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        
R2.0
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]5.0 0.19 25 1.11 28 0.00 1 0.73 3 5.01 3 0.12 2 1.08 3 3.84 2 0.00 1 0.54 4 4.91 4 0.02 3 4.35 2 7.43 2 0.89 2 1.53 1 8.39 2 1.54 3 0.00 1 0.00 1 0.00 1 3.65 7 12.4 17 1.32 2
PMMST [114]8.7 0.20 31 1.20 38 0.03 53 0.57 1 4.20 1 0.21 10 1.12 4 3.98 4 0.06 5 0.16 2 1.79 2 0.00 1 6.17 4 10.4 4 2.09 5 2.24 3 10.3 5 3.42 20 0.00 1 0.00 1 0.00 1 3.14 3 10.1 5 3.34 4
NN-field [71]10.8 0.23 58 1.37 60 0.00 1 0.64 2 4.87 2 0.07 1 1.23 7 4.31 5 0.03 3 0.60 5 5.03 5 0.04 4 4.24 1 7.24 1 0.70 1 5.93 51 6.73 1 2.33 9 0.00 1 0.00 1 0.00 1 3.87 10 13.1 29 1.27 1
OFLAF [77]11.8 0.20 31 1.21 39 0.00 1 0.92 9 5.66 7 0.25 15 1.22 5 4.32 6 0.12 10 1.03 16 8.42 19 0.22 26 7.31 9 12.4 9 2.79 9 3.20 13 11.6 7 3.15 17 0.00 1 0.00 1 0.00 1 3.66 8 9.73 4 7.15 20
Layers++ [37]16.9 0.15 6 0.90 8 0.00 1 0.88 7 6.28 10 0.29 17 1.61 12 5.50 12 0.95 67 0.92 13 5.94 7 0.24 34 6.07 3 9.99 3 3.95 13 6.14 55 15.3 22 5.23 68 0.00 1 0.00 1 0.00 1 4.11 13 10.5 6 7.50 26
ComponentFusion [96]16.9 0.17 14 1.02 18 0.03 53 0.93 10 6.31 11 0.23 14 1.48 10 5.26 10 0.22 16 0.68 6 6.90 11 0.05 5 10.5 39 17.2 41 7.34 40 3.34 15 15.8 26 3.80 29 0.00 1 0.00 1 0.00 1 3.81 9 11.2 11 6.45 15
TC/T-Flow [76]17.1 0.11 2 0.67 2 0.00 1 1.63 46 8.48 32 0.45 24 2.21 18 7.45 19 0.16 13 1.20 39 10.2 47 0.16 7 9.34 31 14.9 28 6.04 29 1.76 2 9.86 4 1.36 1 0.00 1 0.00 1 0.00 1 4.64 21 12.6 20 7.19 21
MDP-Flow2 [68]17.5 0.18 20 1.07 23 0.03 53 0.82 4 5.18 4 0.20 9 1.31 8 4.69 8 0.09 8 1.24 45 11.0 52 0.24 34 9.23 28 15.2 31 5.96 28 2.65 6 11.8 9 3.56 23 0.00 1 0.00 1 0.00 1 3.61 6 11.1 9 5.40 10
CombBMOF [113]21.3 0.20 31 1.18 33 0.03 53 1.05 14 6.42 12 0.16 4 1.66 13 5.67 13 0.01 2 0.79 9 6.82 10 0.16 7 7.66 12 12.5 11 4.37 16 8.16 85 15.3 22 7.67 109 0.00 1 0.00 1 0.00 1 4.31 15 11.0 8 7.79 30
NNF-EAC [103]21.8 0.17 14 1.03 19 0.01 31 1.01 11 5.78 9 0.38 23 1.81 15 6.09 15 0.13 11 1.27 49 11.4 54 0.24 34 8.50 21 14.2 24 5.00 22 4.85 34 12.2 11 4.55 46 0.00 1 0.00 1 0.00 1 4.77 25 13.1 29 7.37 23
WLIF-Flow [93]22.0 0.20 31 1.21 39 0.01 31 0.91 8 5.77 8 0.26 16 2.30 21 7.50 20 0.38 30 1.10 25 8.71 21 0.25 45 8.40 20 14.0 20 4.94 21 4.91 36 13.0 13 3.79 28 0.00 1 0.00 1 0.00 1 4.98 30 12.6 20 8.37 42
MLDP_OF [89]22.9 0.17 14 1.00 16 0.00 1 0.82 4 5.37 5 0.13 3 2.62 37 8.28 30 0.15 12 1.01 15 8.41 18 0.17 14 8.84 25 14.4 25 5.24 24 2.41 4 11.1 6 1.54 3 0.29 106 0.00 1 1.28 109 5.41 40 12.9 26 5.66 11
FC-2Layers-FF [74]23.4 0.19 25 1.10 26 0.00 1 1.53 39 10.0 51 0.68 46 1.47 9 5.05 9 0.37 29 1.07 21 8.29 17 0.22 26 6.46 5 10.5 5 3.24 10 6.93 67 15.2 20 5.43 75 0.00 1 0.00 1 0.00 1 4.89 26 12.6 20 7.93 32
nLayers [57]23.5 0.19 25 1.13 30 0.00 1 1.04 13 7.08 20 0.31 19 2.42 28 8.37 33 0.50 36 1.10 25 8.82 23 0.38 59 6.91 8 11.4 8 3.98 14 6.52 61 12.6 12 5.28 70 0.00 1 0.00 1 0.00 1 4.63 20 12.5 19 8.25 38
FlowFields+ [130]24.1 0.15 6 0.88 6 0.01 31 1.38 31 8.90 38 0.68 46 2.23 20 7.99 23 0.44 34 0.70 7 6.60 8 0.20 20 12.0 48 19.4 51 7.65 43 2.62 5 16.5 40 1.82 7 0.00 1 0.00 1 0.00 1 5.64 45 18.0 55 5.92 12
Correlation Flow [75]24.8 0.25 69 1.46 70 0.00 1 1.10 18 7.16 21 0.22 12 4.18 65 12.3 61 0.35 26 0.74 8 5.14 6 0.22 26 11.5 43 17.7 43 9.04 53 4.12 26 13.1 14 2.69 12 0.00 1 0.00 1 0.00 1 3.48 4 10.9 7 3.71 6
PH-Flow [101]26.0 0.20 31 1.16 31 0.00 1 1.36 28 7.94 26 0.53 34 1.69 14 5.76 14 0.64 50 1.10 25 8.60 20 0.24 34 6.59 6 11.1 6 3.26 11 3.52 19 11.6 7 3.39 18 0.13 96 0.00 1 0.44 91 4.21 14 11.4 13 7.94 34
PMF [73]26.6 0.20 31 1.19 35 0.03 53 1.06 17 6.51 13 0.18 6 1.50 11 5.33 11 0.09 8 1.26 48 9.04 29 0.23 29 7.32 10 12.4 9 1.91 3 5.47 41 16.3 32 4.67 50 0.09 90 0.00 1 0.25 86 3.51 5 9.50 2 6.99 18
IROF++ [58]27.1 0.23 58 1.37 60 0.00 1 1.37 30 8.26 29 0.45 24 2.40 26 7.86 21 0.51 39 1.16 35 9.50 39 0.24 34 8.06 16 13.2 15 4.86 20 5.64 47 16.4 35 4.51 44 0.00 1 0.00 1 0.00 1 4.62 18 12.7 25 7.93 32
AGIF+OF [85]27.2 0.21 43 1.25 49 0.00 1 1.48 37 8.75 35 0.37 21 2.50 33 8.15 27 0.38 30 1.14 30 8.88 24 0.23 29 7.56 11 12.5 11 4.30 15 6.71 64 15.2 20 4.99 61 0.00 1 0.00 1 0.00 1 5.07 33 13.0 28 8.68 49
HAST [109]28.2 0.21 43 1.27 51 0.03 53 1.55 42 6.58 14 0.85 59 1.07 2 3.84 2 0.06 5 1.18 38 9.57 41 0.19 19 6.70 7 11.3 7 2.10 6 5.68 48 14.2 17 5.14 66 0.01 75 0.00 1 0.05 76 2.21 1 7.87 1 2.21 3
ProbFlowFields [128]29.2 0.20 31 1.18 33 0.03 53 1.25 24 7.90 25 0.64 43 2.55 35 8.95 38 1.08 70 0.25 3 2.68 3 0.05 5 12.5 57 19.9 56 8.91 51 2.82 9 15.8 26 2.70 13 0.00 1 0.00 1 0.00 1 5.90 49 18.1 56 6.95 17
SVFilterOh [111]30.5 0.22 51 1.31 53 0.05 71 1.14 20 6.84 17 0.30 18 2.13 17 7.39 17 0.69 54 0.86 10 7.24 12 0.16 7 8.17 17 13.8 18 2.18 7 6.69 62 15.3 22 4.47 43 0.27 105 0.00 1 0.74 96 2.89 2 9.59 3 3.97 8
CostFilter [40]30.8 0.22 51 1.32 56 0.03 53 1.16 21 6.61 15 0.22 12 1.22 5 4.37 7 0.21 15 1.29 50 10.2 47 0.21 24 7.77 14 13.2 15 2.07 4 5.43 39 15.9 29 3.96 34 0.07 87 0.00 1 0.12 81 4.75 24 13.5 35 7.19 21
EPPM w/o HM [88]30.9 0.21 43 1.25 49 0.03 53 1.05 14 6.95 19 0.19 7 2.42 28 8.24 29 0.08 7 1.00 14 7.81 15 0.21 24 7.69 13 13.0 13 2.55 8 6.45 60 18.5 59 4.04 35 0.43 113 0.00 1 0.76 97 3.98 12 11.1 9 7.10 19
TC-Flow [46]30.9 0.13 3 0.77 3 0.00 1 1.38 31 8.10 28 0.47 27 2.97 49 10.0 49 0.34 24 1.36 56 10.5 50 0.25 45 11.2 42 18.1 45 7.49 41 3.36 16 17.1 47 1.78 6 0.00 1 0.00 1 0.00 1 6.35 55 17.8 54 10.0 67
ALD-Flow [66]33.4 0.14 5 0.85 5 0.01 31 1.70 48 8.34 30 0.50 30 2.94 47 9.96 48 0.38 30 1.68 66 13.0 64 0.32 54 11.8 47 18.8 48 8.42 48 2.93 10 16.4 35 1.70 5 0.00 1 0.00 1 0.00 1 5.91 51 17.4 52 8.45 45
FlowFields [110]33.4 0.16 10 0.97 12 0.02 48 1.54 41 9.90 50 0.72 49 2.38 24 8.48 35 0.58 48 1.03 16 9.05 30 0.31 52 12.5 57 20.3 61 8.76 50 3.16 12 18.0 58 3.08 16 0.00 1 0.00 1 0.00 1 6.22 53 19.0 61 6.76 16
RNLOD-Flow [121]34.2 0.17 14 1.03 19 0.00 1 1.50 38 9.63 45 0.56 37 3.15 52 10.1 51 0.56 47 1.14 30 9.02 28 0.20 20 9.73 35 15.7 35 6.54 34 5.43 39 14.7 19 4.56 48 0.06 85 0.00 1 0.34 87 4.41 16 11.3 12 7.56 27
COFM [59]34.2 0.28 77 1.64 77 0.06 76 1.31 27 7.81 23 0.57 38 3.57 57 12.0 59 1.10 72 0.91 12 7.78 14 0.16 7 11.7 46 18.5 47 10.3 68 4.05 24 13.7 16 4.28 39 0.00 1 0.00 1 0.00 1 3.96 11 11.5 14 6.40 14
Sparse-NonSparse [56]35.3 0.22 51 1.31 53 0.00 1 1.87 58 11.4 60 0.80 55 2.47 32 8.05 25 0.52 41 1.15 34 8.89 25 0.24 34 9.37 32 15.3 32 5.94 27 7.18 69 16.3 32 5.47 77 0.00 1 0.00 1 0.00 1 5.08 34 13.1 29 8.42 43
S2F-IF [123]35.3 0.18 20 1.07 23 0.02 48 1.53 39 10.0 51 0.72 49 2.37 23 8.45 34 0.54 44 1.21 40 9.59 42 0.35 55 12.7 61 20.3 61 9.20 57 3.41 17 17.7 55 3.70 26 0.00 1 0.00 1 0.00 1 5.36 39 16.5 48 6.13 13
LSM [39]35.5 0.21 43 1.23 44 0.00 1 1.88 60 11.5 61 0.82 57 2.45 30 8.04 24 0.52 41 1.12 28 9.06 31 0.23 29 9.27 30 15.1 30 6.05 30 7.21 71 16.5 40 5.47 77 0.00 1 0.00 1 0.00 1 5.29 38 13.8 37 8.49 47
LME [70]35.7 0.24 62 1.40 64 0.04 68 0.84 6 5.51 6 0.21 10 3.70 58 8.78 36 5.39 96 1.38 57 11.0 52 0.37 57 9.52 34 15.3 32 7.58 42 3.73 21 16.9 45 4.43 41 0.00 1 0.00 1 0.00 1 4.62 18 12.6 20 7.77 29
FMOF [94]35.8 0.20 31 1.19 35 0.00 1 1.61 45 9.42 43 0.53 34 2.03 16 6.86 16 0.22 16 1.04 18 8.71 21 0.16 7 8.59 22 14.0 20 4.44 17 7.80 79 16.2 30 5.73 84 0.09 90 0.00 1 0.81 99 5.75 47 14.6 42 8.44 44
HBM-GC [105]36.2 0.29 79 1.72 82 0.03 53 1.36 28 8.81 36 0.71 48 2.92 45 10.0 49 0.79 55 1.21 40 8.97 27 0.37 57 8.90 26 14.6 26 5.72 26 5.58 45 9.50 3 3.51 22 0.00 1 0.00 1 0.00 1 5.23 37 15.1 43 8.28 39
MDP-Flow [26]36.3 0.13 3 0.78 4 0.00 1 1.05 14 6.71 16 0.64 43 2.31 22 8.09 26 1.26 78 1.35 55 12.5 63 0.28 48 10.4 38 16.8 40 7.29 38 5.39 38 16.9 45 4.89 57 0.00 1 0.00 1 0.00 1 8.69 82 21.5 77 12.1 80
FESL [72]36.4 0.23 58 1.35 59 0.00 1 1.71 50 9.38 42 0.54 36 2.22 19 7.40 18 0.31 19 1.08 22 9.18 33 0.16 7 7.97 15 13.0 13 4.61 18 7.68 76 16.5 40 5.87 87 0.09 90 0.00 1 0.17 84 4.96 29 12.4 17 8.31 40
NL-TV-NCC [25]37.2 0.24 62 1.43 68 0.01 31 1.43 34 9.86 49 0.16 4 3.10 51 10.1 51 0.20 14 1.13 29 9.56 40 0.16 7 11.5 43 18.3 46 7.31 39 8.51 88 20.7 84 4.68 51 0.00 1 0.00 1 0.00 1 5.59 44 16.1 46 5.10 9
DPOF [18]37.4 0.17 14 0.99 14 0.00 1 2.06 69 10.3 54 0.92 65 0.99 1 3.51 1 0.05 4 1.08 22 9.87 45 0.17 14 8.25 19 13.8 18 3.72 12 9.58 104 18.7 61 5.78 86 1.06 119 0.00 1 2.93 117 4.41 16 13.4 34 3.94 7
Classic+NL [31]38.0 0.23 58 1.34 58 0.01 31 1.93 64 11.7 62 0.80 55 2.57 36 8.35 31 0.58 48 1.22 42 9.29 36 0.24 34 8.66 24 14.1 22 5.48 25 7.52 74 16.3 32 5.42 73 0.00 1 0.00 1 0.00 1 5.06 32 12.9 26 8.47 46
Classic+CPF [83]39.6 0.21 43 1.23 44 0.01 31 1.47 36 8.95 39 0.37 21 2.73 39 8.84 37 0.35 26 1.14 30 9.32 37 0.23 29 8.60 23 14.1 22 5.23 23 8.01 83 16.4 35 5.26 69 0.20 102 0.00 1 0.86 101 4.71 22 12.0 16 8.34 41
Efficient-NL [60]40.0 0.22 51 1.29 52 0.00 1 1.25 24 7.99 27 0.48 29 2.92 45 9.31 40 0.31 19 1.23 44 9.67 44 0.31 52 8.23 18 13.5 17 4.72 19 8.45 87 17.1 47 6.06 89 0.12 95 0.00 1 0.54 93 4.71 22 11.6 15 7.75 28
Aniso-Texture [82]41.1 0.16 10 0.94 10 0.02 48 1.16 21 8.46 31 0.50 30 5.29 79 14.6 80 1.10 72 0.87 11 6.69 9 0.17 14 14.2 79 20.8 66 14.7 85 5.50 43 18.6 60 4.62 49 0.00 1 0.00 1 0.00 1 6.99 61 18.1 56 10.3 70
Complementary OF [21]41.2 0.15 6 0.89 7 0.00 1 1.43 34 8.69 34 0.35 20 2.54 34 8.95 38 0.28 18 1.45 58 12.4 60 0.28 48 14.9 86 21.6 83 15.4 90 7.75 77 17.6 54 3.64 24 0.00 1 0.00 1 0.00 1 7.27 67 22.2 84 9.59 62
SRR-TVOF-NL [91]41.6 0.19 25 1.05 21 0.03 53 3.08 91 13.8 87 1.68 89 3.97 62 12.4 62 0.84 56 1.22 42 9.35 38 0.20 20 11.5 43 16.7 39 12.3 77 2.79 7 13.5 15 3.68 25 0.00 1 0.00 1 0.00 1 5.69 46 13.1 29 10.1 68
Ramp [62]43.0 0.21 43 1.24 47 0.00 1 1.77 51 11.1 58 0.79 53 2.39 25 7.95 22 0.55 46 1.17 37 9.16 32 0.24 34 9.25 29 14.9 28 6.31 31 7.18 69 15.7 25 5.42 73 0.19 101 0.00 1 0.96 103 5.18 36 13.3 33 8.87 55
IROF-TV [53]43.5 0.22 51 1.24 47 0.01 31 1.83 56 11.9 65 0.87 61 2.96 48 9.37 41 0.50 36 1.70 67 14.6 71 0.46 66 9.51 33 15.4 34 6.49 33 4.78 32 22.9 95 4.55 46 0.00 1 0.00 1 0.00 1 5.17 35 14.4 41 8.73 51
OFH [38]43.8 0.17 14 1.00 16 0.00 1 1.80 53 9.80 47 0.66 45 4.49 71 13.2 73 0.47 35 1.62 64 13.6 66 0.35 55 13.2 65 20.8 66 10.2 66 3.85 22 20.4 80 2.41 10 0.00 1 0.00 1 0.00 1 7.06 63 21.6 79 9.31 58
ROF-ND [107]45.1 0.29 79 1.73 84 0.01 31 2.75 86 11.0 56 0.73 51 3.45 55 10.7 54 0.51 39 0.13 1 1.44 1 0.00 1 12.2 50 18.8 48 10.5 69 6.28 58 17.1 47 4.80 55 0.00 1 0.00 1 0.00 1 8.30 79 21.5 77 9.38 59
OAR-Flow [125]45.2 0.19 25 1.12 29 0.06 76 2.86 87 12.0 66 1.41 84 4.36 68 13.9 76 1.43 84 1.51 61 11.7 56 0.23 29 12.6 60 20.0 59 8.47 49 2.80 8 16.4 35 1.37 2 0.00 1 0.00 1 0.00 1 5.56 43 16.7 49 8.15 37
TCOF [69]46.6 0.18 20 1.06 22 0.00 1 1.56 43 9.24 41 0.60 40 4.63 73 12.8 69 0.89 59 1.34 54 12.4 60 0.20 20 12.4 53 19.6 54 9.52 60 6.02 52 14.3 18 5.03 62 0.34 111 0.00 1 1.23 108 4.94 27 13.6 36 8.00 35
TV-L1-MCT [64]46.9 0.22 51 1.33 57 0.00 1 1.64 47 9.85 48 0.52 32 2.86 44 9.38 42 0.32 22 1.14 30 8.89 25 0.24 34 10.6 40 16.4 38 9.05 54 8.81 94 17.2 51 5.12 65 0.08 89 0.00 1 0.84 100 5.93 52 14.3 40 10.1 68
ACK-Prior [27]47.7 0.15 6 0.91 9 0.00 1 1.21 23 7.63 22 0.19 7 2.41 27 8.36 32 0.35 26 1.25 47 10.5 50 0.18 17 12.4 53 18.0 44 11.2 70 9.00 99 19.4 71 6.39 94 0.17 99 0.00 1 1.01 105 9.72 89 20.1 67 13.3 86
2DHMM-SAS [92]48.1 0.20 31 1.21 39 0.00 1 1.80 53 10.4 55 0.63 42 4.15 63 11.3 56 0.86 57 1.24 45 9.61 43 0.25 45 9.18 27 14.8 27 6.44 32 8.98 98 17.3 52 4.98 59 0.13 96 0.00 1 0.69 95 5.55 42 14.2 39 9.22 56
CRTflow [80]49.0 0.18 20 0.99 14 0.03 53 1.70 48 9.09 40 0.59 39 4.56 72 12.8 69 0.68 51 2.03 82 15.1 76 0.64 74 12.4 53 20.0 59 8.26 46 4.42 27 24.0 100 3.47 21 0.00 1 0.00 1 0.00 1 7.88 73 22.0 83 10.4 72
PGM-C [120]49.0 0.20 31 1.19 35 0.07 85 1.87 58 11.8 64 0.85 59 2.76 40 9.82 47 0.92 63 1.99 79 15.1 76 0.74 83 13.1 63 21.2 69 9.19 56 3.52 19 19.2 68 2.47 11 0.00 1 0.00 1 0.00 1 6.38 56 19.5 64 8.65 48
Sparse Occlusion [54]50.2 0.24 62 1.38 62 0.06 76 1.27 26 7.83 24 0.45 24 3.42 53 11.1 55 0.33 23 1.52 62 11.4 54 0.28 48 10.9 41 17.6 42 6.76 36 4.10 25 16.2 30 4.27 38 0.03 77 0.17 121 0.15 82 5.90 49 15.7 44 8.69 50
SimpleFlow [49]50.3 0.22 51 1.31 53 0.00 1 1.78 52 11.0 56 0.82 57 4.30 67 12.5 65 1.22 77 1.16 35 9.20 34 0.24 34 9.84 37 15.8 36 6.94 37 8.51 88 17.3 52 6.11 91 0.09 90 0.00 1 0.39 89 5.01 31 14.1 38 8.00 35
CPM-Flow [116]51.2 0.21 43 1.23 44 0.07 85 1.92 62 12.1 67 0.89 62 2.64 38 9.39 43 0.92 63 1.96 75 14.8 72 0.72 81 13.1 63 21.2 69 8.92 52 4.84 33 19.1 67 3.40 19 0.00 1 0.00 1 0.00 1 6.92 60 20.5 69 9.43 60
ComplOF-FED-GPU [35]52.5 0.19 25 1.10 26 0.03 53 2.32 76 12.5 75 0.92 65 2.76 40 9.65 46 0.31 19 1.65 65 13.1 65 0.38 59 13.4 69 21.2 69 10.2 66 8.60 92 22.8 93 4.22 37 0.00 1 0.00 1 0.00 1 7.44 68 22.4 85 9.81 63
Kuang [131]54.1 0.21 43 1.22 43 0.03 53 1.92 62 12.1 67 0.91 64 3.01 50 10.6 53 0.52 41 1.47 59 11.8 58 0.44 65 13.5 71 21.5 77 9.33 58 6.38 59 20.4 80 5.73 84 0.00 1 0.00 1 0.00 1 7.20 65 18.6 59 13.2 85
EpicFlow [102]54.9 0.20 31 1.17 32 0.07 85 1.91 61 12.1 67 0.90 63 3.70 58 12.7 67 0.89 59 1.96 75 14.8 72 0.74 83 13.4 69 21.3 73 9.97 62 6.71 64 19.3 69 3.90 31 0.00 1 0.00 1 0.00 1 7.03 62 20.1 67 9.91 64
S2D-Matching [84]55.7 0.33 89 1.92 92 0.06 76 2.04 67 12.4 72 0.79 53 4.15 63 13.0 71 1.09 71 1.09 24 8.04 16 0.24 34 9.82 36 15.9 37 6.68 35 7.85 80 16.4 35 5.58 80 0.20 102 0.00 1 0.96 103 4.94 27 12.6 20 8.81 53
AggregFlow [97]56.2 0.53 101 2.62 107 0.12 102 2.72 84 13.2 80 1.45 85 3.90 61 13.0 71 1.85 88 1.06 20 9.26 35 0.18 17 12.1 49 19.4 51 7.83 44 3.05 11 12.1 10 2.29 8 0.04 83 0.00 1 0.44 91 5.82 48 15.9 45 9.26 57
TF+OM [100]56.3 0.16 10 0.98 13 0.01 31 1.85 57 10.0 51 1.15 77 4.71 76 12.6 66 5.84 97 1.79 70 14.0 69 0.69 78 15.4 91 22.1 86 16.5 94 5.62 46 19.8 75 3.95 33 0.00 1 0.00 1 0.00 1 8.18 78 20.6 71 12.0 79
DeepFlow2 [108]56.7 0.26 72 1.53 73 0.08 92 2.56 81 11.7 62 1.30 82 3.73 60 11.5 58 0.90 61 1.99 79 15.1 76 0.65 76 12.3 51 19.5 53 9.07 55 4.57 29 18.7 61 2.81 14 0.00 1 0.00 1 0.00 1 8.01 77 21.0 72 10.8 74
Adaptive [20]57.9 0.29 79 1.72 82 0.06 76 2.04 67 12.5 75 1.13 75 5.51 83 14.7 81 0.68 51 1.83 71 13.9 68 0.59 73 12.7 61 19.9 56 10.1 63 7.15 68 18.9 65 4.08 36 0.00 1 0.00 1 0.00 1 6.38 56 16.4 47 8.82 54
Steered-L1 [118]62.0 0.10 1 0.59 1 0.01 31 1.01 11 6.84 17 0.52 32 2.76 40 9.44 44 0.91 62 1.78 69 14.9 74 0.51 70 14.0 78 20.5 63 15.2 88 9.02 100 19.9 76 6.57 98 1.07 120 0.00 1 7.19 121 12.1 99 22.9 88 20.6 105
RFlow [90]62.3 0.20 31 1.21 39 0.01 31 1.58 44 9.77 46 0.77 52 4.69 75 13.5 74 0.34 24 2.30 93 17.7 93 0.80 88 14.3 80 21.4 75 15.1 87 5.47 41 20.9 86 4.98 59 0.01 75 0.00 1 0.15 82 7.91 75 21.0 72 10.6 73
TriangleFlow [30]63.4 0.24 62 1.39 63 0.00 1 2.50 80 14.3 88 0.98 68 4.46 70 12.7 67 0.41 33 1.49 60 12.2 59 0.42 63 15.8 95 23.1 95 16.4 93 8.57 90 17.7 55 4.86 56 0.03 77 0.00 1 0.05 76 6.59 58 17.3 51 9.55 61
Aniso. Huber-L1 [22]63.6 0.29 79 1.66 78 0.06 76 2.43 79 13.1 79 1.12 74 5.68 84 14.3 79 1.27 81 1.56 63 12.4 60 0.30 51 12.4 53 19.2 50 10.1 63 4.70 31 17.1 47 4.45 42 0.17 99 0.00 1 0.89 102 6.28 54 16.7 49 8.80 52
DeepFlow [86]64.1 0.34 92 1.74 86 0.09 94 2.87 88 12.4 72 1.56 86 4.42 69 12.4 62 2.69 92 2.20 87 16.1 82 0.81 89 12.3 51 19.8 55 8.36 47 4.85 34 20.1 77 2.95 15 0.00 1 0.00 1 0.00 1 9.35 85 23.3 91 12.7 82
Occlusion-TV-L1 [63]64.2 0.27 75 1.55 75 0.06 76 1.99 66 12.1 67 1.14 76 5.42 81 14.9 83 0.93 65 1.83 71 14.0 69 0.49 68 13.6 72 21.2 69 11.5 72 6.13 54 19.6 74 5.37 72 0.00 1 0.00 1 0.00 1 9.19 84 23.4 92 11.5 77
CBF [12]65.6 0.18 20 1.09 25 0.01 31 2.37 77 12.9 77 1.94 92 4.28 66 12.0 59 1.13 75 1.97 78 16.1 82 0.66 77 13.3 68 20.5 63 12.7 80 5.89 50 18.8 64 4.73 52 0.45 115 0.00 1 1.33 111 7.67 70 18.9 60 12.7 82
LocallyOriented [52]66.7 0.49 100 2.66 108 0.06 76 3.28 92 15.4 91 1.91 91 6.59 93 16.9 94 1.20 76 1.29 50 10.1 46 0.52 72 14.6 82 21.5 77 12.6 78 7.79 78 16.7 43 4.33 40 0.00 1 0.00 1 0.00 1 7.87 72 19.1 62 11.1 76
FlowNet2 [122]68.5 0.74 110 3.32 113 0.12 102 5.00 106 17.2 97 2.46 99 6.13 89 15.0 84 5.85 98 1.29 50 10.3 49 0.40 62 13.2 65 21.6 83 8.11 45 7.27 72 17.7 55 6.06 89 0.00 1 0.00 1 0.05 76 5.52 41 17.5 53 3.70 5
DF-Auto [115]69.0 0.61 106 2.33 100 0.10 98 4.04 99 15.3 90 2.49 100 6.59 93 14.8 82 6.66 100 1.84 73 15.0 75 0.51 70 14.9 86 21.5 77 16.8 96 3.47 18 16.7 43 3.82 30 0.00 1 0.00 1 0.00 1 7.99 76 19.5 64 11.6 78
TV-L1-improved [17]69.1 0.25 69 1.46 70 0.07 85 1.82 55 11.1 58 1.02 69 5.46 82 15.0 84 1.32 82 2.26 90 16.4 85 0.79 87 13.8 74 21.5 77 11.8 73 9.40 101 23.6 99 6.48 95 0.00 1 0.00 1 0.00 1 7.89 74 21.3 76 10.3 70
TriFlow [95]69.4 0.27 75 1.62 76 0.01 31 2.27 75 13.2 80 1.24 79 7.10 98 16.9 94 7.37 103 1.31 53 11.7 56 0.43 64 17.3 103 23.4 101 20.6 105 3.24 14 15.8 26 3.91 32 4.67 127 0.00 1 18.1 127 6.86 59 18.1 56 7.89 31
CLG-TV [48]70.8 0.31 86 1.67 80 0.06 76 2.10 71 13.0 78 0.92 65 5.33 80 14.2 78 1.04 69 1.71 68 13.7 67 0.38 59 13.9 76 21.4 75 12.0 74 5.20 37 22.7 92 5.07 63 0.20 102 0.00 1 1.01 105 7.85 71 19.4 63 9.91 64
Bartels [41]72.5 0.24 62 1.40 64 0.01 31 1.42 33 8.88 37 0.62 41 3.51 56 12.4 62 1.00 68 2.26 90 15.8 80 0.95 93 15.5 92 23.3 99 15.8 92 7.99 82 23.0 96 5.20 67 0.33 108 0.00 1 1.92 114 9.95 91 24.0 93 13.7 89
Brox et al. [5]72.9 0.25 69 1.45 69 0.03 53 2.22 74 13.7 86 1.07 71 3.44 54 11.4 57 0.68 51 2.20 87 16.7 89 0.72 81 17.8 107 23.4 101 24.6 113 8.90 97 24.6 102 6.63 99 0.00 1 0.00 1 0.00 1 10.6 94 25.9 100 14.8 93
Fusion [6]73.2 0.24 62 1.41 66 0.05 71 1.13 19 8.57 33 0.47 27 2.45 30 8.15 27 0.93 65 2.12 86 18.3 99 1.21 97 16.2 99 23.1 95 19.6 103 6.72 66 18.7 61 5.67 82 0.07 87 0.15 119 0.10 80 10.4 93 24.9 98 14.6 92
SegOF [10]73.7 0.24 62 1.41 66 0.05 71 4.72 104 21.4 106 3.68 106 9.28 105 19.5 104 4.83 94 1.05 19 7.42 13 0.78 86 20.7 117 27.1 115 28.6 118 10.4 107 26.0 105 7.80 110 0.00 1 0.00 1 0.00 1 7.25 66 20.0 66 7.44 25
Classic++ [32]73.8 0.26 72 1.50 72 0.07 85 2.08 70 12.2 71 1.03 70 4.84 78 14.0 77 1.26 78 2.07 84 16.1 82 0.64 74 13.9 76 22.5 89 10.1 63 6.11 53 23.1 97 5.28 70 0.06 85 0.00 1 0.34 87 8.66 81 21.7 80 11.0 75
Rannacher [23]75.6 0.33 89 1.95 93 0.07 85 2.21 73 13.4 83 1.29 81 5.78 85 15.6 89 1.48 85 2.51 97 17.8 94 0.95 93 14.5 81 22.5 89 12.2 76 9.72 105 24.8 103 6.66 100 0.00 1 0.00 1 0.00 1 7.50 69 21.1 75 9.97 66
SuperFlow [81]76.7 0.45 96 1.75 87 0.10 98 3.01 90 13.4 83 2.04 93 6.82 97 15.2 87 8.24 106 1.96 75 17.0 91 0.50 69 15.6 94 22.2 87 19.2 102 5.87 49 20.6 82 5.46 76 0.00 1 0.00 1 0.00 1 10.1 92 24.6 96 13.4 87
Local-TV-L1 [65]77.5 0.53 101 2.10 94 0.12 102 4.96 105 18.0 101 3.44 105 8.54 103 16.7 93 6.16 99 2.47 96 18.5 101 1.01 96 12.5 57 19.9 56 9.65 61 5.53 44 19.5 72 4.95 58 0.00 1 0.00 1 0.00 1 13.4 104 24.2 94 27.1 114
BriefMatch [124]77.5 0.16 10 0.94 10 0.01 31 1.97 65 9.60 44 1.10 73 2.79 43 9.56 45 0.54 44 2.11 85 15.6 79 0.70 79 14.6 82 21.5 77 15.2 88 10.4 107 22.0 90 8.36 113 2.52 126 0.62 129 13.7 126 13.6 107 25.5 99 22.0 109
SIOF [67]78.0 0.42 95 2.28 96 0.08 92 3.55 95 17.7 100 2.05 94 8.15 102 17.9 101 7.78 105 2.41 95 17.9 95 1.00 95 15.5 92 22.7 92 17.8 100 4.67 30 19.5 72 4.77 54 0.00 1 0.00 1 0.00 1 9.35 85 21.8 81 17.7 99
p-harmonic [29]80.6 0.29 79 1.73 84 0.02 48 2.16 72 13.2 80 1.33 83 5.87 86 15.8 90 1.59 86 2.55 98 17.9 95 1.49 100 17.0 101 22.7 92 23.3 110 4.53 28 21.5 89 4.53 45 0.03 77 0.02 118 0.00 1 9.65 88 23.2 90 15.0 94
Second-order prior [8]80.7 0.26 72 1.53 73 0.05 71 2.88 89 15.5 92 1.60 87 5.87 86 15.3 88 1.11 74 2.21 89 17.2 92 0.94 92 13.8 74 21.3 73 12.6 78 7.46 73 27.8 111 5.71 83 0.16 98 0.00 1 0.76 97 8.65 80 21.0 72 13.9 91
Dynamic MRF [7]82.6 0.30 85 1.79 89 0.04 68 2.37 77 14.9 89 1.09 72 4.81 77 15.0 84 0.86 57 2.66 99 18.2 98 1.25 98 17.6 105 25.7 113 18.1 101 10.9 112 30.4 116 7.45 106 0.00 1 0.00 1 0.00 1 15.1 110 29.9 115 21.9 108
F-TV-L1 [15]82.9 0.46 97 2.58 104 0.07 85 4.05 100 16.2 94 2.21 95 6.59 93 15.9 91 1.39 83 2.35 94 17.9 95 0.88 91 13.7 73 21.5 77 11.4 71 7.53 75 21.1 88 4.75 53 0.03 77 0.17 121 0.05 76 7.15 64 20.5 69 7.39 24
Shiralkar [42]83.0 0.28 77 1.66 78 0.02 48 3.80 97 19.8 105 1.78 90 6.50 91 16.1 92 1.26 78 3.17 103 20.8 105 1.56 102 16.3 100 25.1 111 14.5 84 12.4 116 29.4 114 6.20 92 0.00 1 0.00 1 0.00 1 12.6 100 30.1 116 13.8 90
CNN-flow-warp+ref [117]84.4 0.33 89 1.91 91 0.09 94 2.72 84 12.4 72 2.32 97 6.77 96 18.9 103 2.09 89 2.28 92 16.4 85 0.82 90 17.7 106 23.9 105 22.8 109 9.40 101 24.3 101 6.73 101 0.00 1 0.00 1 0.00 1 14.0 108 26.8 106 20.2 104
GraphCuts [14]86.8 0.29 79 1.67 80 0.16 109 6.77 112 22.4 110 3.81 107 7.73 101 17.2 97 9.04 107 1.86 74 16.8 90 0.46 66 15.8 95 24.0 106 14.1 83 20.2 125 22.8 93 12.5 122 0.00 1 0.00 1 0.00 1 13.4 104 27.0 109 23.4 111
StereoOF-V1MT [119]88.1 0.41 93 2.35 101 0.04 68 4.27 102 21.6 107 1.66 88 6.25 90 17.7 99 0.50 36 3.13 102 23.2 109 1.41 99 19.4 114 27.9 119 20.7 106 11.6 114 32.5 118 7.60 108 0.00 1 0.00 1 0.00 1 16.7 114 32.8 118 21.3 106
Ad-TV-NDC [36]89.2 0.79 111 2.68 109 0.12 102 13.0 120 26.5 114 12.9 120 12.9 113 22.0 108 9.24 108 5.02 108 20.3 104 4.82 108 13.2 65 20.5 63 9.43 59 6.17 56 20.3 79 5.07 63 0.03 77 0.00 1 0.00 1 20.5 119 26.9 107 40.8 125
HBpMotionGpu [43]89.8 0.80 112 2.79 110 0.18 110 5.57 107 23.8 113 4.00 108 13.1 114 27.8 119 11.6 114 2.05 83 16.4 85 0.74 83 17.9 108 25.1 111 22.3 108 6.69 62 21.0 87 6.04 88 0.00 1 0.00 1 0.00 1 14.1 109 27.7 110 25.1 112
Filter Flow [19]91.0 0.58 105 2.59 105 0.11 101 4.48 103 19.7 103 2.66 103 12.1 108 23.7 111 13.5 118 14.5 118 30.4 115 15.0 118 18.7 113 23.7 104 27.5 117 8.11 84 20.7 84 6.48 95 0.00 1 0.00 1 0.00 1 11.0 96 21.9 82 17.2 97
StereoFlow [44]91.2 2.82 128 6.92 127 1.29 127 21.5 126 42.6 129 13.8 121 20.5 127 33.3 128 20.4 123 20.6 125 51.2 127 18.6 123 14.9 86 22.6 91 13.7 82 3.89 23 18.9 65 3.74 27 0.00 1 0.00 1 0.00 1 11.3 98 25.9 100 18.7 102
Modified CLG [34]93.0 0.62 107 2.54 103 0.12 102 3.52 94 18.7 102 2.59 102 12.2 110 23.5 110 12.5 116 3.25 104 20.1 103 2.03 104 18.6 112 25.0 110 25.0 114 8.86 96 26.9 110 7.14 104 0.00 1 0.00 1 0.00 1 13.4 104 29.8 114 21.8 107
2bit-BM-tele [98]93.3 0.54 103 2.59 105 0.20 111 2.58 82 16.3 95 1.26 80 6.04 88 17.8 100 2.26 90 2.77 101 19.7 102 1.50 101 15.8 95 23.3 99 16.5 94 8.58 91 22.4 91 5.62 81 1.37 122 0.00 1 5.84 120 10.7 95 24.8 97 16.5 96
Learning Flow [11]94.2 0.32 88 1.89 90 0.01 31 2.61 83 16.0 93 1.21 78 6.52 92 17.9 101 1.65 87 4.69 107 24.9 112 3.14 107 20.8 118 27.4 118 26.9 116 10.9 112 28.6 113 7.90 111 0.10 94 0.00 1 0.64 94 13.3 103 28.5 113 18.1 100
FlowNetS+ft+v [112]95.5 0.31 86 1.76 88 0.09 94 3.39 93 13.5 85 2.49 100 7.24 99 16.9 94 5.12 95 3.32 105 18.3 99 2.07 105 17.1 102 23.2 98 20.3 104 6.23 57 23.2 98 5.50 79 0.35 112 0.52 126 1.50 113 8.79 83 23.1 89 13.6 88
SPSA-learn [13]95.9 0.86 114 3.30 112 0.28 116 6.02 109 22.0 108 4.09 109 10.6 106 21.3 106 9.82 112 5.83 111 22.9 107 5.66 112 17.9 108 23.4 101 23.4 111 10.2 106 25.0 104 8.09 112 0.00 1 0.00 1 0.00 1 15.9 113 28.1 111 23.3 110
IAOF2 [51]96.5 0.47 99 2.28 96 0.33 117 3.77 96 16.3 95 2.22 96 7.40 100 17.2 97 7.06 102 14.7 119 29.4 114 16.6 120 15.2 90 23.0 94 14.7 85 10.5 109 20.6 82 7.03 103 0.32 107 0.00 1 2.00 116 11.2 97 22.6 87 15.4 95
UnFlow [129]97.1 1.88 123 6.59 125 0.87 124 6.75 111 27.2 115 4.57 111 12.5 112 27.9 120 7.37 103 5.65 110 21.0 106 5.26 110 22.5 121 30.2 122 26.4 115 9.48 103 30.5 117 7.32 105 0.00 1 0.00 1 0.00 1 9.58 87 26.9 107 12.3 81
LDOF [28]97.7 0.41 93 2.31 99 0.09 94 3.85 98 17.3 98 2.32 97 4.68 74 13.5 74 2.59 91 3.97 106 24.8 111 2.14 106 16.1 98 23.1 95 17.6 98 8.24 86 26.0 105 6.50 97 0.33 108 0.34 123 1.95 115 9.77 90 26.7 104 12.9 84
IAOF [50]99.1 0.46 97 2.11 95 0.10 98 6.63 110 19.7 103 4.61 112 13.8 116 23.3 109 9.33 109 9.91 113 23.2 109 11.3 115 14.8 85 22.2 87 15.5 91 10.6 110 26.8 109 6.99 102 0.05 84 0.00 1 0.42 90 18.0 117 24.4 95 35.4 122
Nguyen [33]99.9 0.83 113 3.37 114 0.22 112 7.27 114 22.1 109 6.46 115 15.4 119 26.8 117 12.4 115 17.6 122 30.4 115 20.2 125 18.5 111 24.7 108 24.5 112 8.82 95 28.5 112 8.81 115 0.00 1 0.00 1 0.00 1 18.9 118 31.7 117 29.4 116
BlockOverlap [61]100.0 0.62 107 2.30 98 0.14 108 4.11 101 17.6 99 3.02 104 9.12 104 19.6 105 6.97 101 2.74 100 16.5 88 1.72 103 14.7 84 20.9 68 16.8 96 7.89 81 19.3 69 6.25 93 2.12 123 0.52 126 10.9 125 15.2 111 22.4 85 32.3 120
GroupFlow [9]100.6 0.56 104 3.20 111 0.05 71 9.79 117 32.3 121 7.11 118 11.4 107 24.6 112 9.68 111 2.01 81 16.0 81 0.70 79 19.8 115 29.9 121 12.0 74 15.2 122 32.5 118 15.4 124 0.33 108 0.00 1 1.11 107 13.2 102 28.4 112 17.2 97
2D-CLG [1]103.0 1.77 122 6.22 123 0.51 122 5.91 108 22.4 110 4.54 110 16.4 120 28.6 122 18.1 122 17.9 123 35.8 119 19.9 124 20.4 116 25.8 114 29.3 119 12.0 115 29.6 115 11.4 119 0.00 1 0.00 1 0.00 1 17.7 116 32.8 118 26.2 113
Heeger++ [104]104.1 0.95 115 4.26 117 0.26 115 11.8 119 39.5 127 6.54 116 12.3 111 24.7 114 3.51 93 10.7 114 37.1 121 8.97 113 30.7 126 36.7 126 39.2 125 21.4 127 46.3 128 18.3 127 0.00 1 0.00 1 0.00 1 24.4 122 37.0 121 31.9 118
FFV1MT [106]107.2 1.42 118 6.80 126 0.25 113 10.3 118 35.9 124 6.76 117 18.0 121 30.0 124 16.5 120 17.2 121 51.3 128 16.2 119 31.5 127 37.1 127 43.2 128 20.9 126 44.0 127 17.2 125 0.00 1 0.00 1 0.00 1 24.4 122 37.0 121 31.9 118
TI-DOFE [24]107.3 1.58 120 5.19 120 0.36 119 16.8 122 34.3 122 17.7 123 19.3 126 30.2 126 21.6 125 23.3 126 39.1 123 27.6 126 21.1 119 27.1 115 29.5 120 14.4 120 35.1 122 12.1 121 0.00 1 0.00 1 0.00 1 27.2 126 40.8 125 41.2 126
Black & Anandan [4]108.3 0.68 109 2.46 102 0.13 107 7.01 113 23.6 112 4.65 113 12.1 108 21.6 107 9.40 110 5.45 109 23.1 108 4.84 109 17.5 104 24.3 107 21.6 107 10.6 110 26.6 108 7.49 107 0.43 113 0.15 119 1.31 110 12.7 101 26.7 104 18.8 103
Horn & Schunck [3]109.5 1.05 116 4.22 116 0.25 113 7.74 115 29.1 118 5.17 114 13.6 115 24.6 112 10.8 113 12.7 116 36.1 120 12.8 116 21.4 120 27.3 117 30.9 122 13.9 119 35.2 123 11.6 120 0.03 77 0.00 1 0.17 84 22.3 121 37.9 123 31.7 117
SILK [79]113.0 1.05 116 4.27 118 0.44 120 9.69 116 27.9 116 8.93 119 15.2 118 26.9 118 13.1 117 6.14 112 25.9 113 5.57 111 23.0 122 29.2 120 34.1 123 12.6 117 33.9 120 9.78 117 0.81 118 0.00 1 3.50 118 21.5 120 33.3 120 34.5 121
HCIC-L [99]114.1 1.95 124 6.24 124 0.99 126 28.7 128 32.2 120 35.8 128 18.6 124 26.2 115 25.7 128 25.4 129 46.6 126 27.7 127 15.1 89 21.9 85 12.7 80 8.77 93 20.2 78 9.24 116 6.40 129 0.49 125 23.0 129 15.3 112 26.4 103 18.4 101
Adaptive flow [45]117.5 1.75 121 5.07 119 0.34 118 18.4 124 28.3 117 18.5 125 18.5 122 28.6 122 22.9 126 13.3 117 37.4 122 13.9 117 17.9 108 24.7 108 17.7 99 12.9 118 26.2 107 8.68 114 5.20 128 0.61 128 22.8 128 16.7 114 26.0 102 28.2 115
PGAM+LK [55]117.5 2.98 129 6.17 122 6.36 131 16.8 122 36.2 125 17.8 124 14.7 117 26.5 116 14.5 119 19.1 124 53.9 129 18.3 122 23.1 123 30.6 123 29.9 121 14.4 120 36.8 124 11.1 118 1.07 120 0.00 1 4.16 119 25.9 124 40.1 124 40.3 124
SLK [47]117.8 1.44 119 5.58 121 0.49 121 14.4 121 35.8 123 14.8 122 18.5 122 30.1 125 21.4 124 24.6 127 35.7 118 27.7 127 26.3 125 31.9 124 39.4 126 15.6 123 38.8 125 13.6 123 0.55 117 0.00 1 1.35 112 31.7 127 41.0 126 49.0 127
FOLKI [16]119.5 1.98 125 7.18 128 0.87 124 24.5 127 36.3 126 30.3 127 18.7 125 32.4 127 16.5 120 15.2 120 33.2 117 18.1 121 26.0 124 32.3 125 36.0 124 17.7 124 40.6 126 17.9 126 2.33 125 0.00 1 10.6 123 33.9 128 43.6 127 52.7 128
Periodicity [78]120.1 2.36 127 9.12 129 0.79 123 19.1 125 40.7 128 20.6 126 28.2 129 35.2 129 26.8 129 11.2 115 40.6 124 10.3 114 42.3 129 55.4 129 41.1 127 31.7 128 56.3 129 27.7 128 0.54 116 0.00 1 7.78 122 26.1 125 51.0 128 36.2 123
Pyramid LK [2]126.2 2.31 126 4.20 115 3.47 130 31.6 129 32.0 119 40.4 129 21.0 128 28.5 121 24.0 127 24.6 127 43.7 125 28.6 129 37.5 128 46.6 128 43.7 129 33.1 129 34.2 121 31.3 129 2.17 124 0.47 124 10.7 124 46.5 129 57.3 129 67.2 129
AdaConv-v1 [126]129.9 6.16 130 11.8 130 2.11 128 91.0 130 93.3 130 87.2 130 83.4 130 79.4 130 87.3 130 47.3 130 64.4 130 46.2 130 89.6 130 93.2 130 73.3 130 69.7 130 60.5 130 67.1 130 41.7 130 14.2 130 92.5 130 99.6 130 98.7 130 100.0 130
SepConv-v1 [127]129.9 6.16 130 11.8 130 2.11 128 91.0 130 93.3 130 87.2 130 83.4 130 79.4 130 87.3 130 47.3 130 64.4 130 46.2 130 89.6 130 93.2 130 73.3 130 69.7 130 60.5 130 67.1 130 41.7 130 14.2 130 92.5 130 99.6 130 98.7 130 100.0 130
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.