Computing deviations from convexity in polygons
Pattern Recognition Letters
Active shape models—their training and application
Computer Vision and Image Understanding
Symmetry as a Continuous Feature
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rectilinearity Measurements for Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Measuring shape: ellipticity, rectangularity, and triangularity
Machine Vision and Applications
A Comparative Evaluation of Length Estimators of Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Computer Vision and Image Understanding
Shape Classification Using the Inner-Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Processing, Analysis, and Machine Vision
Image Processing, Analysis, and Machine Vision
A two-component rectilinearity measure
Computer Vision and Image Understanding
Geometry-Based Image Retrieval in Binary Image Databases
IEEE Transactions on Pattern Analysis and Machine Intelligence
High-Precision Boundary Length Estimation by Utilizing Gray-Level Information
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fourier Preprocessing for Hand Print Character Recognition
IEEE Transactions on Computers
On the Orientability of Shapes
IEEE Transactions on Image Processing
ADR shape descriptor - Distance between shape centroids versus shape diameter
Computer Vision and Image Understanding
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In this paper we propose a measure which defines the degree to which a shape differs from a square. The new measure is easy to compute and being area based, is robust--e.g., with respect to noise or narrow intrusions. Also, it satisfies the following desirable properties: it ranges over (0,1] and gives the measured squareness equal to 1 if and only if the measured shape is a square; it is invariant with respect to translations, rotations and scaling. In addition, we propose a generalisation of the new measure so that shape squareness can be computed while controlling the impact of the relative position of points inside the shape. Such a generalisation enables a tuning of the behaviour of the squareness measure and makes it applicable to a range of applications. A second generalisation produces a measure, parameterised by 驴, that ranges in the interval (0,1] and equals 1 if and only if the measured shape is a rhombus whose diagonals are in the proportion 1:驴.The new measures (the initial measure and the generalised ones) are naturally defined and theoretically well founded--consequently, their behaviour can be well understood.As a by-product of the approach we obtain a new method for the orienting of shapes, which is demonstrated to be superior with respect to the standard method in several situations.The usefulness of the methods described in the manuscript is illustrated on three large shape databases: diatoms (ADIAC), MPEG-7 CE-1, and trademarks.