Measuring linearity of planar point sets

Our goal is to design algorithms that give a linearity measure for planar point sets. There is no explicit discussion on linearity in literature, although some existing shape measures may be adapted. We are interested in linearity measures which are invariant to rotation, scaling, and translation. These linearity measures should also be calculated very quickly and be resistant to protrusions in the data set. The measures of eccentricity and contour smoothness were adapted from literature, the other five being triangle heights, triangle perimeters, rotation correlation, average orientations, and ellipse axis ratio. The algorithms are tested on 30 sample curves and the results are compared against the linear classifications of these curves by human subjects. It is found that humans and computers typically easily identify sets of points that are clearly linear, and sets of points that are clearly not linear. They have trouble measuring sets of points which are in the gray area in-between...

• Type: Journal
• Year: 2008
• Where: PR
• Authors: Milos Stojmenovic, Amiya Nayak, Jovisa D. Zunic
• Keywords: Linearity, Linearity Measures, Planar Point Sets, PR 2008