A new characterization of digital lines by least square fits
Pattern Recognition Letters
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
A New Convexity Measure Based on a Probabilistic Interpretation of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Integral Invariants for Shape Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision and Image Understanding
Pattern Recognition
Measuring Elongation from Shape Boundary
Journal of Mathematical Imaging and Vision
A Unified Curvature Definition for Regular, Polygonal, and Digital Planar Curves
International Journal of Computer Vision
Farthest point distance: A new shape signature for Fourier descriptors
Image Communication
A Hu moment invariant as a shape circularity measure
Pattern Recognition
Depth and depth-color coding using shape-adaptive wavelets
Journal of Visual Communication and Image Representation
Measuring Squareness and Orientation of Shapes
Journal of Mathematical Imaging and Vision
On the Orientability of Shapes
IEEE Transactions on Image Processing
Hi-index | 0.00 |
In this paper we study the ADR shape descriptor @r(S), where ADR is short for ''asymmetries in the distribution of roughness''. This descriptor was defined in 1998 as the ratio of the squared distance between two different shape centroids (namely of area and frontier) to the squared shape diameter. After known for more than ten years, the behavior of @r(S) was not well understood till today, thus hindering its application. Two very basic questions remained unanswered so far:-What is the range for @r(S), if S is any bounded compact shape? -How do shapes look like having a large @r(S) value? This paper answers both questions. We show that @r(S) ranges over the interval [0,1). We show that the established upper bound 1 is the best possible by constructing shapes whose @r(S) values are arbitrary close to 1. In experiments we provide examples to indicate the kind of shapes that have relatively large @r(S) values.