A TOPOLOGICAL APPROACH TO RASTER GRAPHICS VECTORIZATION BASED ON SIMPLICIAL COMPLEXES

DOI: 10.31673/2786-8362.2025.017724

Abstract

This paper elaborates a topological approach to raster graphics vectorization using
methods of Topological Data Analysis (TDA): simplicial complexes and persistent homology. The primary
focus is on the development of an algorithm for the construction of simplicial complexes, which is an
essential tool for identifying the structural and spatial characteristics of an image. The properties of
simplicial complexes in the context of pixel-based data analysis are investigated, and an algorithm for
generating simplicial structures from raster images is proposed. The developed approach enables effective
analysis of topological relationships between pixels and facilitates the extraction of significant components
for subsequent transformation into a vector representation. A simplicial homology search algorithm is also
described. The proposed method enhances image segmentation accuracy, which is critical for high-quality
vectorization, particularly in cases of complex geometry, structural heterogeneity, and image noise. The
results demonstrate the potential of topological methods for improving image preprocessing and
segmentation, offering new perspectives in vectorization tasks. The research lays a foundation for further
algorithmic development and practical implementation in computer graphics and image processing
applications.
Keywords: image vectorization, simplicial complexes, topological data analysis, image
segmentation, raster graphics, TDA, topological methods, Vietoris-Rips complex, persistent homology

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