most recent 30 from http://mathoverflow.net 2013-05-25T03:48:32Z http://mathoverflow.net/feeds/question/11521 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11521/what-is-affine-invariant-used-in-computer-vision Aditya 2010-01-12T10:28:20Z 2010-01-12T11:13:50Z

<p>Affine invariant for 4 coplanar points ABCD is said to be <code>Area(ACD)/Area(ABC)</code>. Can somebody provide the proof of this means why is this invariant under affine transformation?</p>

http://mathoverflow.net/questions/11521/what-is-affine-invariant-used-in-computer-vision/11527#11527 Thorny 2010-01-12T11:13:50Z 2010-01-12T11:13:50Z

<p>The ratio of areas of $ABC$ and $ACD$ is the ratio in which the line $AC$ divides the segment $BD$ (and it is the ratio of the heights of $B$ and $D$ over $AC$ respectively). This later ratio is affine invariant as affine transformations preserve length ratios on any line. Do make sure that your points don't collapse onto a single line though.</p>