Method

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


Submitted on 26 May. 2012 19:06 by
Andreas Geiger (MPI Tübingen)

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{Farneback03,
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 each of the first 20 test images, the number of erroneous pixels at all thresholds is depicted in the table. Underneath, the left input image, the disparity / end-point error map and the estimated (and interpolated) disparity / optical flow map are shown. The error map scales linearly between 0 (black) and >=5 (white) pixels error. Red denotes all occluded pixels, falling outside the image boundaries. The false color map is scaled to the largest ground truth disparity / flow value.

Test Set Average

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 50.20 % 56.43 % 17.3 px 25.3 px
3 pixels 47.59 % 54.00 % 17.3 px 25.3 px
4 pixels 45.93 % 52.39 % 17.3 px 25.3 px
5 pixels 44.58 % 51.07 % 17.3 px 25.3 px
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Reflective Regions

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Test Image 0

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 68.06 % 72.79 % 24.6 px 30.7 px
3 pixels 66.74 % 71.66 % 24.6 px 30.7 px
4 pixels 65.87 % 70.92 % 24.6 px 30.7 px
5 pixels 65.13 % 70.29 % 24.6 px 30.7 px
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Test Image 1

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 36.59 % 45.15 % 12.6 px 16.6 px
3 pixels 34.52 % 43.05 % 12.6 px 16.6 px
4 pixels 33.19 % 41.59 % 12.6 px 16.6 px
5 pixels 31.95 % 40.14 % 12.6 px 16.6 px
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Test Image 2

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 43.94 % 52.64 % 17.1 px 23.2 px
3 pixels 42.10 % 50.76 % 17.1 px 23.2 px
4 pixels 40.89 % 49.41 % 17.1 px 23.2 px
5 pixels 39.70 % 48.03 % 17.1 px 23.2 px
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Test Image 3

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 55.22 % 62.23 % 18.6 px 26.8 px
3 pixels 52.43 % 59.59 % 18.6 px 26.8 px
4 pixels 50.88 % 57.98 % 18.6 px 26.8 px
5 pixels 49.68 % 56.68 % 18.6 px 26.8 px
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Test Image 4

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 48.24 % 51.68 % 7.9 px 8.9 px
3 pixels 45.24 % 48.21 % 7.9 px 8.9 px
4 pixels 43.03 % 45.58 % 7.9 px 8.9 px
5 pixels 40.58 % 42.99 % 7.9 px 8.9 px
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Test Image 5

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 44.28 % 53.14 % 12.8 px 22.5 px
3 pixels 40.74 % 50.14 % 12.8 px 22.5 px
4 pixels 38.70 % 48.39 % 12.8 px 22.5 px
5 pixels 37.20 % 47.00 % 12.8 px 22.5 px
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Test Image 6

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 49.76 % 56.08 % 12.7 px 18.8 px
3 pixels 47.73 % 53.95 % 12.7 px 18.8 px
4 pixels 46.08 % 52.23 % 12.7 px 18.8 px
5 pixels 44.00 % 50.16 % 12.7 px 18.8 px
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Test Image 7

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 47.58 % 56.00 % 16.6 px 27.9 px
3 pixels 44.42 % 53.14 % 16.6 px 27.9 px
4 pixels 42.50 % 51.35 % 16.6 px 27.9 px
5 pixels 41.01 % 49.90 % 16.6 px 27.9 px
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Test Image 8

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 49.77 % 58.79 % 16.2 px 29.0 px
3 pixels 47.42 % 56.84 % 16.2 px 29.0 px
4 pixels 46.03 % 55.67 % 16.2 px 29.0 px
5 pixels 44.98 % 54.79 % 16.2 px 29.0 px
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Test Image 9

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 70.81 % 75.32 % 23.7 px 34.7 px
3 pixels 67.73 % 72.71 % 23.7 px 34.7 px
4 pixels 64.71 % 70.15 % 23.7 px 34.7 px
5 pixels 62.15 % 67.99 % 23.7 px 34.7 px
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Test Image 10

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 68.05 % 73.64 % 29.4 px 44.2 px
3 pixels 66.28 % 72.16 % 29.4 px 44.2 px
4 pixels 64.94 % 71.00 % 29.4 px 44.2 px
5 pixels 63.63 % 69.88 % 29.4 px 44.2 px
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Test Image 11

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 53.29 % 60.55 % 12.0 px 20.6 px
3 pixels 48.40 % 56.34 % 12.0 px 20.6 px
4 pixels 45.71 % 53.90 % 12.0 px 20.6 px
5 pixels 43.48 % 51.91 % 12.0 px 20.6 px
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Test Image 12

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 63.42 % 69.22 % 21.8 px 34.4 px
3 pixels 60.94 % 67.12 % 21.8 px 34.4 px
4 pixels 58.57 % 65.13 % 21.8 px 34.4 px
5 pixels 56.59 % 63.46 % 21.8 px 34.4 px
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Test Image 13

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 55.39 % 60.82 % 19.6 px 27.7 px
3 pixels 53.62 % 59.26 % 19.6 px 27.7 px
4 pixels 52.47 % 58.25 % 19.6 px 27.7 px
5 pixels 51.41 % 57.31 % 19.6 px 27.7 px
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Test Image 14

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 70.30 % 75.34 % 29.1 px 39.5 px
3 pixels 69.05 % 74.26 % 29.1 px 39.5 px
4 pixels 68.23 % 73.53 % 29.1 px 39.5 px
5 pixels 67.50 % 72.86 % 29.1 px 39.5 px
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Test Image 15

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 64.39 % 70.59 % 18.9 px 31.5 px
3 pixels 61.14 % 67.85 % 18.9 px 31.5 px
4 pixels 58.83 % 65.87 % 18.9 px 31.5 px
5 pixels 56.66 % 63.99 % 18.9 px 31.5 px
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Test Image 16

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 61.12 % 64.37 % 36.2 px 42.7 px
3 pixels 60.39 % 63.37 % 36.2 px 42.7 px
4 pixels 59.85 % 62.74 % 36.2 px 42.7 px
5 pixels 59.42 % 62.29 % 36.2 px 42.7 px
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Test Image 17

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 51.85 % 59.27 % 12.8 px 21.1 px
3 pixels 48.46 % 56.21 % 12.8 px 21.1 px
4 pixels 46.69 % 54.55 % 12.8 px 21.1 px
5 pixels 45.11 % 53.05 % 12.8 px 21.1 px
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Test Image 18

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 57.65 % 61.72 % 21.7 px 30.3 px
3 pixels 55.96 % 59.92 % 21.7 px 30.3 px
4 pixels 54.79 % 58.72 % 21.7 px 30.3 px
5 pixels 53.92 % 57.85 % 21.7 px 30.3 px
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Test Image 19

Error Out-Noc Out-All Avg-Noc Avg-All
2 pixels 39.70 % 46.77 % 9.7 px 14.8 px
3 pixels 36.63 % 43.96 % 9.7 px 14.8 px
4 pixels 34.76 % 42.23 % 9.7 px 14.8 px
5 pixels 33.05 % 40.64 % 9.7 px 14.8 px
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