18 2.04 12 12.6 10 0.70 15 4.23 34 14.4 36 0.77 11 2.56 47 17.5 50 0.63 30 17.1 40 27.8 41 9.45 30 5.73 12 25.6 43 3.12 6 0.22 61 0.02 30 2.41 92 10.1 52 25.9 48 15.4 71
Efficient-NL [60]33.3 0.93 38 5.47 40 0.39 23 2.76 35 18.0 41 1.11 29 4.12 32 13.3 27 1.15 23 2.15 27 14.1 20 0.66 34 13.0 12 21.3 12 7.16 14 10.6 77 23.4 29 6.41 66 0.26 64 0.02 30 1.13 66 7.35 22 17.4 9 10.9 29
SVFilterOh [111]33.9 1.07 57 6.27 64 0.44 43 2.07 14 13.1 13 0.72 16 3.24 12 11.2 12 1.05 21 1.99 19 13.8 17 0.56 19 12.6 11 21.1 11 3.80 4 10.5 75 22.4 20 5.97 46 2.31 113 0.39 108 6.95 108 4.87 2 14.8 2 6.01 6
FESL [72]34.0 0.83 15 4.91 16 0.36 14 3.90 73 21.6 67 1.75 56 4.06 29 13.4 29 1.61 37 2.02 22 14.1 20 0.56 19 13.3 14 21.7 14 8.08 21 9.19 52 22.0 19 6.25 58 0.34 73 0.02 30 1.16 68 7.51 25 18.3 12 11.0 33
Classic+CPF [83]34.2 0.89 25 5.26 26 0.41 30 3.03 43 19.4 49 1.27 36 4.14 33 13.6 30 1.64 40 2.12 26 14.4 24 0.64 32 13.6 15 22.2 16 7.82 17 9.85 66 22.6 22 6.18 55 0.36 75 0.02 30 1.50 80 7.07 17 18.5 13 10.5 21
FMOF [94]35.2 0.83 15 4.92 17 0.43 39 3.35 55 20.0 54 1.57 50 3.37 16 11.4 15 1.46 32 1.98 18 13.8 17 0.56 19 14.2 22 23.2 22 8.08 21 9.98 70 22.7 23 6.19 56 0.42 81 0.02 30 1.87 86 8.11 36 21.0 30 10.5 21
HBM-GC [105]36.3 1.24 75 7.38 79 0.52 57 2.50 30 15.5 31 1.40 40 4.06 29 14.1 34 1.32 26 1.77 13 13.2 12 0.61 29 13.7 16 22.1 15 8.06 20 8.98 45 16.5 4 4.42 12 1.30 105 0.02 30 3.28 99 7.20 19 19.8 24 10.8 27
Ramp [62]36.7 0.90 27 5.36 30 0.41 30 3.14 46 20.0 54 1.52 45 3.86 21 12.9 21 1.93 46 2.01 20 14.5 27 0.59 25 15.1 29 24.4 28 9.67 32 9.44 56 22.9 26 5.95 44 0.29 68 0.02 30 1.38 75 7.83 30 20.9 28 11.5 43
Aniso-Texture [82]36.7 0.73 4 4.33 4 0.33 7 1.83 8 12.4 9 0.91 23 6.29 60 18.2 54 1.57 35 1.35 6 11.4 8 0.18 4 19.7 57 29.7 49 16.8 76 9.10 49 26.1 45 5.78 38 0.26 64 0.18 96 0.07 42 9.32 47 24.3 45 12.2 51
Sparse-NonSparse [56]37.0 0.88 23 5.21 24 0.40 25 3.16 47 19.8 53 1.53 48 3.90 24 12.9 21 2.00 50 2.18 29 15.2 35 0.66 34 15.6 34 25.4 35 10.1 36 9.38 55 23.7 33 5.97 46 0.31 70 0.00 1 1.28 71 7.74 27 20.9 28 11.2 38
PMF [73]37.2 1.08 58 6.23 62 0.35 12 2.33 21 14.8 24 0.60 10 3.87 22 13.6 30 0.62 9 2.29 36 14.4 24 0.44 11 14.0 19 23.3 23 3.86 5 9.55 57 28.3 63 6.63 71 0.89 99 0.79 118 3.74 103 5.66 5 15.8 4 8.92 8
CombBMOF [113]37.7 0.91 31 5.38 31 0.33 7 2.30 19 13.4 15 0.64 14 3.33 15 11.5 16 0.78 12 2.08 24 15.3 36 0.77 49 13.9 17 22.3 17 8.24 25 13.0 101 26.2 46 11.4 108 0.56 86 0.02 30 0.86 60 8.93 42 21.1 31 15.6 72
NL-TV-NCC [25]38.5 0.96 44 5.68 49 0.22 2 2.93 39 18.4 43 0.59 9 4.37 40 14.6 39 0.47 4 1.63 11 14.6 29 0.17 2 18.6 47 29.8 50 9.76 34 11.8 92 31.2 85 7.70 91 0.12 50 0.00 1 0.30 51 9.40 49 26.0 50 9.75 13
LSM [39]39.0 0.86 21 5.13 22 0.40 25 3.22 49 20.3 57 1.54 49 4.08 31 13.6 30 1.93 46 2.09 25 14.9 33 0.63 30 15.6 34 25.3 34 10.2 37 9.58 58 24.6 36 5.95 44 0.30 69 0.02 30 1.43 76 7.97 32 21.7 34 11.1 34
OFH [38]40.3 0.81 9 4.70 8 0.31 4 2.96 41 17.3 37 1.20 31 6.37 62 19.7 60 1.51 33 2.92 64 20.6 66 0.91 55 20.7 66 32.4 69 14.2 58 6.39 18 31.5 87 3.74 9 0.00 1 0.00 1 0.00 1 11.0 58 33.0 76 12.8 54
Sparse Occlusion [54]40.4 0.90 27 5.06 21 0.46 48 2.35 23 14.9 26 1.01 25 4.83 45 15.7 47 1.09 22 2.38 41 17.2 48 0.66 34 16.7 39 26.9 39 8.75 27 7.98 31 24.6 36 5.42 30 0.60 90 0.61 114 0.84 58 8.41 40 22.7 38 10.5 21
Classic+NL [31]40.8 0.91 31 5.38 31 0.45 47 3.22 49 20.4 58 1.49 44 3.97 26 13.1 24 1.97 49 2.33 37 15.0 34 0.68 38 14.9 26 24.0 26 10.2 37 9.83 63 23.9 34 6.24 57 0.33 72 0.02 30 1.28 71 7.80 29 21.2 32 11.1 34
EPPM w/o HM [88]41.5 1.16 69 5.61 46 0.33 7 2.33 21 15.4 28 0.60 10 4.28 35 14.7 40 0.32 2 2.20 31 14.7 31 0.59 25 14.3 24 23.6 24 5.47 8 12.2 93 29.9 77 7.04 79 2.28 112 0.03 85 6.80 107 6.72 12 19.4 20 8.96 9
MDP-Flow [26]41.6 0.84 17 5.01 19 0.47 49 2.37 24 13.0 11 1.76 57 4.04 27 14.0 33 2.72 65 2.70 53 21.0 67 0.98 60 18.0 44 28.5 44 13.1 54 8.58 40 26.6 50 5.71 35 0.00 1 0.02 30 0.00 1 12.4 74 31.9 68 16.2 76
CostFilter [40]44.2 1.14 65 6.62 70 0.40 25 2.38 25 14.8 24 0.53 6 3.58 17 12.5 18 0.84 14 2.62 50 17.3 49 0.51 15 14.9 26 24.9 32 4.14 7 9.99 71 29.2 72 6.06 51 1.38 106 0.81 119 6.01 106 8.00 33 23.2 42 9.84 17
OAR-Flow [125]44.8 1.00 49 5.81 54 0.55 66 3.94 75 18.5 44 1.99 68 6.44 64 20.5 64 2.66 64 2.84 61 18.5 54 0.71 46 18.9 51 30.1 54 11.2 42 5.95 15 26.2 46 3.42 8 0.00 1 0.00 1 0.00 1 9.00 44 26.4 52 12.2 51
Complementary OF [21]45.4 0.91 31 5.39 33 0.43 39 2.42 27 15.2 27 0.74 17 4.36 39 15.5 45 1.16 24 2.63 51 19.5 59 0.76 48 22.5 83 33.0 74 20.1 82 9.92 68 28.5 66 4.80 22 0.00 1 0.00 1 0.00 1 12.6 77 35.6 95 16.9 80
S2D-Matching [84]46.3 1.09 60 6.39 67 0.51 55 3.35 55 20.9 60 1.52 45 5.55 53 17.8 53 2.21 53 1.91 16 13.6 16 0.56 19 15.2 30 24.5 30 9.72 33 10.1 73 23.6 31 6.34 62 0.52 83 0.02 30 2.09 90 7.62 26 20.0 25 11.6 46
COFM [59]47.1 1.15 66 6.80 75 0.58 74 2.62 31 15.8 34 1.25 35 5.68 55 18.2 54 2.12 51 2.20 31 13.5 15 0.58 24 19.6 56 31.0 61 15.7 70 9.91 67 23.3 28 6.03 50 0.81 96 0.00 1 1.43 76 7.76 28 20.7 27 10.6 25
SimpleFlow [49]47.5 0.94 40 5.57 45 0.44 43 3.52 59 21.7 68 1.79 60 5.82 56 17.6 52 2.36 58 2.55 46 16.5 42 0.81 52 16.3 37 26.0 36 11.8 46 10.3 74 23.1 27 6.33 61 0.24 62 0.00 1 0.81 57 8.33 37 22.7 38 11.5 43
IROF-TV [53]47.5 1.10 62 6.24 63 0.57 71 3.29 54 21.5 65 1.72 55 4.40 41 14.2 35 1.87 45 3.04 68 21.7 73 1.11 64 16.2 36 26.0 36 11.3 44 9.60 60 32.4 92 5.72 36 0.00 1 0.02 30 0.00 1 8.00 33 22.4 37 11.2 38
2DHMM-SAS [92]47.9 0.91 31 5.42 36 0.41 30 3.67 66 21.9 70 1.52 45 5.62 54 16.1 49 2.28 56 2.44 43 15.9 39 0.72 47 15.0 28 24.2 27 9.48 31 11.1 86 25.1 42 6.36 64 0.38 77 0.02 30 1.67 83 8.04 35 21.7 34 11.7 47
ACK-Prior [27]48.1 0.82 12 4.87 13 0.32 6 2.12 16 13.7 19 0.43 3 3.68 19 12.9 21 0.92 19 1.77 13 14.0 19 0.19 5 19.5 55 28.2 43 16.7 75 12.3 95 29.1 71 7.52 89 2.44 115 0.30 103 8.47 114 13.9 84 30.2 63 18.0 83
ROF-ND [107]49.2 1.27 80 6.15 61 0.38 18 4.71 84 18.9 46 1.07 27 4.89 46 15.6 46 1.21 25 0.65 1 6.22 1 0.29 7 19.7 57 30.5 56 14.5 60 11.5 91 26.5 49 6.25 58 0.39 78 0.02 30 0.84 58 12.3 73 31.5 66 13.8 62
TV-L1-MCT [64]50.5 0.90 27 5.30 28 0.41 30 3.73 67 22.1 71 1.79 60 4.61 44 15.3 43 1.63 39 2.16 28 14.7 31 0.67 37 17.6 42 27.1 40 15.2 66 11.0 83 25.0 40 6.58 70 0.36 75 0.02 30 2.46 94 9.73 50 23.0 40 16.2 76
RFlow [90]52.3 0.91 31 5.43 37 0.47 49 2.46 29 15.6 32 1.13 30 6.42 63 19.3 59 1.66 41 2.77 56 21.4 71 1.16 67 20.7 66 31.7 65 18.0 80 9.69 62 30.4 78 6.14 53 0.01 36 0.02 30 0.15 45 10.9 57 30.0 62 13.1 57
S2F-IF [123]53.8 1.28 82 7.44 83 0.84 89 3.48 58 22.4 74 1.86 64 5.52 51 19.0 56 3.05 66 2.96 66 16.9 46 1.21 69 21.3 73 34.1 83 14.5 60 5.45 6 25.6 43 4.62 14 0.00 1 0.00 1 0.00 1 12.0 69 32.3 72 14.7 65
DPOF [18]54.1 1.11 63 6.56 69 0.53 59 4.51 82 21.0 61 2.42 80 3.25 13 11.3 14 0.84 14 2.03 23 15.3 36 0.70 44 17.8 43 28.8 45 9.36 29 11.4 90 26.9 51 6.26 60 4.21 121 0.02 30 10.5 117 10.2 53 26.7 53 11.8 48
Occlusion-TV-L1 [63]54.1 0.98 47 5.50 42 0.48 51 3.25 51 19.5 51 1.82 63 7.36 77 21.2 72 2.44 61 2.73 54 20.4 64 0.93 58 20.5 63 32.1 66 15.5 68 8.22 35 28.1 60 6.69 73 0.00 1 0.00 1 0.00 1 13.1 81 33.5 83 15.9 75
DeepFlow2 [108]54.4 1.04 54 5.76 53 0.54 64 3.86 71 19.7 52 2.02 71 6.79 67 20.5 64 3.55 72 3.64 79 22.5 76 1.44 76 18.8 49 30.1 54 12.0 48 7.01 24 27.7 58 4.65 15 0.00 1 0.02 30 0.00 1 12.6 77 32.0 70 16.9 80
FlowFields+ [130]56.1 1.31 84 7.52 85 0.92 97 3.61 62 23.0 77 1.98 67 6.08 57 20.6 66 3.39 69 2.82 59 16.4 41 1.23 70 21.4 76 34.3 86 14.1 56 5.45 6 27.5 57 4.68 18 0.00 1 0.02 30 0.00 1 11.3 61 33.1 79 11.4 41
TF+OM [100]57.2 1.11 63 6.49 68 0.69 82 2.94 40 16.8 35 1.78 58 7.92 81 20.7 68 9.65 93 2.85 62 20.5 65 1.05 63 22.0 81 32.2 67 20.3 83 8.74 41 28.3 63 4.67 17 0.00 1 0.02 30 0.00 1 12.1 71 30.5 65 15.8 74
AggregFlow [97]58.2 1.68 99 9.22 104 0.86 92 4.76 85 25.3 89 2.56 83 7.33 76 22.6 80 5.07 87 2.64 52 16.5 42 0.69 42 19.1 53 30.7 58 11.2 42 5.11 4 17.3 5 3.29 7 0.14 53 0.02 30 0.96 63 9.35 48 25.7 46 13.1 57
Steered-L1 [118]58.2 0.63 1 3.72 1 0.42 34 1.53 3 10.4 3 0.75 18 3.84 20 13.2 26 1.32 26 2.80 57 21.1 69 0.98 60 21.2 72 31.2 62 20.3 83 10.7 80 29.3 74 7.45 88 4.27 122 0.34 105 19.6 124 16.5 92 33.3 80 24.6 98
FlowFields [110]58.4 1.32 85 7.63 87 0.93 99 3.61 62 22.9 76 2.00 70 6.11 58 20.6 66 3.58 73 2.85 62 16.6 44 1.24 71 21.9 80 35.0 95 15.1 65 5.70 11 28.0 59 4.72 19 0.00 1 0.02 30 0.00 1 11.7 64 33.4 81 11.5 43
CRTflow [80]58.6 1.02 53 5.69 50 0.58 74 3.12 44 18.1 42 1.46 42 6.89 69 20.9 70 2.40 59 3.38 75 22.2 74 1.42 75 19.7 57 31.3 63 12.3 49 11.0 83 35.9 104 10.1 103 0.00 1 0.00 1 0.00 1 12.0 69 33.6 84 14.7 65
ComplOF-FED-GPU [35]59.4 0.85 19 5.04 20 0.42 34 3.90 73 21.4 63 1.78 58 4.90 47 16.8 50 1.41 30 3.18 70 21.1 69 1.03 62 21.6 78 33.8 81 15.4 67 10.8 81 34.7 102 5.93 43 0.12 50 0.02 30 1.43 76 11.9 66 34.2 87 15.3 69
TCOF [69]59.6 1.00 49 5.63 47 0.59 77 3.53 60 21.5 65 1.69 54 7.64 79 22.0 76 3.79 76 2.80 57 19.9 62 0.77 49 21.1 70 32.7 71 13.9 55 7.79 27 20.7 14 5.77 37 0.92 100 0.03 85 3.23 98 8.40 39 23.2 42 11.4 41
Adaptive [20]61.0 1.05 55 6.01 58 0.48 51 3.27 52 20.1 56 1.79 60 7.11 73 20.1 61 1.62 38 3.29 72 22.4 75 1.15 66 18.8 49 29.8 50 12.6 51 10.6 77 28.4 65 6.72 75 0.57 89 0.71 117 0.96 63 8.64 41 23.1 41 10.9 29
SRR-TVOF-NL [91]62.2 1.15 66 6.13 60 0.60 78 5.04 87 23.3 79 2.68 85 8.17 82 22.9 81 4.22 84 2.76 55 16.9 46 0.68 38 19.8 60 29.0 46 17.7 79 8.07 32 27.0 53 6.17 54 0.16 55 0.02 30 0.86 60 11.8 65 25.9 48 15.3 69
TV-L1-improved [17]63.4 0.94 40 5.45 38 0.52 57 2.91 38 17.8 39 1.58 51 7.00 71 20.2 63 2.24 55 3.00 67 21.5 72 1.16 67 20.6 64 32.3 68 15.0 63 12.2 93 34.2 100 7.87 92 0.19 57 0.30 103 0.49 54 10.7 55 29.7 61 12.8 54
DeepFlow [86]63.6 1.19 71 6.04 59 0.57 71 4.41 79 21.3 62 2.41 79 8.35 85 22.9 81 6.63 92 4.03 88 24.5 84 1.69 84 19.0 52 30.9 59 11.8 46 7.29 25 29.5 76 4.88 23 0.00 1 0.02 30 0.00 1 15.7 91 35.1 93 23.4 95
PGM-C [120]64.8 1.52 92 8.68 98 0.99 104 3.66 64 23.0 77 2.03 72 6.30 61 21.2 72 3.90 78 3.82 84 22.9 80 1.68 83 21.3 73 34.3 86 14.1 56 6.89 23 28.8 68 5.60 33 0.00 1 0.02 30 0.00 1 11.9 66 34.3 88 14.2 64
Aniso. Huber-L1 [22]66.0 1.06 56 5.69 50 0.65 79 5.24 88 25.4 90 3.29 89 8.19 83 21.4 75 4.09 82 3.10 69 21.0 67 0.97 59 18.5 46 29.1 47 12.6 51 9.08 47 27.0 53 5.56 32 0.68 92 0.08 93 2.93 97 9.25 46 24.1 44 11.8 48
Classic++ [32]67.1 1.00 49 5.92 57 0.56 68 3.28 53 19.2 47 1.87 65 6.88 68 20.7 68 3.38 68 3.41 77 23.6 82 1.30 72 20.8 68 33.2 77 15.0 63 10.0 72 31.8 89 6.69 73 0.66 91 0.02 30 2.59 95 11.3 61 29.5 58 13.5 60
CPM-Flow [116]67.1 1.53 93 8.72 100 0.98 101 3.74 68 23.5 80 2.08 73 6.22 59 20.9 70 3.88 77 3.78 82 22.5 76 1.64 81 21.3 73 34.4 88 14.2 58 7.87 29 28.8 68 6.40 65 0.00 1 0.02 30 0.00 1 12.5 76 35.6 95 14.9 67
Bartels [41]67.9 1.28 82 7.59 86 0.50 53 2.39 26 15.4 28 1.04 26 5.52 51 19.2 57 2.54 63 2.83 60 19.9 62 1.30 72 22.7 86 34.1 83 20.4 85 9.92 68 30.5 79 6.93 78 1.88 111 0.02 30 12.3 119 12.7 79 31.9 68 16.4 78
CBF [12]68.5 0.85 19 4.89 15 0.43 39 4.99 86 22.3 73 4.63 96 6.60 65 19.2 57 4.08 81 3.61 78 24.5 84 1.49 77 20.0 61 30.9 59 16.2 73 9.67 61 27.4 56 5.64 34 2.65 116 0.37 106 6.97 109 11.5 63 28.4 57 16.9 80
Kuang [131]68.8 1.38 87 8.01 90 0.89 93 4.13 76 25.8 91 2.18 75 6.98 70 23.6 85 3.42 70 3.29 72 19.2 56 1.38 74 23.1 89 36.8 102 15.8 71 9.05 46 31.3 86 7.14 82 0.00 1 0.02 30 0.00 1 11.2 60 30.4 64 16.6 79
EpicFlow [102]69.4 1.51 90 8.63 97 0.98 101 3.76 69 23.5 80 2.11 74 7.14 74 23.6 85 3.97 80 3.79 83 22.6 78 1.64 81 21.5 77 34.4 88 14.8 62 8.97 44 29.2 72 6.53 67 0.00 1 0.02 30 0.00 1 12.4 74 34.5 89 15.2 68
LocallyOriented [52]70.5 1.78 105 9.64 107 0.77 86 6.11 96 28.2 97 3.79 93 10.9 93 28.0 98 5.52 89 3.28 71 19.5 59 1.55 78 22.8 87 33.9 82 17.6 78 9.84 65 24.6 36 6.63 71 0.00 1 0.00 1 0.00 1 11.9 66 29.6 60 15.7 73
CLG-TV [48]71.4 1.01 52 5.46 39 0.50 53 4.16 78 23.5 80 2.40 78 7.52 78 21.2 72 2.51 62 3.33 74 22.8 79 1.14 65 20.9 69 32.4 69 15.6 69 8.94 43 31.7 88 6.35 63 1.27 104 1.18 122 3.55 101 11.1 59 28.2 56 13.5 60
TriangleFlow [30]71.8 1.19 71 6.73 74 0.53 59 3.88 72 21.8 69 1.64 53 6.61 66 20.1 61 1.59 36 2.35 39 19.3 57 0.89 54 25.6 99 37.3 104 23.5 97 13.4 103 30.5 79 8.48 98 0.81 96 0.17 95 1.33 74 10.7 55 28.1 55 13.1 57
Rannacher [23]72.5 1.09 60 6.27 64 0.54 64 3.77 70 22.1 71 2.27 76 7.89 80 22.4 78 3.34 67 3.67 80 23.5 81 1.61 79 21.1 70 33.1 75 15.8 71 12.9 99 35.4 103 7.98 93 0.43 82 0.02 30 1.63 81 10.5 54 29.5 58 12.8 54
Fusion [6]72.5 1.15 66 6.83 76 0.71 84 2.10 15 14.5 22 1.23 34 4.58 43 15.4 44 3.60 74 3.73 81 27.2 93 2.38 90 23.9 92 33.7 79 26.4 102 8.36 37 27.3 55 7.11 81 1.00 101 0.64 116 2.66 96 14.5 89 34.0 86 18.7 85
SIOF [67]73.2 1.24 75 6.63 71 0.51 55 5.26 89 26.2 92 3.22 88 11.5 94 26.1 89 12.3 96 4.49 90 27.4 96 2.29 89 22.8 87 33.3 78 23.4 96 8.56 39 28.8 68 7.15 83 0.00 1 0.02 30 0.00 1 13.6 83 32.1 71 23.6 97
F-TV-L1 [15]74.0 1.22 73 6.63 71 0.53 59 5.86 94 24.8 87 3.51 92 9.25 88 23.4 84 3.44 71 3.91 85 24.9 86 1.61 79 20.3 62 31.5 64 16.2 73 11.3 88 30.9 83 7.40 87 0.15 54 0.47 111 0.17 46 9.88 51 27.6 54 11.1 34
Local-TV-L1 [65]75.8 1.57 94 7.45 84 0.67 81 7.93 100 28.0 96 5.97 101 12.9 100 26.6 91 12.2 95 6.04 104 31.1 103 3.55 103 18.7 48 29.9 53 12.9 53 9.33 54 28.1 60 5.97 46 0.00 1 0.02 30 0.00 1 21.0 107 37.7 100 37.5 113
p-harmonic [29]76.1 1.08 58 6.28 66 0.55 66 3.66 64 20.5 59 2.48 82 8.22 84 23.0 83 3.92 79 5.04 93 28.4 99 3.51 101 24.8 96 34.1 83 30.1 105 7.78 26 32.3 91 6.54 68 0.19 57 0.44 110 0.00 1 14.2 88 33.0 76 21.8 91
BriefMatch [124]76.6 0.96 44 5.52 44 0.53 59 3.55 61 18.6 45 1.97 66 4.95 48 16.9 51 1.82 44 2.57 48 19.7 61 0.92 57 21.8 79 32.7 71 20.8 88 16.2 112 33.7 98 13.5 114 3.95 120 0.97 121 15.8 120 17.3 97 34.7 91 25.4 100
TriFlow [95]79.0 1.51 90 8.71 99 0.78 87 4.56 83 22.8 75 3.37 91 12.5 98 28.2 99 17.8 100 2.41 42 18.3 52 0.91 55 24.8 96 34.4 88 25.7 100 5.97 16 23.5 30 4.74 20 19.3 128 0.27 101 59.0 128 13.2 82 32.5 74 14.1 63
Dynamic MRF [7]79.1 1.26 78 7.42 81 0.57 71 3.39 57 21.4 63 1.58 51 7.00 71 22.5 79 2.22 54 3.40 76 24.1 83 1.69 84 25.9 103 37.6 105 24.8 99 14.4 107 41.5 113 9.85 102 0.09 48 0.00 1 0.96 63 19.2 103 39.4 105 25.5 101
DF-Auto [115]79.8 1.84 106 8.87 102 0.90 94 8.40 101 30.1 100 6.82 102 13.3 101 27.9 97 19.6 101 5.29 95 26.6 89 3.01 94 22.2 82 32.9 73 21.0 89 5.80 13 23.6 31 5.02 25 0.18 56 0.61 114 0.00 1 14.8 90 32.4 73 19.9 86
Brox et al. [5]82.0 1.22 73 6.66 73 0.70 83 4.15 77 24.3 85 2.39 77 7.21 75 22.1 77 4.18 83 4.91 91 26.3 88 2.65 91 26.2 106 35.7 99 31.4 107 10.5 75 33.4 97 7.34 86 0.01 36 0.13 94 0.00 1 17.1 96 39.1 104 23.0 94
FlowNet2 [122]83.2 2.63 111 12.9 114 1.14 108 17.9 112 43.1 114 16.1 114 17.0 104 32.9 104 25.3 112 3.92 86 16.7 45 2.16 87 25.8 102 40.2 112 17.0 77 10.6 77 28.2 62 8.09 94 0.02 39 0.00 1 0.20 48 12.2 72 34.5 89 9.71 12
SuperFlow [81]84.4 1.26 78 5.91 56 0.66 80 6.58 98 24.8 87 5.70 100 12.7 99 26.7 92 20.1 102 5.60 99 28.6 100 3.33 98 24.6 95 33.7 79 31.7 110 8.09 33 30.8 82 7.19 84 0.02 39 0.07 91 0.02 41 16.6 93 37.3 98 22.5 92
Second-order prior [8]88.2 1.24 75 6.93 78 0.58 74 5.26 89 27.0 94 3.34 90 9.68 90 26.8 93 5.39 88 4.25 89 26.1 87 2.25 88 22.5 83 34.4 88 19.0 81 12.9 99 41.2 112 8.26 97 1.14 103 0.07 91 2.41 92 12.7 79 32.5 74 18.2 84
SegOF [10]90.1 1.62 97 9.24 105 1.14 108 14.8 111 38.8 111 14.3 112 17.8 106 33.2 105 22.3 106 6.57 105 27.5 97 4.43 106 32.5 116 41.8 115 43.4 120 14.1 106 38.0 107 10.5 104 0.00 1 0.00 1 0.00 1 14.0 85 33.7 85 12.6 53
StereoOF-V1MT [119]91.1 1.42 89 8.08 93 0.56 68 6.56 97 34.1 106 2.73 86 10.0 92 29.8 101 2.19 52 4.91 91 34.6 108 2.66 92 31.4 115 44.5 117 31.4 107 15.8 111 48.0 119 11.6 109 0.05 46 0.00 1 0.52 55 24.0 110 48.7 117 28.5 104
Shiralkar [42]91.7 1.27 80 7.43 82 0.53 59 5.83 93 30.1 100 2.93 87 9.62 89 26.2 90 3.70 75 5.11 94 30.7 102 3.08 95 25.7 100 39.1 109 22.5 94 17.9 113 45.5 115 9.73 101 1.80 109 0.00 1 8.23 113 18.4 101 44.9 113 19.9 86
FlowNetS+ft+v [112]92.8 1.40 88 7.39 80 0.80 88 5.75 92 23.6 83 4.35 95 11.7 96 27.3 95 12.4 97 5.33 96 27.2 93 3.18 97 25.7 100 35.4 98 26.9 103 8.52 38 32.0 90 6.85 76 2.34 114 1.61 125 10.1 116 14.0 85 34.9 92 20.1 89
CNN-flow-warp+ref [117]93.2 1.63 98 9.14 103 0.91 96 5.41 91 24.0 84 4.66 97 11.6 95 29.8 101 10.7 94 5.59 98 27.1 92 3.43 99 26.6 108 36.0 100 31.5 109 11.3 88 33.1 95 7.62 90 0.03 42 0.25 99 0.07 42 20.4 105 40.5 108 28.3 103
Ad-TV-NDC [36]93.5 3.59 116 8.26 94 6.67 125 21.3 116 38.0 109 22.4 119 19.7 109 33.6 106 21.8 105 13.5 111 33.9 107 15.0 112 19.4 54 30.6 57 12.5 50 9.58 58 28.6 67 6.54 68 0.21 59 0.37 106 0.17 46 28.1 116 43.2 111 47.4 122
Learning Flow [11]93.8 1.35 86 7.83 89 0.56 68 4.48 81 26.8 93 2.43 81 9.85 91 27.1 94 5.06 86 6.65 106 33.5 106 4.13 104 29.9 112 40.0 111 34.1 114 12.8 97 38.5 109 8.86 100 0.28 67 0.29 102 1.13 66 17.0 95 37.6 99 22.8 93
StereoFlow [44]93.8 7.67 126 21.8 123 3.86 122 51.5 128 74.0 129 46.2 125 43.7 129 63.5 129 36.8 122 51.6 128 79.4 129 47.5 127 26.1 104 38.0 106 21.1 90 5.83 14 26.9 51 4.93 24 0.00 1 0.02 30 0.00 1 20.7 106 38.1 102 29.7 105
2bit-BM-tele [98]94.2 1.75 101 9.59 106 0.85 90 4.44 80 24.7 86 2.62 84 8.64 86 25.8 88 4.56 85 3.99 87 27.8 98 1.98 86 22.6 85 33.1 75 20.5 86 14.6 108 32.7 94 10.7 105 5.96 125 1.68 126 21.9 126 14.1 87 33.4 81 19.9 86
SPSA-learn [13]94.9 1.77 103 7.72 88 0.90 94 11.0 105 33.2 103 9.40 107 17.3 105 34.2 107 22.7 108 11.0 108 32.2 104 10.9 108 26.1 104 34.9 94 31.8 112 12.8 97 34.2 100 11.9 110 0.00 1 0.03 85 0.00 1 25.5 114 39.4 105 39.6 115
LDOF [28]95.0 1.59 96 8.06 91 0.97 100 6.08 95 27.9 95 3.79 93 8.98 87 25.2 87 6.05 90 5.90 102 33.2 105 3.14 96 23.5 90 34.5 92 22.7 95 9.83 63 34.0 99 7.30 85 0.86 98 1.28 123 3.67 102 16.7 94 39.7 107 23.5 96
BlockOverlap [61]96.2 1.73 100 8.32 95 1.07 105 8.43 102 28.3 98 7.39 103 14.3 102 29.4 100 16.3 99 6.01 103 26.7 91 4.24 105 20.6 64 29.8 50 20.6 87 12.4 96 29.4 75 8.20 96 3.91 119 0.92 120 16.5 122 19.1 102 31.7 67 36.0 109
Filter Flow [19]96.7 1.97 108 10.2 109 1.14 108 8.79 103 33.9 105 5.66 98 18.8 107 35.7 108 26.2 113 21.9 115 42.4 112 22.0 115 27.9 110 36.8 102 35.0 115 13.2 102 32.6 93 8.11 95 0.05 46 0.02 30 0.37 53 17.5 98 33.0 76 25.2 99
HBpMotionGpu [43]97.2 2.47 110 11.8 111 1.09 106 11.4 107 35.3 107 10.0 109 20.3 112 38.5 112 26.3 114 5.67 100 26.6 89 3.51 101 24.1 93 34.8 93 26.1 101 10.9 82 30.7 81 7.04 79 0.27 66 0.05 89 0.89 62 19.3 104 37.1 97 32.8 107
GraphCuts [14]100.7 1.57 94 8.32 95 0.92 97 12.3 109 39.3 112 8.40 104 15.2 103 31.3 103 23.1 109 5.40 97 28.8 101 2.88 93 25.4 98 38.0 106 21.1 90 24.5 123 31.1 84 14.4 116 1.86 110 0.02 30 7.91 112 23.9 109 41.6 110 37.4 112
UnFlow [129]100.9 7.34 123 24.6 128 3.32 119 21.7 117 50.1 118 19.1 115 26.8 119 53.1 125 25.0 110 13.7 112 42.5 113 12.5 111 42.2 124 53.7 125 45.6 123 15.1 110 46.2 116 12.1 111 0.00 1 0.00 1 0.00 1 17.5 98 43.7 112 21.5 90
IAOF [50]101.0 1.77 103 8.80 101 0.98 101 11.2 106 32.5 102 9.32 106 19.8 110 35.7 108 20.2 103 17.5 113 37.6 109 19.8 113 23.7 91 35.0 95 22.3 93 18.1 116 40.2 110 10.9 106 0.56 86 0.02 30 2.17 91 24.8 112 37.8 101 43.9 117
IAOF2 [51]103.2 1.85 107 9.64 107 1.13 107 7.56 99 29.4 99 5.66 98 12.2 97 27.5 96 15.7 98 32.6 121 43.3 115 38.7 124 24.3 94 35.0 95 23.9 98 17.9 113 33.1 95 13.0 112 1.11 102 0.25 99 4.83 104 17.8 100 35.5 94 25.9 102
Black & Anandan [4]103.7 1.75 101 8.07 92 0.73 85 11.6 108 36.6 108 8.94 105 18.9 108 36.4 110 20.3 104 12.4 110 40.5 111 12.0 110 26.3 107 36.2 101 30.5 106 13.4 103 37.3 105 11.0 107 0.75 94 0.42 109 1.90 88 21.4 108 38.6 103 32.5 106
Nguyen [33]105.5 2.73 112 11.0 110 1.16 112 33.4 122 38.0 109 43.1 124 24.6 116 41.9 113 32.1 119 28.7 119 46.5 116 32.2 120 29.8 111 39.8 110 35.5 116 13.9 105 40.4 111 13.0 112 0.03 42 0.02 30 0.20 48 31.6 117 46.3 115 50.5 124
Modified CLG [34]106.7 2.46 109 12.2 112 1.37 113 10.5 104 33.6 104 9.99 108 20.2 111 37.9 111 27.9 116 9.52 107 38.0 110 7.95 107 27.6 109 38.6 108 31.7 110 11.2 87 37.6 106 8.53 99 0.70 93 0.24 98 3.33 100 24.7 111 45.8 114 38.5 114
2D-CLG [1]107.6 6.98 122 23.0 125 3.54 120 20.1 115 40.7 113 21.4 117 26.6 118 44.0 114 36.7 120 34.7 122 55.1 120 39.7 125 31.1 114 41.5 114 38.2 117 15.0 109 42.0 114 13.6 115 0.02 39 0.02 30 0.12 44 31.7 118 51.0 119 44.9 118
GroupFlow [9]110.2 3.39 114 16.8 119 1.37 113 23.0 118 51.6 120 21.5 118 20.7 113 45.1 117 22.3 106 5.67 100 27.3 95 3.50 100 34.6 118 51.5 123 22.0 92 22.4 120 47.9 118 25.4 124 0.55 85 0.47 111 1.70 84 25.2 113 47.9 116 33.5 108
SILK [79]110.6 3.45 115 15.8 117 2.61 117 19.0 113 44.9 115 19.5 116 23.5 115 44.1 115 26.6 115 12.0 109 42.7 114 11.1 109 35.3 119 46.3 120 44.8 121 18.0 115 49.4 120 14.5 117 1.53 107 0.00 1 5.00 105 32.1 121 50.8 118 47.1 121
Horn & Schunck [3]112.8 3.02 113 12.7 113 1.15 111 14.5 110 45.9 116 11.1 110 22.6 114 44.4 116 25.2 111 21.6 114 47.3 117 22.5 116 34.0 117 43.8 116 43.1 119 19.6 117 51.5 122 18.6 120 0.56 86 0.22 97 1.77 85 34.9 123 55.9 123 46.4 120
Heeger++ [104]113.9 3.74 117 16.1 118 1.49 115 23.6 119 64.4 128 14.1 111 36.0 125 49.4 123 37.3 123 38.6 126 67.3 126 38.6 123 46.7 127 58.2 127 50.9 126 36.6 127 68.1 129 34.5 128 0.41 80 0.00 1 1.87 86 31.8 119 51.3 120 37.0 110
TI-DOFE [24]114.2 7.50 124 18.0 120 10.6 126 41.8 126 54.1 123 49.7 126 31.9 123 54.7 128 39.7 125 41.8 127 61.8 123 48.6 128 35.5 121 45.7 119 45.0 122 21.9 119 52.6 123 21.7 122 0.25 63 0.00 1 1.31 73 43.7 126 61.4 126 58.6 126
FFV1MT [106]116.2 4.51 119 19.1 121 2.74 118 19.4 114 58.6 127 14.7 113 40.8 127 53.4 127 50.0 128 38.5 125 73.8 128 37.7 121 46.4 126 56.0 126 56.7 129 33.1 126 66.2 127 31.1 126 0.75 94 0.02 30 2.04 89 31.8 119 51.3 120 37.0 110
Periodicity [78]117.5 6.73 121 29.6 131 3.88 123 24.0 120 52.2 121 25.5 120 36.6 126 47.1 120 40.1 126 23.0 116 60.3 122 20.8 114 53.1 129 69.7 129 49.1 125 36.9 128 67.0 128 33.4 127 0.54 84 0.02 30 7.78 111 34.7 122 64.9 128 46.1 119
Adaptive flow [45]118.1 4.48 118 15.3 116 1.90 116 37.1 124 47.9 117 40.5 122 28.1 120 45.1 117 37.9 124 23.3 117 53.8 119 24.8 117 30.1 113 41.4 113 28.5 104 22.6 121 46.3 117 15.6 118 17.3 127 5.51 128 58.1 127 26.0 115 41.5 109 40.5 116
SLK [47]119.4 8.22 129 24.0 127 12.3 127 41.4 125 57.7 126 50.8 127 29.7 122 53.3 126 36.7 120 52.4 129 57.7 121 61.8 129 42.6 125 52.1 124 54.9 127 23.9 122 54.4 125 24.4 123 3.11 118 0.00 1 7.07 110 45.8 128 61.9 127 61.9 127
PGAM+LK [55]122.4 7.83 127 22.3 124 13.7 128 29.1 121 54.2 124 31.3 121 25.6 117 48.1 122 29.9 118 29.7 120 68.4 127 28.3 119 38.2 122 50.8 122 43.0 118 25.1 124 56.4 126 21.4 121 6.54 126 0.57 113 19.1 123 38.5 124 60.8 125 51.7 125
FOLKI [16]122.8 5.65 120 23.4 126 4.60 124 35.1 123 52.9 122 42.6 123 28.3 121 52.7 124 29.6 117 24.1 118 53.7 118 27.7 118 38.9 123 49.3 121 47.8 124 25.3 125 54.3 124 27.7 125 5.73 124 1.38 124 20.1 125 43.9 127 60.5 124 62.2 128
HCIC-L [99]123.0 8.04 128 19.9 122 3.64 121 56.4 129 56.0 125 70.0 129 40.9 128 45.5 119 62.3 129 38.3 124 62.5 124 38.2 122 35.3 119 45.3 118 32.0 113 20.7 118 38.1 108 18.5 119 26.5 129 13.0 129 59.2 129 40.6 125 51.8 122 48.7 123
Pyramid LK [2]125.4 7.59 125 14.5 115 15.4 129 47.0 127 50.5 119 58.8 128 32.1 124 47.7 121 42.4 127 36.1 123 62.9 125 41.1 126 48.9 128 61.1 128 55.0 128 41.7 129 50.3 121 40.3 129 4.64 123 2.07 127 16.3 121 56.9 129 71.9 129 77.2 129
AdaConv-v1 [126]130.0 25.9 130 27.4 129 29.8 130 96.8 130 97.6 130 95.4 130 93.0 130 90.8 130 99.0 130 88.2 130 85.6 130 91.5 130 97.0 130 98.5 130 88.6 130 86.2 130 81.3 130 83.9 130 64.9 130 56.4 130 97.3 130 100.0 130 99.9 130 99.9 130
SepConv-v1 [127]130.0 25.9 130 27.4 129 29.8 130 96.8 130 97.6 130 95.4 130 93.0 130 90.8 130 99.0 130 88.2 130 85.6 130 91.5 130 97.0 130 98.5 130 88.6 130 86.2 130 81.3 130 83.9 130 64.9 130 56.4 130 97.3 130 100.0 130 99.9 130 99.9 130
Move the mouse over the numbers in the table to see the corresponding images. Click to compare with the ground truth.

References

Methodtime*framescolor Reference and notes
[1] 2D-CLG 844 2 gray The 2D-CLG method by Bruhn et al. as implemented by Stefan Roth. [A. Bruhn, J. Weickert, and C. Schnörr. Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods. IJCV 63(3), 2005.] Parameters were set to match the published performance on Yosemite sequence, which may not be optimal for other sequences.
[2] Pyramid LK 12 2 color A modification of Bouguet's pyramidal implementation of Lucas-Kanade.
[3] Horn & Schunck 49 2 gray A modern Matlab implementation of the Horn & Schunck method by Deqing Sun. Parameters set to optimize AAE on all training data.
[4] Black & Anandan 328 2 gray A modern Matlab implementation of the Black & Anandan method by Deqing Sun.
[5] Brox et al. 18 2 color T. Brox, A. Bruhn, N. Papenberg, and J. Weickert. High accuracy optical flow estimation based on a theory for warping. ECCV 2004. (Improved using separate robust functions as proposed in A. Bruhn and J. Weickert, Towards ultimate motion estimation, ICCV 2005; improved by training on the training set.)
[6] Fusion 2,666 2 color V. Lempitsky, S. Roth, and C. Rother. Discrete-continuous optimization for optical flow estimation. CVPR 2008.
[7] Dynamic MRF 366 2 gray B. Glocker, N. Paragios, N. Komodakis, G. Tziritas, and N. Navab. Optical flow estimation with uncertainties through dynamic MRFs. CVPR 2008. (Method improved since publication.)
[8] Second-order prior 14 2 gray W. Trobin, T. Pock, D. Cremers, and H. Bischof. An unbiased second-order prior for high-accuracy motion estimation. DAGM 2008. (Method improved since publication; for details see W. Trobin, Ph.D. thesis, 2009.)
[9] GroupFlow 600 2 gray X. Ren. Local Grouping for Optical Flow. CVPR 2008.
[10] SegOF 60 2 color L. Xu, J. Chen, and J. Jia. Segmentation based variational model for accurate optical flow estimation. ECCV 2008. Code available.
[11] Learning Flow 825 2 gray D. Sun, S. Roth, J.P. Lewis, and M. Black. Learning optical flow (SRF-LFC). ECCV 2008.
[12] CBF 69 2 color W. Trobin, T. Pock, D. Cremers, and H. Bischof. Continuous energy minimization via repeated binary fusion. ECCV 2008. (Method improved since publication; for details see W. Trobin, Ph.D. thesis, 2009.)
[13] SPSA-learn 200 2 color Y. Li and D. Huttenlocher. Learning for optical flow using stochastic optimization. ECCV 2008.
[14] GraphCuts 1,200 2 color T. Cooke. Two applications of graph-cuts to image processing. DICTA 2008.
[15] F-TV-L1 8 2 gray A. Wedel, T. Pock, J. Braun, U. Franke, and D. Cremers. Duality TV-L1 flow with fundamental matrix prior. IVCNZ 2008.
[16] FOLKI 1.4 2 gray G. Le Besnerais and F. Champagnat. Dense optical flow by iterative local window registration. ICIP 2005.
[17] TV-L1-improved 2.9 2 gray A. Wedel, T. Pock, C. Zach, H. Bischof, and D. Cremers. An improved algorithm for TV-L1 optical flow computation. Proceedings of the Dagstuhl Visual Motion Analysis Workshop 2008. Code at GPU4Vision.
[18] DPOF 287 2 color C. Lei and Y.-H. Yang. Optical flow estimation on coarse-to-fine region-trees using discrete optimization. ICCV 2009. (Method improved since publication.)
[19] Filter Flow 34,000 2 color S. Seitz and S. Baker. Filter flow. ICCV 2009.
[20] Adaptive 9.2 2 gray A. Wedel, D. Cremers, T. Pock, and H. Bischof. Structure- and motion-adaptive regularization for high accuracy optic flow. ICCV 2009.
[21] Complementary OF 44 2 color H. Zimmer, A. Bruhn, J. Weickert, L. Valgaerts, A. Salgado, B. Rosenhahn, and H.-P. Seidel. Complementary optic flow. EMMCVPR 2009.
[22] Aniso. Huber-L1 2 2 gray M. Werlberger, W. Trobin, T. Pock, A. Wedel, D. Cremers, and H. Bischof. Anisotropic Huber-L1 optical flow. BMVC 2009. Code at GPU4Vision.
[23] Rannacher 0.12 2 gray J. Rannacher. Realtime 3D motion estimation on graphics hardware. Bachelor thesis, Heidelberg University, 2009.
[24] TI-DOFE 260 2 gray C. Cassisa, S. Simoens, and V. Prinet. Two-frame optical flow formulation in an unwarped multiresolution scheme. CIARP 2009.
[25] NL-TV-NCC 20 2 color M. Werlberger, T. Pock, and H. Bischof. Motion estimation with non-local total variation regularization. CVPR 2010.
[26] MDP-Flow 188 2 color L. Xu, J. Jia, and Y. Matsushita. Motion detail preserving optical flow estimation. CVPR 2010.
[27] ACK-Prior 5872 2 color K. Lee, D. Kwon, I. Yun, and S. Lee. Optical flow estimation with adaptive convolution kernel prior on discrete framework. CVPR 2010.
[28] LDOF 122 2 color T. Brox and J. Malik. Large displacement optical flow: descriptor matching in variational motion estimation. PAMI 33(3):500-513, 2011.
[29] p-harmonic 565 2 gray J. Gai and R. Stevenson. Optical flow estimation with p-harmonic regularization. ICIP 2010.
[30] TriangleFlow 4200 2 gray B. Glocker, H. Heibel, N. Navab, P. Kohli, and C. Rother. TriangleFlow: Optical flow with triangulation-based higher-order likelihoods. ECCV 2010.
[31] Classic+NL 972 2 color D. Sun, S. Roth, and M. Black. Secrets of optical flow estimation and their principles. CVPR 2010. Matlab code.
[32] Classic++ 486 2 gray A modern implementation of the classical formulation descended from Horn & Schunck and Black & Anandan; see D. Sun, S. Roth, and M. Black, Secrets of optical flow estimation and their principles, CVPR 2010.
[33] Nguyen 33 2 gray D. Nguyen. Tuning optical flow estimation with image-driven functions. ICRA 2011.
[34] Modified CLG 133 2 gray R. Fezzani, F. Champagnat, and G. Le Besnerais. Combined local global method for optic flow computation. EUSIPCO 2010.
[35] ComplOF-FED-GPU 0.97 2 color P. Gwosdek, H. Zimmer, S. Grewenig, A. Bruhn, and J. Weickert. A highly efficient GPU implementation for variational optic flow based on the Euler-Lagrange framework. CVGPU Workshop 2010.
[36] Ad-TV-NDC 35 2 gray M. Nawaz. Motion estimation with adaptive regularization and neighborhood dependent constraint. DICTA 2010.
[37] Layers++ 18206 2 color D. Sun, E. Sudderth, and M. Black. Layered image motion with explicit occlusions, temporal consistency, and depth ordering. NIPS 2010.
[38] OFH 620 3 color H. Zimmer, A. Bruhn, J. Weickert. Optic flow in harmony. IJCV 93(3) 2011.
[39] LSM 1615 2 color K. Jia, X. Wang, and X. Tang. Optical flow estimation using learned sparse model. ICCV 2011.
[40] CostFilter 55 2 color C. Rhemann, A. Hosni, M. Bleyer, C. Rother, and M. Gelautz. Fast cost-volume filtering for visual correspondence and beyond. CVPR 2011.
[41] Bartels 0.15 2 gray C. Bartels and G. de Haan. Smoothness constraints in recursive search motion estimation for picture rate conversion. IEEE TCSVT 2010. Version improved since publication: mapped on GPU.
[42] Shiralkar 600 2 gray M. Shiralkar and R. Schalkoff. A self organization-based optical flow estimator with GPU implementation. MVA 23(6):1229-1242.
[43] HBpMotionGpu 1000 5 gray S. Grauer-Gray and C. Kambhamettu. Hierarchical belief propagation to reduce search space using CUDA for stereo and motion estimation. WACV 2009. (Method improved since publication.)
[44] StereoFlow 7200 2 color G. Rosman, S. Shem-Tov, D. Bitton, T. Nir, G. Adiv, R. Kimmel, A. Feuer, and A. Bruckstein. Over-parameterized optical flow using a stereoscopic constraint. SSVM 2011:761-772.
[45] Adaptive flow 121 2 gray T. Arici. Energy minimization based motion estimation using adaptive smoothness priors. Submitted to IEEE TIP 2011.
[46] TC-Flow 2500 5 color S. Volz, A. Bruhn, L. Valgaerts, and H. Zimmer. Modeling temporal coherence for optical flow. ICCV 2011.
[47] SLK 300 2 gray T. Corpetti and E. Mémin. Stochastic uncertainty models for the luminance consistency assumption. IEEE TIP 2011.
[48] CLG-TV 29 2 gray M. Drulea. Total variation regularization of local-global optical flow. ITSC 2011. Matlab code.
[49] SimpleFlow 1.7 2 color M. Tao, J. Bai, P. Kohli, S. Paris. SimpleFlow: a non-iterative, sublinear optical flow algorithm. EUROGRAPHICS 2012.
[50] IAOF 57 2 gray D. Nguyen. Improving motion estimation using image-driven functions and hybrid scheme. PSIVT 2011.
[51] IAOF2 56 2 gray D. Nguyen. Enhancing the sharpness of flow field using image-driven functions with occlusion-aware filter. Submitted to TIP 2011.
[52] LocallyOriented 9541 2 gray Y.Niu, A. Dick, and M. Brooks. Locally oriented optical flow computation. To appear in TIP 2012.
[53] IROF-TV 261 2 color H. Rashwan, D. Puig, and M. Garcia. On improving the robustness of differential optical flow. ICCV 2011 Artemis workshop.
[54] Sparse Occlusion 2312 2 color A. Ayvaci, M. Raptis, and S. Soatto. Sparse occlusion detection with optical flow. Submitted to IJCV 2011.
[55] PGAM+LK 0.37 2 gray A. Alba, E. Arce-Santana, and M. Rivera. Optical flow estimation with prior models obtained from phase correlation. ISVC 2010.
[56] Sparse-NonSparse 713 2 color L. Chen, J. Wang, and Y. Wu. Decomposing and regularizing sparse/non-sparse components for motion field estimation. Submitted to PAMI 2013.
[57] nLayers 36150 4 color D. Sun, E. Sudderth, and M. Black. Layered segmentation and optical flow estimation over time. CVPR 2012.
[58] IROF++ 187 2 color H. Rashwan, D. Puig, and M. Garcia. Variational optical flow estimation based on stick tensor voting. IEEE TIP 2013.
[59] COFM 600 3 color M. Mozerov. Constrained optical flow estimation as a matching problem. IEEE TIP 2013.
[60] Efficient-NL 400 2 color P. Krähenbühl and V. Koltun. Efficient nonlocal regularization for optical flow. ECCV 2012.
[61] BlockOverlap 2 2 gray M. Santoro, G. AlRegib, and Y. Altunbasak. Motion estimation using block overlap minimization. Submitted to MMSP 2012.
[62] Ramp 1200 2 color A. Singh and N. Ahuja. Exploiting ramp structures for improving optical flow estimation. ICPR 2012.
[63] Occlusion-TV-L1 538 3 gray C. Ballester, L. Garrido, V. Lazcano, and V. Caselles. A TV-L1 optical flow method with occlusion detection. DAGM-OAGM 2012.
[64] TV-L1-MCT 90 2 color M. Mohamed and B. Mertsching. TV-L1 optical flow estimation with image details recovering based on modified census transform. ISVC 2012.
[65] Local-TV-L1 500 2 gray L. Raket. Local smoothness for global optical flow. ICIP 2012.
[66] ALD-Flow 61 2 color M. Stoll, A. Bruhn, and S. Volz. Adaptive integration of feature matches into variational optic flow methods. ACCV 2012.
[67] SIOF 234 2 color L. Xu, Z. Dai, and J. Jia. Scale invariant optical flow. ECCV 2012.
[68] MDP-Flow2 342 2 color L. Xu, J. Jia, and Y. Matsushita. Motion detail preserving optical flow estimation. PAMI 34(9):1744-1757, 2012. Code available.
[69] TCOF 1421 all gray J. Sanchez, A. Salgado, and N. Monzon. Optical flow estimation with consistent spatio-temporal coherence models. VISAPP 2013.
[70] LME 476 2 color W. Li, D. Cosker, M. Brown, and R. Tang. Optical flow estimation using Laplacian mesh energy. CVPR 2013.
[71] NN-field 362 2 color L. Chen, H. Jin, Z. Lin, S. Cohen, and Y. Wu. Large displacement optical flow from nearest neighbor fields. CVPR 2013.
[72] FESL 3310 2 color W. Dong, G. Shi, X. Hu, and Y. Ma. Nonlocal sparse and low-rank regularization for optical flow estimation. Submitted to IEEE TIP 2013.
[73] PMF 35 2 color J. Lu, H. Yang, D. Min, and M. Do. PatchMatch filter: efficient edge-aware filtering meets randomized search for fast correspondence field estimation. CVPR 2013.
[74] FC-2Layers-FF 2662 4 color D. Sun, J. Wulff, E. Sudderth, H. Pfister, and M. Black. A fully-connected layered model of foreground and background flow. CVPR 2013.
[75] Correlation Flow 290 2 color M. Drulea and S. Nedevschi. Motion estimation using the correlation transform. TIP 2013. Matlab code.
[76] TC/T-Flow 341 5 color M. Stoll, S. Volz, and A. Bruhn. Joint trilateral filtering for multiframe optical flow. ICIP 2013.
[77] OFLAF 1530 2 color T. Kim, H. Lee, and K. Lee. Optical flow via locally adaptive fusion of complementary data costs. ICCV 2013.
[78] Periodicity 8000 4 color G. Khachaturov, S. Gonzalez-Brambila, and J. Gonzalez-Trejo. Periodicity-based computation of optical flow. Submitted to Computacion y Sistemas (CyS) 2013.
[79] SILK 572 2 gray P. Zille, C. Xu, T. Corpetti, L. Shao. Observation models based on scale interactions for optical flow estimation. Submitted to IEEE TIP.
[80] CRTflow 13 3 color O. Demetz, D. Hafner, and J. Weickert. The complete rank transform: a tool for accurate and morphologically invariant matching of structures. BMVC 2013.
[81] SuperFlow 178 2 color Anonymous. Superpixel based optical flow estimation. ICCV 2013 submission 507.
[82] Aniso-Texture 300 2 color Anonymous. Texture information-based optical flow estimation using an incremental multi-resolution approach. ITC-CSCC 2013 submission 267.
[83] Classic+CPF 640 2 gray Z. Tu, R. Veltkamp, and N. van der Aa. A combined post-filtering method to improve accuracy of variational optical flow estimation. Submitted to Pattern Recognition 2013.
[84] S2D-Matching 1200 2 color Anonymous. Locally affine sparse-to-dense matching for motion and occlusion estimation. ICCV 2013 submission 1479.
[85] AGIF+OF 438 2 gray Z. Tu, R. Poppe, and R. Veltkamp. Adaptive guided image filter to warped interpolation image for variational optical flow computation. Submitted to Signal Processing 2015.
[86] DeepFlow 13 2 color P. Weinzaepfel, J. Revaud, Z. Harchaoui, and C. Schmid. DeepFlow: large displacement optical flow with deep matching. ICCV 2013.
[87] NNF-Local 673 2 color Z. Chen, H. Jin, Z. Lin, S. Cohen, and Y. Wu. Large displacement optical flow with nearest neighbor field. Submitted to PAMI 2014.
[88] EPPM w/o HM 2.5 2 color L. Bao, Q. Yang, and H. Jin. Fast edge-preserving PatchMatch for large displacement optical flow. CVPR 2014.
[89] MLDP_OF 165 2 gray M. Mohamed, H. Rashwan, B. Mertsching, M. Garcia, and D. Puig. Illumination-robust optical flow approach using local directional pattern. IEEE TCSVT 24(9):1499-1508, 2014.
[90] RFlow 20 2 gray S. Ali, C. Daul, and W. Blondel. Robust and accurate optical flow estimation for weak texture and varying illumination condition: Application to cystoscopy. IPTA 2014.
[91] SRR-TVOF-NL 32 all color P. Pohl, M. Sirotenko, E. Tolstaya, and V. Bucha. Edge preserving motion estimation with occlusions correction for assisted 2D to 3D conversion. IS&T/SPIE Electronic Imaging 2014.
[92] 2DHMM-SAS 157 2 color M.-C. Shih, R. Shenoy, and K. Rose. A two-dimensional hidden Markov model with spatially-adaptive states with application of optical flow. ICIP 2014 submission.
[93] WLIF-Flow 700 2 color Z. Tu, R. Veltkamp, N. van der Aa, and C. Van Gemeren. Weighted local intensity fusion method for variational optical flow estimation. Submitted to TIP 2014.
[94] FMOF 215 2 color N. Jith, A. Ramakanth, and V. Babu. Optical flow estimation using approximate nearest neighbor field fusion. ICASSP 2014.
[95] TriFlow 150 2 color TriFlow. Optical flow with geometric occlusion estimation and fusion of multiple frames. ECCV 2014 submission 914.
[96] ComponentFusion 6.5 2 color Anonymous. Fast optical flow by component fusion. ECCV 2014 submission 941.
[97] AggregFlow 1642 2 color D. Fortun, P. Bouthemy, and C. Kervrann. Aggregation of local parametric candidates and exemplar-based occlusion handling for optical flow. Preprint arXiv:1407.5759.
[98] 2bit-BM-tele 124 2 gray R. Xu and D. Taubman. Robust dense block-based motion estimation using a two-bit transform on a Laplacian pyramid. ICIP 2013.
[99] HCIC-L 330 2 color Anonymous. Globally-optimal image correspondence using a hierarchical graphical model. NIPS 2014 submission 114.
[100] TF+OM 600 2 color R. Kennedy and C. Taylor. Optical flow with geometric occlusion estimation and fusion of multiple frames. EMMCVPR 2015.
[101] PH-Flow 800 2 color J. Yang and H. Li. Dense, accurate optical flow estimation with piecewise parametric model. CVPR 2015.
[102] EpicFlow 16 2 color J. Revaud, P. Weinzaepfel, Z. Harchaoui, and C. Schmid. EpicFlow: edge-preserving interpolation of correspondences for optical flow. CVPR 2015.
[103] NNF-EAC 380 2 color Anonymous. Variational method for joint optical flow estimation and edge-aware image restoration. CVPR 2015 submission 2336.
[104] Heeger++ 6600 5 gray Anonymous. A context aware biologically inspired algorithm for optical flow (updated results). CVPR 2015 submission 2238.
[105] HBM-GC 330 2 color A. Zheng and Y. Yuan. Motion estimation via hierarchical block matching and graph cut. Submitted to ICIP 2015.
[106] FFV1MT 358 5 gray F. Solari, M. Chessa, N. Medathati, and P. Kornprobst. What can we expect from a V1-MT feedforward architecture for optical flow estimation? Submitted to Signal Processing: Image Communication 2015.
[107] ROF-ND 4 2 color S. Ali, C. Daul, E. Galbrun, and W. Blondel. Illumination invariant large displacement optical flow using robust neighbourhood descriptors. Submitted to CVIU 2015.
[108] DeepFlow2 16 2 color J. Revaud, P. Weinzaepfel, Z. Harchaoui, and C. Schmid. Deep convolutional matching. Submitted to IJCV, 2015.
[109] HAST 2667 2 color Anonymous. Highly accurate optical flow estimation on superpixel tree. ICCV 2015 submission 2221.
[110] FlowFields 15 2 color C. Bailer, B. Taetz, and D. Stricker. Flow Fields: Dense unregularized correspondence fields for highly accurate large displacement optical flow estimation. ICCV 2015.
[111] SVFilterOh 1.56 2 color Anonymous. Fast estimation of large displacement optical flow using PatchMatch and dominant motion patterns. CVPR 2016 submission 1788.
[112] FlowNetS+ft+v 0.5 2 color Anonymous. Learning optical flow with convolutional neural networks. ICCV 2015 submission 235.
[113] CombBMOF 51 2 color M. Brüggemann, R. Kays, P. Springer, and O. Erdler. Combined block-matching and adaptive differential motion estimation in a hierarchical multi-scale framework. ICGIP 2014. (Method improved since publication.)
[114] PMMST 182 2 color F. Zhang, S. Xu, and X. Zhang. High accuracy correspondence field estimation via MST based patch matching. Submitted to TIP 2015.
[115] DF-Auto 70 2 color N. Monzon, A. Salgado, and J. Sanchez. Regularization strategies for discontinuity-preserving optical flow methods. Submitted to TIP 2015.
[116] CPM-Flow 3 2 color Anonymous. Efficient coarse-to-fine PatchMatch for large displacement optical flow. CVPR 2016 submission 241.
[117] CNN-flow-warp+ref 1.4 3 color D. Teney and M. Hebert. Learning to extract motion from videos in convolutional neural networks. ArXiv 1601.07532, 2016.
[118] Steered-L1 804 2 color Anonymous. Optical flow estimation via steered-L1 norm. Submitted to WSCG 2016.
[119] StereoOF-V1MT 343 2 gray Anonymous. Visual features for action-oriented tasks: a cortical-like model for disparity and optic flow computation. BMVC 2016 submission 132.
[120] PGM-C 5 2 color Y. Li. Pyramidal gradient matching for optical flow estimation. Submitted to PAMI 2016.
[121] RNLOD-Flow 1040 2 gray C. Zhang, Z. Chen, M. Wang, M. Li, and S. Jiang. Robust non-local TV-L1 optical flow estimation with occlusion detection. Submitted to TIP 2016.
[122] FlowNet2 0.091 2 color Anonymous. FlowNet 2.0: Evolution of optical flow estimation with deep networks. CVPR 2017 submission 900.
[123] S2F-IF 20 2 color Anonymous. S2F-IF: Slow-to-fast interpolator flow. CVPR 2017 submission 765.
[124] BriefMatch 0.068 2 gray G. Eilertsen, P.-E. Forssen, and J. Unger. Dense binary feature matching for real-time optical flow estimation. SCIA 2017 submission 62.
[125] OAR-Flow 60 2 color Anonymous. Order-adaptive regularisation for variational optical flow: global, local and in between. SSVM 2017 submission 20.
[126] AdaConv-v1 2.8 2 color S. Niklaus, L. Mai, and F. Liu. (Interpolation results only.) Video frame interpolation via adaptive convolution. CVPR 2017.
[127] SepConv-v1 0.2 2 color S. Niklaus, L. Mai, and F. Liu. (Interpolation results only.) Video frame interpolation via adaptive separable convolution. ICCV 2017.
[128] ProbFlowFields 37 2 color A. Wannenwetsch, M. Keuper, and S. Roth. ProbFlow: joint optical flow and uncertainty estimation. ICCV 2017.
[129] UnFlow 0.12 2 color Anonymous. UnFlow: Unsupervised learning of optical flow with a bidirectional census loss. Submitted to AAAI 2018.
[130] FlowFields+ 10.5 2 color C. Bailer, B. Taetz, and D. Stricker. Flow fields: Dense correspondence fields for highly accurate large displacement optical flow estimation. Submitted to PAMI 2017.
[131] Kuang 9.9 2 gray F. Kuang. PatchMatch algorithms for motion estimation and stereo reconstruction. Master thesis, University of Stuttgart, 2017.
* The "time" column lists the reported runtime in seconds on the "Urban" sequence. Note that these runtimes are not normalized by processor speed or type.