Abstract
We present an approach to compute the number of holes in binary images using the Vertex Chain Code (VCC); the VCC was developed for representing and analyzing 2D shapes composed of cells. Using this code, it is possible to relate the outer to inner vertices of any 2D shape and to find interesting properties. Now, in this paper, we describe more properties of the VCC, such as the computation of the connected regions in a hole, the analysis of complementary chains, the computation of the number of holes in a binary shape or image, the computation of the Euler number, and the detection of convex and concave shapes. Finally, in order to illustrate the capabilities of proposed methods, we present the computation of topological properties of examples of objects of the real world.
Highlights
This work focuses on image representation by means of the Vertex Chain Code (VCC) [1], in order to obtain different properties of binary shapes, such as the computation of the connected regions in a hole and the computation of the Euler number
We present the computation of the connected regions in a hole, the analysis of complementary chains, the computation of the number of holes in a binary shape or image, the computation of the Euler number, and the detection of convex and concave shapes
5, we describe the computation of the Euler number via the VCC
Summary
This work focuses on image representation by means of the Vertex Chain Code (VCC) [1], in order to obtain different properties of binary shapes, such as the computation of the connected regions in a hole and the computation of the Euler number. Wulandhari and Haron [14] proposed an interesting approach to compute the Euler number by means of the chain elements They analyzed shapes with only one hole and obtained two VCC chains of the outer and inner boundaries of the analyzed shape. [16], the authors propose two equations based on the pixel geometry and connectivity properties, which can be used to efficiently compute the Euler number of a binary digital image with either thick or thin boundaries. Despite computing this feature, the authors’ technique extracts the underlying topological information provided by the shape pixels of the given image.
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