Topological Consistency, Not Fidelity, Bounds the Cost Relief of Simplified EEG Brain Maps

Abstract

The Neurophysiological Biomarker Toolbox (NBT) visualises biomarkers on two-dimensional cortical parcellations, where rendering cost limits use at clinical scale. Currently, NBT fits each region's boundary independently, leaving gaps and overlaps between adjacent regions that simplification only worsens. This work applies a shared-arc representation that is gap- and overlap-free by construction. Because boundaries are shared, simplification acts on both sides of the boundary at once, so gaps and overlaps cannot form during simplification. Two failure modes remain: a boundary can cross another, or a region can collapse to a degenerate polygon. Five established simplification algorithms are evaluated on the representation across six atlases and across three axes: geometric fidelity, topological consistency, and rendering cost.

The evaluation shows that the algorithms differ little on fidelity. The axis separating them is topological consistency, specifically whether they allow collapse. This matters for cost because in the evaluated algorithms the dominant predictor of rendering time is the number of faces, not the number of vertices. The algorithms that provide the strongest topological guarantees therefore deliver the least cost relief, since they collapse the fewest faces. On this representation, simplification stays free of gaps and overlaps at a small, bounded fidelity cost.