迭代最近點(ICP) 演算法及其變體是實現兩個點集之間剛性配準的重要方
法，廣泛應用於機器人學和3D重建等領域。儘管ICP具有重要性，但它存在收
斂速度慢且對離群值、不完整數據和部分重疊非常敏感的缺點。在本工作中，
我們基於一個關鍵觀察，即計算配準變換類似於點對投票機制：距離較大的點
對會投票進行較大的調整以適應其最接近的對應點，而距離較小的點對則傾向
於投票進行最小的移動。通過在計算配準時移除重疊點對（通常在前幾次迭
代中非常接近但不正確的點對），我們可以顯著加快收斂速度。此外，我們
引入了一種基於Welsch函數的穩健誤差度量，有效減少了離群值的影響。為了
解決較大點雲數據集的計算需求，我們開發了該演算法的GPU加速版本。這
個GPU實現利用了並行處理能力，使得處理龐大數據集更加高效，並大大提高
了演算法的整體速度。這些改進使我們的方法在需要精確和快速點雲配準的實
際應用中極具效能。

The algorithm of tackling Point Cloud Registration (PCR), the Iterative Clos
est Point (ICP), along with its various adaptations, is a crucial method for rigid
registration within two point cloud sets, widely used in fields such as robotics and
3D surface reconstruction. Despite its significance, ICP suffers from slow conver
gence and is highly sensitive to outliers, incomplete data, and partial overlaps. In
this work, we build on our key observation that computing alignment transforma
tion resembles a point pair voting mechanism: point pairs with larger distances
vote for larger adjustments to fit their closest corresponding points, while point
pairs with smaller distances tend to vote for minimal movement. By removing
overlapping point pairs, which are typically very close but incorrect in the first
few iterations, from the computation of alignment, we can significantly accelerate
the convergence speed. Additionally, we incorporate an insensitive to outliers er
ror metric using the Welsch’s function, which significantly mitigates the influence
of outliers. Furthermore, to address the computational demands of larger point
cloud datasets, we develop a GPU-accelerated version of the algorithm. This GPU
implementation leverages parallel processing capabilities, enabling the handling of
extensive datasets with greater efficiency and substantially improving the overall
speed of the algorithm. These advancements make our approach highly effective
for real-world applications requiring precise and rapid point cloud registration.