Second-Order Kinetic Approach for Anatomical Shape Analysis and Symmetry-Based Core-Line Detection

Ismaila IO and Lawal AA

Published on: 2026-02-17

Abstract

Anatomical shape analysis and symmetry detection are fundamental to biomedical image interpretation, supporting diagnostics, disease progression monitoring, and surgical planning. However, traditional geometric models often fail to preserve anatomical continuity and structural fidelity when confronted with complex deformable biological forms. This research introduces a novel framework grounded in second-order kinetic theory to examine anatomical shape, extract symmetry properties, and identify core lines that serve as structural skeletons of organs and tissues.

The model employs second-order differential operators that capture both inertial and diffusive aspects of anatomical form evolution, enabling robust core-line detection under varying imaging conditions. Through the integration of partial differential equations (PDEs) and computational symmetry constraints, the framework provides a mathematically consistent approach for examining shape smoothness, curvature stability, and intrinsic symmetry.

Experimental validation on synthetic and real biomedical datasets demonstrates superior accuracy and continuity in core-line extraction compared to classical level-set and morphological skeletonization methods. The proposed approach establishes a bridge between kinetic modeling, biomedical shape analysis, and computational anatomy, offering a promising direction for advanced diagnostic and morphometric systems.

Keywords

Second-order kinetics; Anatomical symmetry; Core-line detection; Shape analysis; Biomedical imaging; PDE modeling

Introduction

Background of the Study

The accurate analysis of anatomical structures is central to biomedical imaging, facilitating the extraction of meaningful patterns in organs, vessels, and tissues. Recent advances in computational anatomy and image processing have provided algorithms capable of delineating structural boundaries and detecting essential morphological features. Yet, these approaches often rely on first-order differential operators, which may inadequately capture the dynamical properties of tissue geometry and motion [5].

Second-order kinetic theory, traditionally developed in physics to describe momentum-dependent diffusion and energy transfer, offers new possibilities for modeling anatomical shapes. By incorporating second-order derivatives, it enables the representation of curvature, acceleration, and geometric flow within anatomical structures [6]. This property aligns closely with the behavior of biological forms, which evolve and deform under smooth, continuous transformations.

The examination of anatomical symmetry—the degree to which biological structures maintain bilateral or radial regularity—is crucial for identifying deviations caused by pathologies. Symmetry-based measures are increasingly employed in diagnostics, particularly in brain imaging, craniofacial analysis, and cardiovascular modeling [14]. Core-line detection, or the identification of the intrinsic centerlines of organs and vessels, further enhances shape representation, simplifying volumetric data into compact, interpretable forms.

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