150809 + Mahalanobis Distance

In the current visibility based prediction, if a line p is termed to be visible, it means that the line p is visible from the mean of the position of the robot. However, the position of the robot is not necessarily at the mean. Hence, the prediction of lines might go haywire when a few lines are visible from the mean but not from the current position of the robot which is not at the mean. In other words, we would forcibly be associating lines as we estimated them to be visible.

To prevent this, we need to test visibility from extrema of the error ellipse for x, y and theta. Upon finding the line visible from both extrema only, we should add it to pakka lines.

Excerpts from RS:

evaluating an outlier from a distribution.

if two points are at the same distance from the mean of a 2-d distribution, a euclidean distance measure from the mean would term them to be at equal distance from the distribution. However, if the density of the distribution is low in one direction and high in another, then the distance of the two points should not be shown as equal. However, a euclidean distance measure does not respect that. Hence the need for Mahalanobis distance.

Useful links to udnerstand :
http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_mahalanobis.htm