A parametrization of digital planes by least-squares fits and generalizations
Graphical Models and Image Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Graphics (TOG)
Rectilinearity Measurements for Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Measuring shape: ellipticity, rectangularity, and triangularity
Machine Vision and Applications
Generalizations of angular radial transform for 2D and 3D shape retrieval
Pattern Recognition Letters
A New Convexity Measure Based on a Probabilistic Interpretation of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
An easy measure of compactness for 2D and 3D shapes
Pattern Recognition
Measuring Elongation from Shape Boundary
Journal of Mathematical Imaging and Vision
A Hu moment invariant as a shape circularity measure
Pattern Recognition
Measuring Cubeness of 3D Shapes
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
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In this paper we introduce cubeness measure C(S): a shape similarity measure between a given 3D shape and a cube. The cubeness measure has several desirable properties: it ranges over (0,1] and reaches 1 only when the given shape is a cube, it is invariant with respect to rotation, translation and scaling, and is also robust with respect to noise. The measure is compared with discrete 3D compactness measure from the existing literature. A modification of the basic definition of cubeness is also given. This modification enables the creation of a family of descriptors C"@c","@d(S), which vary their behaviour depending on the choice of parameters (@c,@d). Several examples are given, which illustrates the behaviour of these measures. Also some shape retrieval experiments are presented which illustrate the suitability of cubeness measures for such applications. The experimental results are in accordance with theoretical considerations and with our perception.