Cost Function Comparison for Horizon Detection

(Note: videos below are given in both quicktime and mpeg formats; however, the quicktime videos tend to be higher quality and are therefore recommended. If you do not have quicktime installed, you can download the free player (Mac/Windows) from Apple.)
Below, we compare three different optimization criteria for horizon detection -- that is, separating the sky from the ground -- for a flight clip recorded at the 6th International MAV Competition in Provo, Utah. This video is challenging for two important reasons. First, the vertical black bands on the left and right edges of the video clip bias the computed statistics significantly. Second, when the plane is heading towards the mountains in the background, the sky/cloud line and mountain/grass lines are both lined up with the bank angle of the true horizon.

The table below gives the definition for each of the three optimization criteria. For more information on the whole horizon-detection algorithm, you can look at our IROS2002 paper.

Optimization criterion Explanation
Minimizes intra-class variance
Minimizes intra-class variance (guards against singular covariance matrices)
Maximizes inter-class variance

The following table illustrates the horizon-detection performance for each of the optimization criteria. In each case, we show the flight video with the estimated horizon superimposed, the optimization criterion (top view and side view), and the distribution of sky and ground pixels, given the estimated horizon line. Note that J3 appears to be more robust than either J1 or J2.

Horizon tracking video
(click on the thumbnails to download/view the movies)

Detailed horizon tracking example (J1)
(640 x 560, 30Hz, 0:09)
(high-quality, quicktime, 16.9 Mb)
(lower-quality, mpeg, 4.1 Mb)
Detailed horizon tracking example (J2)
(640 x 560, 30Hz, 0:09)
(high-quality, quicktime, 17.2 Mb)
(lower-quality, mpeg, 4.3 Mb)
Detailed horizon tracking example (J3)
(640 x 560, 30Hz, 0:09)
(high-quality, quicktime, 16.2 Mb)
(lower-quality, mpeg, 4 Mb)

Last updated Spetember 2, 2002 by Michael C. Nechyba