Computing deviations from convexity in polygons
Pattern Recognition Letters
Machine Vision and Applications
Rectilinearity Measurements for Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Measuring shape: ellipticity, rectangularity, and triangularity
Machine Vision and Applications
A New Convexity Measure for Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Processing, Analysis, and Machine Vision
Image Processing, Analysis, and Machine Vision
Measuring the Related Properties of Linearity and Elongation of Point Sets
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
A Hu moment invariant as a shape circularity measure
Pattern Recognition
Robust line extraction based on repeated segment directions on image contours
CISDA'09 Proceedings of the Second IEEE international conference on Computational intelligence for security and defense applications
Shape elongation from optimal encasing rectangles
Computers & Mathematics with Applications
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Measuring linearity of open planar curve segments
Image and Vision Computing
Measuring linearity of closed curves and connected compound curves
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part III
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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. Although they appear to be conceptually very different approaches, we prove, theoretically and experimentally, that eccentricity and rotation correlation yield exactly the same linearity measurements. They however provide results which are furthest from human measurements. The average orientations method provides the closest results to human perception, while the other algorithms proved themselves to be very competitive.