Connect Component Labeling (CCL) has been a fundamental operation in Computer Vision for decades. Most of the literature deals with 2D algorithms for applications like video surveillance or autonomous driving. Nonetheless, the need for 3D algorithms is rising, notably for medical imaging. While 2D CCL algorithms already generate large amounts of memory accesses and comparisons, 3D ones are even worse. This is the curse of dimensionality. Designing an efficient algorithm should address this problem. This paper introduces a segment-based algorithm for 3D labeling that uses a new strategy to accelerate label equivalence processing to mitigate the impact of higher dimensions. We claim that this new algorithm outperforms State-of-the-Art algorithms by a factor from ×1.5 up to ×3.1 for usual medical datasets and random images.