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        
R0.5
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
OFLAF [77]10.8 1.67 4 9.54 5 0.81 11 4.12 7 23.1 5 2.26 15 3.43 1 11.8 1 1.47 7 2.31 8 15.3 5 0.67 8 18.1 2 27.2 3 8.68 5 12.6 35 27.0 11 6.93 29 0.78 18 1.08 29 3.37 24 11.6 8 25.9 3 16.2 15
MDP-Flow2 [68]12.5 1.76 8 9.93 9 0.86 13 3.26 2 20.6 2 1.44 3 4.04 3 13.6 3 1.26 5 3.09 26 21.8 30 0.88 19 22.4 15 32.2 12 14.3 14 9.15 12 23.6 3 5.83 10 2.18 40 0.32 17 4.78 37 10.8 5 26.3 4 15.0 9
NNF-Local [87]13.1 1.75 7 9.66 6 0.87 14 4.56 14 27.6 16 2.46 19 4.52 4 15.6 7 2.18 16 2.57 15 18.4 15 0.86 16 18.8 5 29.2 5 8.22 3 9.37 15 24.2 6 5.22 7 0.95 20 2.02 62 1.90 13 10.6 4 31.8 24 8.21 2
NN-field [71]15.4 2.01 19 11.0 20 1.10 27 5.74 26 30.7 31 3.21 27 4.57 5 15.7 8 2.22 18 1.81 2 15.7 7 0.54 5 19.0 6 29.4 6 8.42 4 10.5 21 20.3 1 3.83 1 1.43 26 2.03 63 3.72 25 10.1 2 31.1 19 6.81 1
PMMST [114]17.3 1.43 2 8.08 2 0.38 1 6.05 32 28.6 20 4.40 40 6.13 17 19.1 16 4.02 39 2.21 5 11.7 1 1.09 27 21.2 9 30.5 9 13.2 11 9.59 17 23.8 4 5.71 9 2.28 43 1.95 57 4.36 31 11.8 9 29.1 8 13.1 6
WLIF-Flow [93]20.9 1.80 10 9.97 10 0.94 16 6.24 35 28.7 22 4.52 42 5.74 12 18.5 11 3.13 25 3.03 25 19.9 22 1.01 24 21.9 10 32.0 11 14.1 12 12.4 32 27.2 12 6.44 13 3.40 64 0.07 7 8.69 62 11.4 7 26.8 5 15.7 12
ComponentFusion [96]21.1 1.73 6 9.92 8 0.77 8 3.75 5 22.3 4 2.27 16 5.02 9 17.1 10 2.21 17 2.87 19 19.3 20 0.93 20 24.1 19 35.1 22 18.6 34 12.4 32 39.0 71 8.29 55 2.41 44 0.13 15 4.73 36 11.9 11 30.0 15 15.5 11
Correlation Flow [75]22.0 1.96 17 10.9 18 0.66 5 4.21 9 25.5 12 1.35 2 6.69 29 20.7 24 0.94 2 1.68 1 13.3 2 0.48 4 25.4 27 36.9 29 16.3 24 13.5 52 32.5 35 7.88 49 2.82 53 1.63 44 10.8 70 11.3 6 29.7 11 9.89 4
NNF-EAC [103]23.5 1.95 16 10.5 15 1.10 27 4.29 11 25.1 10 2.20 12 5.06 10 16.6 9 1.81 11 3.94 52 23.4 39 1.63 52 22.5 16 32.5 15 14.7 16 11.3 25 25.8 8 6.81 23 2.71 50 2.13 65 4.63 35 12.4 14 30.2 17 16.5 16
Layers++ [37]24.5 1.85 13 10.1 11 1.03 23 6.26 36 27.9 19 4.58 44 4.88 8 15.2 5 3.65 33 2.26 7 14.4 3 0.68 9 17.8 1 25.4 1 12.2 8 13.3 46 28.3 16 6.81 23 4.53 73 2.71 82 7.34 53 13.2 22 29.7 11 19.2 40
LME [70]24.5 1.89 15 10.6 16 0.75 6 3.53 3 21.3 3 1.83 8 7.04 40 18.6 14 8.24 71 3.10 28 23.0 37 0.86 16 24.8 25 35.5 24 17.9 31 10.1 19 30.1 26 6.46 14 2.67 49 1.51 41 5.54 41 12.8 16 30.9 18 17.7 27
RNLOD-Flow [121]26.6 1.68 5 9.49 4 0.75 6 5.76 27 30.6 30 3.18 25 6.58 26 21.1 28 2.92 22 2.61 16 17.5 12 0.74 11 22.0 11 32.8 16 14.9 19 11.5 27 28.0 15 7.37 37 5.53 87 4.17 95 15.2 93 11.8 9 27.7 7 15.1 10
nLayers [57]26.8 1.40 1 7.64 1 0.64 3 8.47 67 30.5 29 7.07 79 6.80 35 20.0 20 5.79 63 2.13 4 14.7 4 0.78 14 18.3 3 26.0 2 12.2 8 12.9 41 25.6 7 6.84 25 1.93 36 2.24 69 3.35 23 14.5 34 32.0 27 20.9 49
HAST [109]28.1 1.57 3 8.65 3 0.60 2 5.82 30 24.9 9 3.84 32 3.85 2 12.5 2 0.41 1 2.82 18 18.8 17 0.58 6 18.7 4 27.9 4 8.00 1 15.9 87 32.6 36 9.69 78 9.89 112 4.87 104 36.9 119 8.55 1 22.0 1 9.33 3
FC-2Layers-FF [74]28.8 1.81 11 9.71 7 1.07 26 6.99 44 33.9 45 4.71 45 4.71 6 15.0 4 3.63 32 2.67 17 18.3 14 0.87 18 20.6 8 29.7 7 14.5 15 13.3 46 28.4 17 7.26 34 5.67 91 1.82 52 14.9 89 12.9 19 29.4 9 18.4 34
SVFilterOh [111]29.7 2.18 29 11.4 24 0.78 9 5.94 31 29.2 24 3.13 23 4.85 7 15.2 5 2.01 13 2.35 9 17.4 10 0.63 7 20.4 7 30.1 8 8.12 2 14.7 79 29.5 22 8.51 62 10.3 113 3.98 93 31.3 111 12.0 12 26.9 6 13.4 7
TC/T-Flow [76]29.8 2.19 31 11.8 31 1.21 36 5.00 17 29.4 25 1.89 9 5.57 11 18.5 11 1.28 6 3.63 41 23.7 42 1.24 34 24.1 19 35.4 23 15.2 21 7.02 2 25.8 8 5.43 8 3.79 68 2.13 65 19.3 102 14.6 37 36.2 40 17.9 29
AGIF+OF [85]30.5 1.99 18 10.9 18 1.16 32 8.96 72 37.8 65 6.95 74 6.31 20 20.4 21 3.86 37 2.89 20 19.1 18 0.93 20 22.1 12 32.4 13 14.8 17 12.9 41 28.6 19 6.79 22 3.48 67 0.08 13 8.67 61 12.8 16 29.9 14 17.5 23
TC-Flow [46]30.8 2.04 20 11.0 20 0.94 16 3.69 4 23.4 6 1.68 5 5.96 16 19.9 19 1.06 3 3.73 44 23.6 41 1.24 34 25.7 31 38.0 34 14.8 17 8.99 11 34.6 45 5.03 6 2.82 53 2.47 75 15.9 97 16.0 44 38.1 46 22.0 53
HBM-GC [105]31.5 2.10 24 10.8 17 0.94 16 7.69 57 31.9 38 6.10 66 6.21 19 18.5 11 3.82 35 2.22 6 15.5 6 0.78 14 22.1 12 31.8 10 14.2 13 13.3 46 24.1 5 7.49 41 8.91 109 1.87 53 21.4 106 12.7 15 31.1 19 16.7 19
ALD-Flow [66]33.1 2.22 33 11.8 31 1.02 22 4.33 12 24.7 7 2.04 11 6.35 22 20.9 25 1.56 8 3.67 42 24.0 46 1.10 28 25.8 32 37.5 33 15.8 23 8.24 5 32.7 38 4.68 3 3.06 58 2.62 81 16.6 99 15.6 43 39.3 48 19.8 44
ProbFlowFields [128]35.2 3.29 69 17.1 72 1.88 83 6.54 38 29.8 26 5.50 56 7.69 47 23.8 45 6.90 66 3.09 26 17.1 9 1.28 36 27.8 39 39.5 40 19.2 40 6.56 1 27.2 12 5.00 5 0.09 3 0.03 3 0.86 7 17.1 51 39.4 49 17.5 23
IROF++ [58]35.5 2.18 29 11.5 27 1.33 43 7.91 58 36.5 60 5.96 63 6.71 31 21.7 34 4.85 56 3.62 40 22.8 33 1.63 52 24.2 22 34.9 21 17.1 28 13.3 46 33.4 41 7.82 47 0.55 15 1.09 30 1.01 9 12.8 16 32.9 31 16.7 19
FESL [72]36.2 1.86 14 10.2 12 0.99 19 10.4 88 39.3 76 7.94 87 6.79 34 21.2 30 4.35 46 2.39 10 16.2 8 0.76 13 24.2 22 34.7 19 19.2 40 12.6 35 27.7 14 7.10 33 3.35 62 2.20 68 8.03 57 14.5 34 31.2 21 17.6 26
FMOF [94]36.5 2.09 22 11.2 23 1.44 56 9.20 74 37.9 66 6.96 75 6.14 18 19.5 17 3.82 35 2.52 13 17.4 10 0.73 10 24.1 19 34.8 20 17.7 30 13.5 52 28.4 17 6.99 30 4.64 76 1.63 44 14.5 85 14.5 34 32.7 29 17.2 22
Classic+CPF [83]37.1 2.16 27 11.6 28 1.42 54 8.04 60 36.6 61 5.76 60 6.70 30 21.8 36 3.86 37 3.02 24 21.2 28 1.14 30 23.6 18 34.2 18 17.0 27 13.4 51 29.1 20 7.03 32 4.58 75 1.50 40 13.6 82 12.9 19 29.7 11 17.5 23
MLDP_OF [89]37.4 2.46 45 13.6 48 1.14 31 4.43 13 27.8 18 1.99 10 6.80 35 21.7 34 1.89 12 2.52 13 19.6 21 0.75 12 28.2 40 40.4 43 19.2 40 11.8 29 29.6 23 9.40 74 8.30 107 2.15 67 31.7 113 13.3 23 33.4 34 15.9 13
PH-Flow [101]38.0 2.30 38 12.2 35 1.45 58 7.61 55 35.2 50 5.81 61 5.92 15 19.0 15 4.67 54 3.52 36 22.1 31 1.49 46 23.4 17 33.9 17 16.3 24 12.4 32 29.4 21 6.87 26 4.88 80 2.25 71 14.0 83 12.2 13 30.1 16 16.6 17
Efficient-NL [60]39.3 2.41 43 11.8 31 1.55 69 8.28 63 35.4 53 5.90 62 6.72 32 20.9 25 3.78 34 2.95 23 19.1 18 1.20 32 22.1 12 32.4 13 15.3 22 14.6 77 31.0 30 8.05 53 3.32 60 2.40 74 7.02 49 13.6 27 29.6 10 18.2 31
PMF [73]39.7 2.30 38 12.8 41 1.01 20 5.64 25 31.4 35 2.51 20 6.83 37 22.5 41 1.72 10 3.26 29 21.1 26 0.94 22 24.3 24 36.7 28 9.56 6 14.4 73 40.0 77 8.40 59 7.45 104 8.62 121 24.8 107 10.4 3 25.6 2 12.7 5
Aniso-Texture [82]40.2 1.84 12 10.4 14 0.81 11 4.68 15 24.7 7 3.74 30 8.07 51 23.8 45 3.23 28 2.10 3 18.4 15 0.46 2 29.0 51 41.0 48 22.9 55 12.7 37 32.7 38 8.37 58 6.63 99 5.87 112 14.8 88 16.4 45 35.2 38 24.2 63
OAR-Flow [125]40.4 2.96 63 15.1 63 1.58 71 6.72 41 31.3 34 4.10 37 9.12 59 27.1 56 4.72 55 3.73 44 23.9 44 1.17 31 28.3 42 40.8 45 17.6 29 8.30 6 33.5 43 4.69 4 0.25 7 0.17 16 2.56 18 17.5 55 40.5 51 22.6 56
Sparse-NonSparse [56]41.4 2.11 25 11.7 29 1.39 49 7.47 54 35.1 49 5.75 59 6.48 24 21.2 30 4.34 44 3.52 36 22.9 34 1.38 41 26.1 35 37.3 32 19.6 47 13.5 52 31.2 32 7.42 38 5.02 84 1.18 34 13.5 81 13.5 25 31.7 22 18.8 38
Ramp [62]42.2 2.21 32 12.1 34 1.45 58 7.45 53 35.5 55 5.63 58 6.33 21 20.6 23 4.23 41 3.43 33 22.5 32 1.38 41 25.8 32 37.0 30 19.3 44 13.5 52 30.3 27 7.45 39 4.89 81 1.97 59 15.1 92 13.1 21 31.9 25 18.0 30
NL-TV-NCC [25]42.4 2.25 35 11.7 29 0.78 9 6.94 43 35.5 55 2.54 21 6.48 24 21.1 28 1.08 4 2.48 12 21.5 29 0.46 2 31.5 64 46.7 81 16.7 26 17.3 91 41.0 86 10.2 81 4.41 72 0.10 14 10.1 67 18.4 56 43.2 57 18.2 31
LSM [39]42.6 2.24 34 12.4 37 1.39 49 7.37 51 35.4 53 5.47 55 6.61 27 21.6 33 4.24 42 3.46 35 23.8 43 1.30 38 25.8 32 37.0 30 19.3 44 13.7 58 32.1 34 7.36 36 5.34 86 1.11 32 14.5 85 13.7 30 32.3 28 18.2 31
OFH [38]42.7 2.82 58 13.9 51 2.01 84 4.91 16 28.6 20 2.33 17 8.97 58 28.0 61 2.88 21 4.00 55 27.0 56 1.43 44 31.0 61 44.5 68 22.7 53 10.5 21 41.8 88 6.88 27 0.03 1 0.02 1 0.27 3 17.1 51 46.4 70 19.2 40
Sparse Occlusion [54]43.4 2.14 26 11.4 24 1.03 23 7.32 49 31.0 32 6.11 67 7.29 44 22.9 43 2.48 20 3.29 30 22.9 34 1.03 25 26.9 37 39.4 38 14.9 19 13.0 43 33.3 40 7.63 44 7.80 105 8.76 124 12.2 77 14.8 39 34.8 37 16.9 21
Classic+NL [31]43.5 2.08 21 11.4 24 1.35 45 7.33 50 35.9 58 5.30 52 6.47 23 21.0 27 4.53 51 3.59 38 22.9 34 1.49 46 25.4 27 36.3 26 19.4 46 13.8 61 31.1 31 7.57 42 5.78 93 2.32 73 15.0 90 13.5 25 31.9 25 18.7 37
IROF-TV [53]45.9 2.51 48 13.5 46 1.41 52 8.08 61 38.7 73 6.19 69 6.97 39 22.3 38 4.43 48 4.23 58 28.8 64 1.72 57 28.3 42 39.9 41 22.6 52 13.8 61 40.0 77 8.01 51 0.23 6 0.39 21 0.67 5 13.7 30 33.6 35 17.8 28
RFlow [90]46.2 2.42 44 13.5 46 1.16 32 3.98 6 25.2 11 1.81 7 8.89 57 27.5 58 3.13 25 3.45 34 26.8 54 1.60 50 30.5 59 43.6 59 24.5 63 14.2 68 38.1 65 7.94 50 3.36 63 1.65 47 8.47 60 16.9 50 42.3 53 20.5 48
TV-L1-MCT [64]46.4 2.09 22 11.1 22 1.39 49 9.67 77 39.0 75 7.35 80 7.11 42 22.3 38 4.27 43 2.94 22 20.7 25 1.13 29 28.4 44 39.4 38 25.8 70 16.0 89 35.0 48 9.27 71 1.27 24 0.57 23 7.24 51 14.8 39 33.2 33 23.3 60
COFM [59]47.0 2.51 48 13.9 51 1.42 54 5.54 21 28.9 23 3.40 28 7.79 49 23.6 44 4.53 51 2.90 21 18.2 13 0.95 23 29.1 52 40.8 45 25.4 67 15.5 85 30.7 29 9.39 73 4.69 77 1.23 35 15.4 96 16.8 49 37.1 41 21.8 52
S2D-Matching [84]47.1 2.39 41 13.0 42 1.52 66 7.22 47 35.6 57 5.13 50 7.63 46 24.4 48 4.38 47 3.30 31 20.5 24 1.35 40 25.3 26 36.0 25 19.2 40 14.1 65 31.5 33 7.77 46 6.21 96 2.24 69 16.9 100 13.6 27 31.7 22 19.3 42
Occlusion-TV-L1 [63]48.9 2.47 46 13.1 43 1.12 29 6.32 37 32.2 40 4.45 41 9.86 64 28.3 62 4.44 49 3.86 50 26.7 53 1.43 44 31.9 70 44.3 65 27.1 76 11.3 25 35.3 52 10.4 83 0.47 13 1.16 33 0.67 5 19.8 64 46.6 72 22.9 58
Complementary OF [21]49.0 2.69 55 15.0 61 1.33 43 4.19 8 26.9 14 1.70 6 7.15 43 24.4 48 3.09 24 3.86 50 26.1 50 1.41 43 33.2 76 44.6 70 29.7 87 13.3 46 40.7 85 7.00 31 0.74 17 0.03 3 7.12 50 23.9 85 53.1 91 33.9 91
ACK-Prior [27]49.1 2.16 27 12.4 37 0.64 3 4.26 10 25.9 13 1.33 1 5.91 14 20.4 21 1.67 9 2.39 10 20.4 23 0.33 1 30.0 56 41.1 49 24.4 62 19.2 102 40.3 82 12.2 94 14.4 122 6.30 115 40.9 122 21.0 69 43.6 59 27.5 77
CostFilter [40]49.2 2.65 52 14.9 59 1.01 20 5.51 20 31.6 36 2.23 14 7.39 45 24.1 47 3.06 23 3.82 48 26.1 50 1.08 26 25.4 27 38.9 37 10.2 7 15.1 82 42.7 91 8.52 63 8.99 110 10.3 126 29.5 110 14.4 33 37.2 42 16.1 14
MDP-Flow [26]49.4 2.33 40 13.4 45 1.20 34 5.61 24 26.9 14 4.88 47 6.76 33 22.6 42 5.72 62 4.13 56 29.5 69 1.92 61 28.7 47 40.8 45 23.2 58 12.8 39 36.7 57 8.04 52 2.54 46 2.96 84 4.43 33 19.4 63 44.6 63 26.0 72
2DHMM-SAS [92]51.1 2.28 37 12.3 36 1.46 60 8.45 66 38.1 68 6.02 65 8.34 53 24.4 48 5.21 58 3.73 44 23.4 39 1.62 51 25.5 30 36.6 27 18.8 35 14.5 74 33.4 41 8.46 61 5.07 85 2.05 64 15.3 94 13.3 23 32.9 31 18.5 36
SimpleFlow [49]51.6 2.39 41 12.6 40 1.60 73 9.03 73 38.3 69 7.38 81 8.52 55 25.7 52 5.41 59 4.36 63 25.5 49 2.48 70 26.8 36 38.0 34 21.6 49 14.0 64 29.7 24 7.65 45 2.77 52 1.97 59 6.48 46 14.3 32 32.8 30 19.7 43
Steered-L1 [118]52.7 1.78 9 10.2 12 0.92 15 2.76 1 19.0 1 1.44 3 5.78 13 19.7 18 2.10 14 3.99 54 27.5 59 1.53 49 31.3 63 43.3 57 27.6 78 14.6 77 39.2 73 9.88 79 14.6 123 5.70 110 47.1 123 22.4 76 48.1 76 29.3 82
AggregFlow [97]54.1 3.49 77 17.6 76 1.74 75 10.4 88 42.0 87 6.99 76 11.4 74 30.6 67 9.73 80 3.75 47 21.1 26 1.52 48 28.9 50 41.8 53 18.2 32 7.46 3 22.8 2 4.30 2 1.95 37 2.54 77 4.24 29 20.5 66 42.7 56 25.8 70
TF+OM [100]54.5 2.89 62 14.7 57 1.35 45 5.44 19 27.6 16 3.94 33 10.2 65 26.3 53 12.8 90 3.61 39 24.6 48 1.28 36 29.8 55 40.5 44 25.7 68 12.7 37 34.9 47 6.11 11 5.62 90 4.89 105 14.0 83 21.5 71 46.5 71 23.8 62
EPPM w/o HM [88]56.5 3.53 79 16.6 68 1.44 56 5.80 28 35.3 52 2.22 13 8.01 50 26.3 53 2.45 19 4.38 64 28.0 60 1.77 59 27.0 38 40.0 42 13.0 10 18.6 97 44.4 100 10.8 86 10.5 115 2.30 72 37.7 120 13.6 27 35.6 39 13.9 8
DeepFlow2 [108]56.9 3.18 67 16.9 71 1.48 62 6.68 40 33.7 44 4.15 38 10.7 69 31.1 68 7.69 69 5.96 82 31.1 77 3.33 81 28.5 45 41.3 50 19.1 37 9.45 16 34.7 46 6.60 17 1.60 29 1.66 49 10.4 68 23.5 80 47.9 75 30.2 85
CombBMOF [113]57.2 2.67 53 14.4 54 1.05 25 7.17 45 33.9 45 4.00 34 6.89 38 21.4 32 4.18 40 5.20 75 28.8 64 3.04 79 28.2 40 41.7 52 18.5 33 21.8 106 39.5 74 20.1 110 4.02 69 4.61 102 6.08 43 17.1 51 37.5 43 24.5 66
Adaptive [20]57.4 2.49 47 13.2 44 1.13 30 7.17 45 34.5 48 4.97 48 10.2 65 28.7 64 4.34 44 4.31 62 28.2 61 1.66 54 34.5 83 48.1 87 28.2 80 14.3 71 36.1 54 8.24 54 4.04 70 4.49 101 7.32 52 14.7 38 34.7 36 18.9 39
ComplOF-FED-GPU [35]59.9 2.87 61 15.6 65 1.35 45 6.14 33 33.6 43 3.15 24 8.26 52 27.4 57 3.30 29 4.29 59 28.2 61 1.71 56 33.1 75 47.9 86 24.1 61 14.7 79 45.7 103 9.19 69 3.33 61 1.48 39 15.0 90 18.8 59 48.4 78 22.0 53
TCOF [69]60.4 3.05 65 15.4 64 1.75 76 8.12 62 38.6 71 5.20 51 13.8 86 34.5 81 13.2 92 8.75 98 29.0 66 8.90 103 33.8 79 47.3 83 23.1 57 9.33 14 25.9 10 6.64 19 2.59 47 1.95 57 6.38 45 15.3 42 39.1 47 18.4 34
ROF-ND [107]61.3 3.29 69 14.7 57 1.29 40 7.42 52 31.8 37 2.42 18 7.10 41 22.1 37 2.13 15 3.68 43 23.2 38 2.87 77 31.1 62 43.7 60 23.6 60 19.3 104 38.5 67 10.7 85 8.90 108 2.99 85 24.8 107 21.9 73 48.6 79 22.7 57
BriefMatch [124]61.4 2.27 36 12.5 39 1.23 38 6.23 34 32.1 39 3.54 29 6.68 28 22.3 38 3.16 27 3.32 32 23.9 44 1.23 33 30.8 60 43.3 57 26.8 73 23.9 109 43.6 95 21.0 112 11.0 118 4.44 100 33.1 116 21.5 71 44.8 64 29.2 81
DeepFlow [86]62.0 3.36 72 17.3 73 1.54 68 7.91 58 35.2 50 5.35 53 12.1 78 33.0 76 10.5 86 6.24 84 32.1 79 3.55 83 28.8 48 42.3 54 18.8 35 9.77 18 37.4 61 6.90 28 1.30 25 0.37 18 9.70 66 27.4 95 52.7 87 35.8 93
Classic++ [32]62.0 2.59 51 13.9 51 1.51 65 6.79 42 32.3 41 5.37 54 9.15 60 27.8 60 5.54 60 4.29 59 29.0 66 1.77 59 30.2 58 43.9 61 22.8 54 14.8 81 40.0 77 8.36 57 6.82 100 4.17 95 16.5 98 16.5 46 39.5 50 19.8 44
TV-L1-improved [17]63.1 2.56 50 13.6 48 1.20 34 5.80 28 30.0 28 4.04 35 9.84 63 28.4 63 4.60 53 4.16 57 27.0 56 1.66 54 31.5 64 45.4 75 23.0 56 17.5 92 45.5 102 13.7 99 7.01 102 4.32 99 20.5 104 17.1 51 42.5 55 20.4 47
Bartels [41]64.3 3.26 68 16.7 70 1.37 48 5.33 18 29.8 26 3.18 25 8.40 54 26.9 55 4.45 50 4.40 65 26.9 55 2.16 63 32.7 72 45.4 75 28.4 83 14.3 71 38.1 65 12.9 95 8.20 106 3.82 91 31.3 111 18.4 56 43.7 61 23.3 60
S2F-IF [123]64.8 4.50 93 23.8 98 2.14 90 8.86 69 42.8 91 6.52 70 11.0 70 34.0 80 9.17 75 4.86 68 29.2 68 2.39 68 35.6 89 51.0 100 26.9 74 8.49 8 36.6 56 6.30 12 0.60 16 0.03 3 2.49 17 23.6 81 52.7 87 25.9 71
SIOF [67]65.4 2.67 53 13.6 48 1.23 38 7.65 56 37.9 66 4.78 46 14.2 89 32.9 75 15.4 94 6.36 85 34.7 85 3.84 85 34.0 80 45.8 78 33.2 91 13.5 52 35.7 53 10.5 84 1.99 38 0.99 27 4.21 28 20.5 66 45.6 66 30.7 87
F-TV-L1 [15]66.5 3.34 71 17.3 73 1.80 80 9.99 85 38.6 71 7.03 77 13.2 84 32.6 74 7.82 70 5.85 81 32.9 80 2.91 78 31.5 64 45.0 72 25.2 65 15.1 82 38.7 68 8.99 67 2.19 41 3.29 88 3.03 21 15.1 41 38.0 45 16.6 17
CRTflow [80]67.0 3.53 79 18.6 80 1.79 78 6.54 38 34.0 47 4.08 36 10.5 67 31.6 71 5.02 57 4.95 73 30.6 73 2.31 64 30.1 57 44.2 64 19.1 37 24.2 110 50.1 109 26.0 116 1.80 34 0.92 26 6.63 47 22.7 77 52.1 85 30.0 84
PGM-C [120]67.8 4.80 99 24.9 105 2.34 98 9.79 78 42.4 88 7.86 85 11.3 73 34.5 81 9.49 76 5.28 78 34.6 84 2.54 73 34.5 83 49.1 93 26.5 71 9.26 13 37.2 58 6.72 21 0.42 11 0.07 7 1.85 12 23.7 82 53.0 90 25.6 69
FlowFields [110]68.8 4.67 95 24.4 101 2.22 92 9.80 79 44.3 95 7.67 83 11.8 76 36.4 88 10.1 83 4.90 70 30.5 72 2.63 75 36.4 92 51.6 103 28.9 85 8.76 10 38.7 68 6.48 15 0.85 19 0.03 3 2.71 19 23.3 79 53.7 95 22.3 55
TriangleFlow [30]69.0 2.81 57 14.9 59 1.22 37 7.27 48 37.1 63 3.76 31 9.83 62 30.2 66 3.34 30 3.84 49 27.1 58 1.72 57 39.4 106 53.7 108 34.8 96 21.8 106 43.5 94 16.0 102 4.72 79 7.40 118 8.30 59 18.5 58 44.3 62 21.5 51
FlowFields+ [130]69.1 4.68 96 24.5 102 2.22 92 9.86 82 44.7 97 7.63 82 12.1 78 37.3 91 10.3 85 4.92 72 30.3 71 2.61 74 36.3 91 51.6 103 28.3 82 8.62 9 38.7 68 6.57 16 0.41 9 0.02 1 1.92 14 23.7 82 53.6 94 25.5 68
Rannacher [23]69.6 3.03 64 16.1 66 1.59 72 8.35 64 36.9 62 6.87 73 11.1 71 31.8 72 6.71 65 4.88 69 29.7 70 2.34 65 31.7 69 45.9 79 23.3 59 16.8 90 44.0 97 10.3 82 4.89 81 2.57 79 12.1 76 16.7 48 41.9 52 19.9 46
SRR-TVOF-NL [91]69.7 3.16 66 16.2 67 1.49 63 8.87 70 38.5 70 5.57 57 12.3 80 33.4 77 8.53 72 3.96 53 26.6 52 1.34 39 32.8 73 44.6 70 27.2 77 13.8 61 39.0 71 8.34 56 5.55 89 5.38 109 17.8 101 22.0 74 43.3 58 25.2 67
CPM-Flow [116]69.9 4.79 98 24.9 105 2.32 96 9.83 80 42.4 88 7.89 86 11.2 72 33.9 79 9.50 77 5.25 76 34.3 82 2.50 72 34.7 86 49.3 96 26.7 72 10.3 20 37.5 63 7.62 43 0.42 11 0.07 7 1.82 11 24.5 87 54.2 96 26.8 75
LocallyOriented [52]70.1 4.06 87 20.2 88 1.87 82 12.1 92 47.6 100 8.49 90 15.9 93 39.1 98 11.1 88 5.10 74 28.6 63 2.84 76 34.0 80 47.4 84 25.7 68 11.8 29 32.6 36 7.84 48 1.10 21 1.51 41 6.95 48 20.3 65 46.8 73 23.1 59
EpicFlow [102]70.4 4.80 99 24.9 105 2.33 97 9.90 83 42.9 92 7.95 88 11.8 76 35.7 86 9.56 78 5.26 77 34.4 83 2.49 71 34.6 85 49.2 95 27.0 75 10.8 24 37.5 63 7.33 35 0.41 9 0.07 7 1.80 10 24.1 86 53.5 93 26.4 73
Aniso. Huber-L1 [22]70.6 2.84 60 14.5 55 1.46 60 14.0 94 42.6 90 12.9 93 13.4 85 31.3 69 13.0 91 6.50 86 35.2 87 4.19 88 29.7 54 42.4 55 21.8 51 14.5 74 35.0 48 8.43 60 5.54 88 3.18 87 12.8 79 16.6 47 37.7 44 20.9 49
Kuang [131]71.6 4.54 94 24.0 99 2.07 86 9.42 75 45.2 98 6.53 71 12.5 81 38.7 96 8.97 74 4.91 71 31.0 76 2.36 67 37.7 98 53.5 107 29.5 86 12.8 39 42.9 93 9.24 70 0.53 14 0.07 7 2.71 19 18.9 60 47.6 74 24.3 64
Dynamic MRF [7]71.9 3.39 73 18.9 83 1.30 41 5.60 23 33.5 42 2.81 22 9.67 61 31.3 69 3.54 31 4.64 67 33.7 81 2.39 68 38.0 99 51.2 101 34.9 97 19.2 102 51.8 112 15.2 101 3.41 65 0.37 18 20.9 105 25.1 89 52.2 86 31.7 89
DPOF [18]74.1 4.03 85 21.8 92 2.11 87 9.50 76 40.4 79 5.97 64 8.88 56 27.5 58 6.05 64 4.29 59 30.8 74 2.08 62 31.5 64 45.1 73 21.6 49 15.9 87 37.3 60 9.53 76 15.3 124 1.61 43 47.3 124 22.1 75 46.3 69 28.5 78
CBF [12]76.5 2.82 58 15.0 61 1.32 42 18.0 99 40.4 79 21.6 101 10.6 68 29.2 65 9.72 79 6.57 87 34.8 86 4.55 90 31.5 64 44.0 63 24.5 63 14.5 74 35.0 48 8.92 66 10.9 117 6.02 113 26.2 109 20.7 68 43.6 59 27.2 76
Brox et al. [5]76.7 3.55 82 18.8 82 1.64 74 10.1 87 39.6 77 8.97 91 11.7 75 33.4 77 8.96 73 6.57 87 36.4 89 3.41 82 38.2 101 47.6 85 45.3 113 13.5 52 42.4 90 9.63 77 0.27 8 0.99 27 0.47 4 31.0 101 56.4 102 43.3 105
Fusion [6]76.7 3.40 74 19.1 84 2.16 91 5.57 22 31.1 33 4.53 43 7.70 48 25.2 51 7.53 68 5.78 80 35.6 88 4.10 87 36.6 93 47.1 82 38.8 102 14.2 68 41.9 89 13.2 96 6.84 101 5.31 107 11.7 74 24.8 88 51.1 84 31.6 88
Local-TV-L1 [65]77.7 4.05 86 19.4 86 2.51 100 17.1 98 43.6 94 15.9 96 19.8 100 37.3 91 23.3 97 9.20 101 43.3 97 6.89 100 28.6 46 41.3 50 20.2 48 14.1 65 35.1 51 8.67 64 1.24 22 0.62 24 3.94 26 33.5 108 57.2 103 49.6 112
CLG-TV [48]78.3 2.80 56 14.6 56 1.41 52 14.0 94 40.7 82 14.1 95 12.7 82 32.0 73 11.0 87 8.13 94 47.7 105 5.99 96 32.0 71 45.2 74 25.2 65 14.1 65 40.1 81 10.9 87 6.45 97 5.82 111 10.4 68 19.0 61 42.4 54 26.6 74
LDOF [28]80.1 4.09 89 20.0 87 2.31 95 9.96 84 41.8 85 7.06 78 14.1 87 37.0 89 10.1 83 8.41 95 43.3 97 4.97 91 34.4 82 46.2 80 32.5 89 12.2 31 41.0 86 8.88 65 1.63 31 2.00 61 5.79 42 29.9 96 56.0 100 38.8 100
p-harmonic [29]80.1 3.47 76 19.1 84 2.29 94 8.40 65 35.9 58 6.80 72 12.8 83 34.6 83 9.84 82 9.04 99 47.6 104 6.72 98 37.1 95 48.7 91 39.6 103 13.1 44 44.0 97 11.2 88 3.43 66 2.50 76 6.33 44 21.2 70 45.2 65 30.5 86
DF-Auto [115]80.5 4.71 97 22.2 93 2.11 87 21.1 102 49.4 102 21.6 101 20.3 101 39.8 100 31.0 103 7.62 91 37.5 91 5.08 93 33.6 77 43.9 61 33.3 92 8.36 7 29.8 25 7.48 40 2.60 48 5.21 106 2.22 15 32.4 104 53.1 91 43.2 104
TriFlow [95]81.9 3.53 79 17.9 77 1.77 77 11.0 91 37.3 64 10.6 92 16.7 96 35.8 87 25.3 99 4.44 66 30.9 75 2.34 65 35.0 88 44.3 65 35.7 98 10.7 23 30.4 28 6.68 20 33.4 127 9.63 125 90.0 129 30.3 99 55.2 99 36.8 96
FlowNetS+ft+v [112]84.3 3.75 84 18.5 79 2.13 89 10.0 86 38.8 74 8.25 89 16.3 94 37.5 94 20.0 95 7.89 92 37.0 90 5.17 94 36.9 94 48.2 88 35.7 98 11.6 28 40.0 77 9.13 68 4.56 74 4.02 94 14.6 87 23.8 84 51.0 82 31.9 90
SuperFlow [81]84.5 3.40 74 16.6 68 1.81 81 15.3 96 41.5 83 15.9 96 17.0 97 35.2 85 27.6 100 10.0 103 43.1 96 8.60 102 36.1 90 44.3 65 46.7 114 13.1 44 39.8 76 11.3 89 2.49 45 4.24 98 4.26 30 30.0 97 54.7 97 40.8 102
Second-order prior [8]85.8 3.49 77 18.6 80 1.79 78 9.83 80 40.6 81 7.83 84 14.1 87 39.0 97 9.82 81 6.20 83 31.4 78 3.83 84 34.7 86 49.4 97 27.6 78 18.7 98 52.1 113 11.4 90 9.18 111 3.60 90 20.1 103 19.1 62 48.2 77 24.4 65
Learning Flow [11]85.9 3.56 83 18.2 78 1.56 70 8.71 68 41.5 83 6.17 68 14.5 90 37.8 95 11.8 89 7.92 93 41.1 95 5.02 92 40.9 109 51.7 105 42.4 105 15.4 84 47.2 105 11.4 90 2.73 51 6.19 114 7.64 56 23.0 78 49.9 80 28.9 80
Ad-TV-NDC [36]87.8 10.3 115 20.2 88 18.1 124 38.1 114 53.0 108 43.3 116 28.0 110 45.6 106 35.7 107 20.6 110 48.9 108 23.8 111 29.1 52 42.5 56 19.1 37 13.7 58 36.1 54 9.46 75 2.03 39 1.43 38 4.38 32 41.4 116 65.3 114 57.0 118
CNN-flow-warp+ref [117]88.4 4.85 101 24.6 103 2.62 102 13.2 93 41.8 85 12.9 93 17.7 99 39.6 99 25.0 98 8.67 97 44.8 100 5.78 95 38.1 100 48.2 88 43.5 108 13.7 58 40.4 83 9.32 72 1.80 34 1.29 37 9.16 63 33.2 105 57.7 105 42.9 103
StereoOF-V1MT [119]89.8 4.08 88 23.0 94 1.49 63 10.4 88 53.3 109 4.35 39 16.3 94 49.5 111 5.71 61 7.37 90 48.5 106 4.03 86 46.7 113 62.9 116 42.9 107 21.9 108 64.7 119 17.0 103 1.58 28 1.87 53 9.43 65 33.2 105 66.2 115 36.5 95
BlockOverlap [61]92.0 4.14 92 17.3 73 3.50 105 23.3 103 43.1 93 25.5 105 21.0 102 37.2 90 27.8 101 13.1 104 39.0 93 13.7 106 28.8 48 38.6 36 28.2 80 18.7 98 37.2 58 13.3 97 12.6 120 6.40 117 40.8 121 26.8 93 45.8 67 43.3 105
Shiralkar [42]93.7 4.11 90 23.3 95 1.52 66 8.88 71 44.5 96 5.07 49 14.5 90 41.9 102 6.96 67 7.32 89 44.7 99 4.37 89 38.8 105 55.2 111 33.1 90 26.7 115 60.7 114 18.5 108 10.4 114 3.38 89 32.9 115 26.7 92 61.6 109 29.5 83
SegOF [10]94.1 6.07 109 25.2 108 3.62 107 36.7 112 55.3 110 41.7 114 26.1 106 43.8 104 39.2 110 15.2 106 45.4 101 12.3 104 46.5 112 56.0 112 57.5 118 18.2 96 49.9 108 14.9 100 0.19 4 0.71 25 0.86 7 31.1 102 52.9 89 35.9 94
StereoFlow [44]94.8 28.4 128 55.1 129 37.7 128 81.1 129 92.6 129 77.8 128 65.0 127 82.9 129 51.1 123 69.6 129 90.7 129 65.5 126 52.7 120 67.5 120 44.9 112 8.13 4 33.5 43 6.60 17 0.05 2 0.37 18 0.17 2 32.2 103 54.8 98 40.4 101
HBpMotionGpu [43]95.4 5.00 102 21.6 91 2.81 104 31.1 109 49.5 103 35.0 109 26.3 108 45.3 105 37.1 109 9.18 100 39.3 94 7.65 101 33.7 78 45.6 77 32.2 88 15.7 86 37.4 61 9.89 80 5.71 92 4.19 97 12.5 78 33.4 107 56.3 101 47.8 110
SPSA-learn [13]96.4 5.52 106 25.3 110 4.12 109 25.2 106 50.0 104 26.8 106 25.1 105 45.7 107 36.7 108 19.0 107 54.2 110 20.8 108 38.6 102 48.4 90 44.4 110 17.9 94 45.3 101 17.6 105 1.60 29 0.54 22 5.27 40 39.6 113 57.9 106 53.3 115
2bit-BM-tele [98]96.8 5.17 104 23.4 96 3.54 106 16.3 97 40.3 78 16.7 98 15.2 92 34.6 83 14.2 93 8.49 96 37.6 92 6.75 99 32.8 73 44.5 68 28.6 84 24.3 111 43.9 96 22.5 114 15.6 125 8.72 123 50.0 126 26.2 90 50.8 81 37.5 98
FlowNet2 [122]97.6 7.84 111 30.7 111 2.58 101 41.4 116 65.2 116 44.4 117 29.6 112 48.0 109 46.8 118 5.31 79 24.0 46 3.06 80 47.8 114 64.8 119 36.3 101 17.8 93 44.3 99 13.4 98 2.93 56 8.71 122 5.22 38 30.2 98 61.7 110 28.8 79
IAOF2 [51]98.2 4.13 91 20.4 90 2.02 85 18.0 99 45.9 99 18.0 99 17.1 98 37.3 91 21.4 96 46.4 120 57.8 112 56.1 123 37.4 97 48.8 92 35.9 100 25.5 112 42.7 91 20.4 111 6.62 98 3.04 86 15.3 94 26.8 93 51.0 82 37.9 99
Black & Anandan [4]98.9 5.52 106 25.2 108 4.71 111 24.4 105 52.8 106 24.4 104 26.8 109 48.3 110 34.4 105 20.9 111 60.4 113 22.4 110 38.7 104 49.7 98 42.8 106 18.9 100 49.4 106 17.1 104 1.78 33 2.57 79 3.30 22 36.0 109 57.3 104 49.5 111
Filter Flow [19]99.1 5.13 103 23.5 97 2.40 99 20.5 101 51.3 105 19.6 100 23.3 104 42.6 103 35.3 106 27.2 113 48.8 107 28.3 113 39.4 106 49.1 93 44.6 111 17.9 94 40.5 84 11.8 93 7.39 103 7.67 120 11.5 73 26.6 91 46.0 68 33.9 91
Modified CLG [34]101.1 7.42 110 31.9 113 5.50 112 31.7 110 52.9 107 37.6 112 28.4 111 50.8 112 40.4 112 20.3 109 60.5 114 21.3 109 39.5 108 51.2 101 42.2 104 14.2 68 45.8 104 11.5 92 3.24 59 1.70 51 9.31 64 40.3 114 65.1 113 54.7 117
IAOF [50]102.1 5.70 108 24.0 99 3.65 108 30.0 108 48.7 101 33.9 108 26.2 107 47.8 108 29.5 102 28.0 114 51.3 109 32.9 114 37.3 96 50.2 99 34.4 95 26.2 113 50.9 111 18.0 107 5.85 94 1.63 44 11.7 74 36.3 110 59.4 108 51.9 113
GraphCuts [14]104.0 5.45 105 24.7 104 2.64 103 24.3 104 55.8 112 21.9 103 21.4 103 40.8 101 32.4 104 9.25 102 46.4 102 6.31 97 38.6 102 51.7 105 33.8 93 28.8 118 39.7 75 18.7 109 12.1 119 2.87 83 35.1 118 38.5 111 58.4 107 53.9 116
2D-CLG [1]104.5 14.0 119 40.7 120 8.09 117 45.8 118 59.5 113 54.5 121 36.8 118 60.4 119 47.3 119 48.9 122 75.1 123 54.2 122 44.9 110 54.8 109 52.5 115 19.0 101 50.3 110 17.8 106 1.26 23 0.07 7 4.43 33 47.4 121 71.2 121 59.9 122
GroupFlow [9]104.9 8.95 114 33.2 114 7.07 114 43.6 117 70.7 121 45.5 118 32.7 114 59.8 118 42.4 115 13.2 105 46.6 103 12.4 105 51.1 117 70.0 122 34.2 94 30.8 120 62.8 116 33.8 121 1.54 27 2.56 78 4.14 27 39.0 112 67.0 117 47.4 109
UnFlow [129]106.0 22.1 126 43.6 123 7.44 116 52.6 122 73.8 125 54.3 120 47.7 124 74.9 127 47.5 120 26.4 112 68.7 118 24.7 112 64.5 125 75.5 126 65.6 125 28.5 117 67.0 123 27.1 118 0.19 4 1.87 53 0.05 1 30.4 100 62.4 111 36.8 96
Nguyen [33]107.0 8.19 112 31.4 112 4.40 110 54.9 123 55.7 111 70.2 124 33.6 116 54.6 113 43.3 116 43.5 119 60.9 115 50.5 120 45.1 111 54.9 110 54.2 116 21.1 105 49.4 106 21.0 112 2.92 55 1.87 53 7.39 54 44.7 119 66.2 115 58.5 120
Horn & Schunck [3]108.2 8.56 113 35.5 115 7.11 115 29.4 107 65.4 117 28.1 107 33.4 115 64.4 121 41.2 114 30.6 115 67.2 117 33.6 115 49.1 116 61.3 113 55.5 117 26.4 114 64.7 119 26.1 117 3.02 57 3.95 92 2.44 16 48.8 122 75.0 123 58.8 121
SILK [79]110.2 10.7 116 35.7 116 14.6 121 37.7 113 64.2 114 42.5 115 32.3 113 59.3 116 40.6 113 19.9 108 56.8 111 20.4 107 51.6 119 62.6 115 59.6 121 27.2 116 63.0 117 23.2 115 4.92 83 1.68 50 13.1 80 46.9 120 71.6 122 61.7 124
TI-DOFE [24]113.7 21.2 124 43.7 124 34.5 127 64.6 127 71.9 124 76.5 127 47.1 123 75.6 128 53.7 124 57.3 124 76.4 124 65.6 127 51.5 118 63.9 117 60.0 122 30.4 119 65.8 122 33.2 119 2.24 42 1.65 47 5.22 38 59.1 126 82.1 128 71.2 127
Periodicity [78]114.0 11.0 117 41.5 121 5.85 113 35.3 111 64.5 115 36.8 111 51.0 125 55.5 114 61.7 126 49.6 123 81.4 126 48.4 119 66.0 127 83.6 129 59.0 119 46.1 125 76.4 127 43.0 125 1.67 32 5.33 108 8.13 58 48.8 122 78.9 125 57.5 119
Heeger++ [104]115.0 24.4 127 45.8 125 9.72 119 47.8 120 85.9 128 37.8 113 66.2 128 69.8 124 75.2 127 59.7 126 88.6 128 56.9 124 66.6 128 80.3 128 62.4 124 65.6 129 87.3 129 67.1 129 4.14 71 1.26 36 7.39 54 41.9 117 68.8 118 43.4 107
SLK [47]117.6 17.8 122 50.1 128 21.7 125 62.2 126 77.8 127 74.7 126 40.4 121 72.7 126 48.1 121 66.2 127 73.9 121 76.1 129 60.9 123 71.2 123 72.9 129 33.1 121 68.3 125 35.4 123 5.99 95 1.09 30 11.4 72 60.5 128 81.9 127 75.0 128
FFV1MT [106]118.1 22.0 125 42.2 122 9.20 118 41.0 115 76.9 126 36.1 110 66.5 129 71.9 125 79.2 128 58.5 125 87.7 127 57.1 125 64.8 126 76.5 127 70.3 128 64.8 128 85.8 128 65.3 128 4.70 78 4.86 103 11.3 71 41.9 117 68.8 118 43.4 107
Adaptive flow [45]119.1 16.0 120 36.3 117 17.5 123 57.9 124 67.3 118 64.2 123 38.7 120 59.2 115 48.8 122 39.9 117 69.2 119 44.2 118 49.0 115 62.0 114 43.6 109 39.1 124 62.2 115 34.3 122 34.2 128 23.4 128 82.8 127 40.6 115 64.9 112 51.9 113
FOLKI [16]120.3 13.4 118 45.9 126 16.0 122 48.5 121 67.4 119 57.8 122 36.6 117 66.2 122 40.3 111 32.2 116 66.9 116 37.2 116 52.9 121 64.2 118 60.1 123 34.7 122 65.7 121 40.2 124 12.9 121 7.56 119 33.8 117 55.3 125 78.0 124 70.7 126
PGAM+LK [55]122.3 17.6 121 48.4 127 26.7 126 45.8 118 71.8 123 49.9 119 38.3 119 67.6 123 44.6 117 42.8 118 79.5 125 42.6 117 56.5 122 69.9 121 59.0 119 37.8 123 70.5 126 33.6 120 23.5 126 15.0 127 48.8 125 54.6 124 80.9 126 61.1 123
Pyramid LK [2]122.8 19.8 123 36.7 118 40.3 129 61.8 125 68.8 120 74.6 125 43.5 122 63.7 120 58.2 125 46.9 121 72.7 120 54.1 121 61.5 124 74.5 125 65.8 126 51.3 126 64.1 118 50.1 126 10.8 116 6.30 115 31.9 114 68.2 129 84.9 129 84.8 129
HCIC-L [99]125.5 29.6 129 37.7 119 11.4 120 77.3 128 71.7 122 90.9 129 63.0 126 59.4 117 83.6 129 66.9 128 74.8 122 69.8 128 68.1 129 74.1 124 66.1 127 54.4 127 67.4 124 52.5 127 58.9 129 43.5 129 89.4 128 59.4 127 70.0 120 67.4 125
AdaConv-v1 [126]130.0 82.5 130 78.4 130 94.0 130 98.6 130 99.3 130 97.9 130 99.9 130 99.9 130 99.9 130 97.4 130 96.9 130 99.7 130 100.0 130 99.9 130 99.8 130 93.4 130 95.5 130 93.4 130 86.5 130 85.7 130 99.4 130 99.9 130 99.9 130 99.9 130
SepConv-v1 [127]130.0 82.5 130 78.4 130 94.0 130 98.6 130 99.3 130 97.9 130 99.9 130 99.9 130 99.9 130 97.4 130 96.9 130 99.7 130 100.0 130 99.9 130 99.8 130 93.4 130 95.5 130 93.4 130 86.5 130 85.7 130 99.4 130 99.9 130 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.