A new shape descriptor based on a Q-convexity measure

In this paper we define a new measure for shape descriptor. The measure is based on the concept of convexity by quadrant, called Q-convexity. Mostly studied in Discrete Tomography, this convexity generalizes hv-convexity to any two or more directions, and presents interesting connections with âtotalâ convexity. The new measure generalizes that proposed by Balázs and Brunetti (A measure of Q-convexity, LNCS 9647 (2016) 219â230), and therefore it has the same desirable features: (1) its values range intrinsically from 0 to 1; (2) its values equal 1 if and only if the binary image is Q-convex; (3) its efficient computation can be easily implemented; (4) it is invariant under translation, reflection, and rotation by 90°. We test the new measure for assessing sensitivity using a set of synthetic polygons with rotation and translation of intrusions/protrusions and global skew, and for a ranking task using a variety of shapes. Based on the geometrical properties of Q-convexity, we also provide a characterization of any binary image by the matrix of its âgeneralized salient pointsâ, and we design a linear-time algorithm for the construction of the binary image from its associated matrix

A Q-Convexity Vector Descriptor for Image Analysis

Shape representation is a main problem in computer vision, and shape descriptors are widely used for image analysis. In this paper, based on the previous work Balázs, P., Brunetti, S.: A New Shape Descriptor Based on a Q-convexity Measure, Lecture Notes in Computers Science 10502, 20th Discrete Geometry for Computer Imagery (DGCI) (2017) 267–278, we design a new convexity vector descriptor derived by the notion of the so-called generalized salient points matrix. We investigate properties of the vector descriptor, such as scale invariance and its behavior in a ranking task. Moreover, we present results on a binary and a multiclass classification problem using k-nearest neighbor, decision tree, and support vector machine methods. Results of these experiments confirm the good behavior of our proposed descriptor in accuracy, and its performance is comparable and, in some cases, superior to some recently published similar methods