Geometric Shape Characterisation Based on a Multi-Sweeping Paradigm

The characterisation of geometric shapes produces their concise description and is, therefore, important for subsequent analyses, for example in Computer Vision, Machine Learning, or shape matching. A new method for extracting characterisation vectors of 2D geometric shapes is proposed in this paper. The shape of interest, embedded into a raster space, is swept several times by sweep-lines having different slopes. The interior shape's points, being in the middle of its boundary and laying on the actual sweep-line, are identified at each stage of the sweeping process. The midpoints are then connected iteratively into chains. The chains are filtered, vectorised, and normalised. The obtained polylines from the vectorisation step are used to design the shape's characterisation vector for further application-specific analyses. The proposed method was verified on numerous shapes, where single- and multi-threaded implementations were compared. Finally, characterisation vectors, among which some were rotated and scaled, were determined for these shapes. The proposed method demonstrated a good rotation- and scaling-invariant identification of equal shapes.

Automated summary

A new method for extracting characterisation vectors of 2D geometric shapes is proposed in this paper, which involves scanning the shape of interest embedded in a raster space with sweep-lines of different slopes multiple times. The interior points of the shape's boundary on the actual sweep-line are identified and connected iteratively into chains, which are then filtered, vectorised, and normalised to obtain polylines. These polylines are used to design the shape's characterisation vector, demonstrating a good rotation- and scaling-invariant identification of equal shapes.