Method

Two-Frame Motion Estimation Based on Polynomial Expansion [PolyExpand]


Submitted on 18 Sep. 2015 17:25 by
Moritz Menze (Leibniz Universität Hannover)

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

Method Description:
Two-frame motion estimation algorithm. The first step is to approximate each neighborhood of both frames by quadratic polynomials, which can be done efficiently using the polynomial expansion transform. From observing how an exact polynomial transforms under translation a method to estimate displacement fields from the polynomial expansion coefficients is derived and after a series of refinements leads to a robust algorithm.

The OpenCV implementation has been used.
Parameters:
pyr_scale = 0.5
levels = 10
winsize = 11
iterations = 20
poly_n = 5
poly_sigma = 1.0
Latex Bibtex:
@InProceedings{Farneback2003SCIA,
author = {Gunnar Farneback},
title = {Two-Frame Motion Estimation Based on Polynomial Expansion},
booktitle = {SCIA},
pages = {363--370},
year = {2003},
series = {{LNCS} 2749},
address = {Gothenburg, Sweden},
month = {June-July}
}

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 52.00 58.56 53.09
All / Est 52.00 58.56 53.09
Noc / All 43.77 55.90 45.97
Noc / Est 43.77 55.90 45.97
This table as LaTeX

Test Image 0

Error Fl-bg Fl-fg Fl-all
All / All 39.69 80.80 45.33
All / Est 39.69 80.80 45.33
Noc / All 34.06 80.80 41.15
Noc / Est 34.06 80.80 41.15
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 1

Error Fl-bg Fl-fg Fl-all
All / All 41.99 80.91 46.34
All / Est 41.99 80.91 46.34
Noc / All 37.63 80.91 42.98
Noc / Est 37.63 80.91 42.98
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 2

Error Fl-bg Fl-fg Fl-all
All / All 60.23 24.58 58.50
All / Est 60.23 24.58 58.50
Noc / All 52.53 24.58 50.91
Noc / Est 52.53 24.58 50.91
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 3

Error Fl-bg Fl-fg Fl-all
All / All 70.91 91.39 72.80
All / Est 70.91 91.39 72.80
Noc / All 64.16 88.51 66.26
Noc / Est 64.16 88.51 66.26
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 4

Error Fl-bg Fl-fg Fl-all
All / All 65.22 93.80 69.96
All / Est 65.22 93.80 69.96
Noc / All 58.52 93.58 65.07
Noc / Est 58.52 93.58 65.07
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 5

Error Fl-bg Fl-fg Fl-all
All / All 56.05 0.17 51.03
All / Est 56.05 0.17 51.03
Noc / All 49.62 0.17 44.53
Noc / Est 49.62 0.17 44.53
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 6

Error Fl-bg Fl-fg Fl-all
All / All 62.55 5.59 56.54
All / Est 62.55 5.59 56.54
Noc / All 57.73 5.59 51.52
Noc / Est 57.73 5.59 51.52
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 7

Error Fl-bg Fl-fg Fl-all
All / All 7.26 82.57 22.00
All / Est 7.26 82.57 22.00
Noc / All 7.26 81.56 21.15
Noc / Est 7.26 81.56 21.15
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 8

Error Fl-bg Fl-fg Fl-all
All / All 8.29 96.74 24.62
All / Est 8.29 96.74 24.62
Noc / All 8.29 96.74 24.62
Noc / Est 8.29 96.74 24.62
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 9

Error Fl-bg Fl-fg Fl-all
All / All 5.13 100.00 29.36
All / Est 5.13 100.00 29.36
Noc / All 5.13 100.00 29.36
Noc / Est 5.13 100.00 29.36
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 10

Error Fl-bg Fl-fg Fl-all
All / All 47.79 71.61 53.22
All / Est 47.79 71.61 53.22
Noc / All 38.61 71.61 47.19
Noc / Est 38.61 71.61 47.19
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 11

Error Fl-bg Fl-fg Fl-all
All / All 40.02 66.78 44.82
All / Est 40.02 66.78 44.82
Noc / All 31.14 66.75 38.31
Noc / Est 31.14 66.75 38.31
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 12

Error Fl-bg Fl-fg Fl-all
All / All 53.82 16.99 51.34
All / Est 53.82 16.99 51.34
Noc / All 45.00 16.99 42.77
Noc / Est 45.00 16.99 42.77
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 13

Error Fl-bg Fl-fg Fl-all
All / All 46.19 95.04 52.19
All / Est 46.19 95.04 52.19
Noc / All 35.14 93.63 41.94
Noc / Est 35.14 93.63 41.94
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 14

Error Fl-bg Fl-fg Fl-all
All / All 50.09 29.23 49.73
All / Est 50.09 29.23 49.73
Noc / All 40.26 29.23 40.03
Noc / Est 40.26 29.23 40.03
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 15

Error Fl-bg Fl-fg Fl-all
All / All 63.24 67.10 63.59
All / Est 63.24 67.10 63.59
Noc / All 52.74 67.10 54.39
Noc / Est 52.74 67.10 54.39
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 16

Error Fl-bg Fl-fg Fl-all
All / All 68.53 98.85 72.99
All / Est 68.53 98.85 72.99
Noc / All 60.13 98.85 67.09
Noc / Est 60.13 98.85 67.09
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 17

Error Fl-bg Fl-fg Fl-all
All / All 55.21 87.30 58.56
All / Est 55.21 87.30 58.56
Noc / All 42.93 87.30 48.68
Noc / Est 42.93 87.30 48.68
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 18

Error Fl-bg Fl-fg Fl-all
All / All 55.52 100.00 76.65
All / Est 55.52 100.00 76.65
Noc / All 40.43 100.00 56.86
Noc / Est 40.43 100.00 56.86
This table as LaTeX

Input Image

Flow Result

Flow Error


Test Image 19

Error Fl-bg Fl-fg Fl-all
All / All 55.96 88.55 59.65
All / Est 55.96 88.55 59.65
Noc / All 42.16 88.55 48.88
Noc / Est 42.16 88.55 48.88
This table as LaTeX

Input Image

Flow Result

Flow Error




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