GD4Shapes: Geodesic distance with fixed parameterization for 2D Shapes

Abstract

Shape analysis within shape space provides a robust framework for examining geometric properties of objects, enabling comparisons invariant to translation, rotation, and scaling. A key task is computing geodesic distances between shapes, which quantify similarity but are computationally intensive due to the need for exhaustive parameterization searches. Recent advancements propose heuristic methods to simplify these computations, such as fixing parameterizations based on the major axis of shapes, significantly reducing computational costs while maintaining high accuracy (e.g., 96.03% in erythrocyte classification). This article introduces a software tool that leverages this heuristic to efficiently compute shape-space distances, aligning shapes considering their major axis, and using templates like circles and ellipses. The tool accelerates morphological analysis, making it ideal for high performance applications in fields like biology and medicine. By streamlining the computation of geodesic distances between shapes and enabling rapid retrieval of information, this software improves research workflows and supports the study of shape-dependent features in diverse fields from cellular morphology to diagnostic hematology.