Hexagonality as a New Shape-Based Descriptor of Object
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Hexagonality as a New Shape‑Based Descriptor of Object Vladimir Ilić1 · Nebojša M. Ralević1 Received: 7 June 2019 / Accepted: 12 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we define a new shape-based measure which evaluates how much a given shape is hexagonal. Such an introduced measure ranges through the interval (0, 1] and reaches the maximal possible value 1 if and only if the shape considered is a hexagon. The new measure is also invariant with respect to rotation, translation and scaling transformations. A number of experiments, performed on both synthetic and real image data, are shown in order to confirm theoretical observations and illustrate the behavior of the new measure. The new hexagonality measure also provides several useful side results whose theoretical properties are discussed and experimentally evaluated. As side results, we obtain a new method that computes the shape orientation as the direction which optimizes the new hexagonality measure and a new shape elongation measure which computes the elongation of a given shape as the ratio of the lengths of the longer and shorter semi-axis of the appropriate associated hexagon. Several experiments relating to three well-known image datasets, such as MPEG-7 CE-1, Swedish Leaf, and Galaxy Zoo datasets, are also provided to illustrate effectiveness and benefits of the new introduced shape measures. Keywords Shape · Hexagonality measure · Measuring orientation · Shape elongation · Object classification
1 Introduction In different fields of research and applications, thanks to the rapid development of image acquisition technologies, we have an opportunity to work with a large amount of image based data. Challenges when working with such generated images can be multiple, given that there is a permanent need that these images be analyzed, processed, compared or classified. In all of these tasks, depending on the applications and requests that are set against us, in order to understand the content of the image itself, it is necessary to identify and also understand the context of the objects captured by an image. Consequently, as an answer to these challenges, a number of different approaches, and also computing methods have been developed to date, both from theoretical and experimental points of view. It is worth mentioning that generality and usability of these methods depend primarily on their applicability in wide range of different domains of * Vladimir Ilić [email protected] Nebojša M. Ralević [email protected] 1
research. To mention only some of them: agriculture [26], astronomy [8, 15], biology [21], medicine [12], mobile robots [22], traffic [32], etc. In this paper, we focus our attention on the object’s characterization based on the shape of the object. Shape-based approach has become very popular in the diverse object analysis tasks, given that a shape as one of the elementary property of the object (together with color and texture) has a variety of attributes which can be evalu
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