Important note: On September 7, 2026, the KITTI and KITTI-360 servers had to be restored to the backed-up state of August 7, 2026. Results within this period have to be resubmitted.

Method

Unrolled Half Quadratic Splitting for Optical Flow Estimation [HQSFlow]
[Anonymous Submission]

Submitted on 20 Oct. 2026 00:20 by
[Anonymous Submission]

Running time:0.12 s
Environment:GPU @ 2.5 Ghz (Python)

Method Description:
HQSFlow estimates dense optical flow from two consecutive images
using a multiscale, half-quadratic-splitting-inspired recurrent
architecture. A feature extractor using a transformer architecture
provides correspondence evidence, while recurrent updates combine
analytic data-consistency corrections with learned residual
corrections. A learned reliability gate controls the admission of
target-derived updates, and a separate source-conditioned proximal
pathway provides motion regularisation. This submission uses the
A0 reference model, trained through a universal learned curriculum
of synthetic and real optical-flow datasets, including KITTI 2015
training data. HQSFlow was not further finetuned to specialise on
KITTI data.
Parameters:
| Parameter | Setting |
|---|---|
| Pyramid scales | \(1/16,\ 1/8,\ 1/4,\ 1/2\) |
| Recurrent updates per scale | \(2,\ 4,\ 2,\ 2\)—**10 updates total** |
| Jacobi sweeps per update, by scale | \(2,\ 2,\ 1,\ 1\) |
| Data-correction bounds | \(2.0,\ 2.0,\ 1.5,\ 1.0\) |
| Proximal-correction bounds | \(0.50,\ 0.50,\ 0.50,\ 0.25\) |
Latex Bibtex:

Detailed Results

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

Test Set Average

Error Fl-bg Fl-fg Fl-all
All / All 19.69 18.22 19.44
All / Est 19.69 18.22 19.44
Noc / All 10.07 14.06 10.80
Noc / Est 10.07 14.06 10.80
This table as LaTeX

Test Image 0

Error Fl-bg Fl-fg Fl-all
All / All 6.15 16.55 7.58
All / Est 6.15 16.55 7.58
Noc / All 3.01 16.55 5.06
Noc / Est 3.01 16.55 5.06
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 1

Error Fl-bg Fl-fg Fl-all
All / All 7.14 20.41 8.62
All / Est 7.14 20.41 8.62
Noc / All 3.76 20.41 5.82
Noc / Est 3.76 20.41 5.82
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 2

Error Fl-bg Fl-fg Fl-all
All / All 15.93 18.27 16.04
All / Est 15.93 18.27 16.04
Noc / All 6.99 18.27 7.65
Noc / Est 6.99 18.27 7.65
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 3

Error Fl-bg Fl-fg Fl-all
All / All 21.78 76.40 26.83
All / Est 21.78 76.40 26.83
Noc / All 10.62 68.50 15.60
Noc / Est 10.62 68.50 15.60
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 4

Error Fl-bg Fl-fg Fl-all
All / All 34.10 28.98 33.25
All / Est 34.10 28.98 33.25
Noc / All 25.15 28.44 25.77
Noc / Est 25.15 28.44 25.77
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 5

Error Fl-bg Fl-fg Fl-all
All / All 12.91 0.03 11.75
All / Est 12.91 0.03 11.75
Noc / All 6.49 0.03 5.83
Noc / Est 6.49 0.03 5.83
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 6

Error Fl-bg Fl-fg Fl-all
All / All 13.30 1.43 12.05
All / Est 13.30 1.43 12.05
Noc / All 7.24 1.43 6.55
Noc / Est 7.24 1.43 6.55
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 7

Error Fl-bg Fl-fg Fl-all
All / All 0.82 81.72 16.66
All / Est 0.82 81.72 16.66
Noc / All 0.82 80.65 15.75
Noc / Est 0.82 80.65 15.75
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 8

Error Fl-bg Fl-fg Fl-all
All / All 0.55 12.73 2.80
All / Est 0.55 12.73 2.80
Noc / All 0.55 12.73 2.80
Noc / Est 0.55 12.73 2.80
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 9

Error Fl-bg Fl-fg Fl-all
All / All 0.84 32.52 8.93
All / Est 0.84 32.52 8.93
Noc / All 0.84 32.52 8.93
Noc / Est 0.84 32.52 8.93
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 10

Error Fl-bg Fl-fg Fl-all
All / All 8.30 9.65 8.61
All / Est 8.30 9.65 8.61
Noc / All 4.78 9.65 6.05
Noc / Est 4.78 9.65 6.05
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 11

Error Fl-bg Fl-fg Fl-all
All / All 7.94 6.55 7.69
All / Est 7.94 6.55 7.69
Noc / All 4.24 6.56 4.70
Noc / Est 4.24 6.56 4.70
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 12

Error Fl-bg Fl-fg Fl-all
All / All 14.04 3.70 13.34
All / Est 14.04 3.70 13.34
Noc / All 3.65 3.70 3.65
Noc / Est 3.65 3.70 3.65
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 13

Error Fl-bg Fl-fg Fl-all
All / All 13.73 25.62 15.19
All / Est 13.73 25.62 15.19
Noc / All 3.15 17.33 4.80
Noc / Est 3.15 17.33 4.80
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 14

Error Fl-bg Fl-fg Fl-all
All / All 14.97 6.13 14.81
All / Est 14.97 6.13 14.81
Noc / All 3.39 6.13 3.45
Noc / Est 3.39 6.13 3.45
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 15

Error Fl-bg Fl-fg Fl-all
All / All 30.34 3.19 27.88
All / Est 30.34 3.19 27.88
Noc / All 12.32 3.19 11.27
Noc / Est 12.32 3.19 11.27
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 16

Error Fl-bg Fl-fg Fl-all
All / All 32.30 26.15 31.39
All / Est 32.30 26.15 31.39
Noc / All 14.67 26.15 16.74
Noc / Est 14.67 26.15 16.74
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 17

Error Fl-bg Fl-fg Fl-all
All / All 24.40 17.01 23.63
All / Est 24.40 17.01 23.63
Noc / All 7.07 17.01 8.36
Noc / Est 7.07 17.01 8.36
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 18

Error Fl-bg Fl-fg Fl-all
All / All 36.83 96.38 65.12
All / Est 36.83 96.38 65.12
Noc / All 16.49 88.45 36.34
Noc / Est 16.49 88.45 36.34
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 19

Error Fl-bg Fl-fg Fl-all
All / All 39.42 11.27 36.23
All / Est 39.42 11.27 36.23
Noc / All 21.60 11.27 20.11
Noc / Est 21.60 11.27 20.11
This table as LaTeX

Input Image

Flow Result

Flow Error




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