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main.tex

@@ -321,9 +321,9 @@ Here, inspired by \cite{o3d}\cite{pointnet}, the max pooling aims to get the mos
 \label{node_layer}
 \end{align}
 
-\textbf{Dual Confidence Selection.} We use dual confidence thresholds $\lambda_{o2m}^g$ and $\lambda_{o2o}^g$ to selected the positive (\textit{i.e.}, foreground) predictions. In the traditional NMS paradigm, the predictions output by the O2M classification heads with confidences $\left\{ s_{i}^{g} \right\} $ higher than $\lambda_{o2m}^g$ are selected as the positive predictions and subsequently fed into the NMS postprocessing to eliminate the redundant predictions. In the NMS-free paradigm, the final non-redundant predictions are selected as following:
+\textbf{Dual Confidence Selection.} We use dual confidence thresholds $\lambda_{o2m}^s$ and $\lambda_{o2o}^s$ to selected the positive (\textit{i.e.}, foreground) predictions. In the traditional NMS paradigm, the predictions output by the O2M classification heads with confidences $\left\{ s_{i}^{g} \right\} $ higher than $\lambda_{o2m}^s$ are selected as the positive predictions and subsequently fed into the NMS postprocessing to eliminate the redundant predictions. In the NMS-free paradigm, the final non-redundant predictions are selected as following:
 \begin{align}
-        \varOmega _{o2o}^{pos}\equiv \left\{ i|\tilde{s}_{i}^{g}>\lambda _{o2o}^{s} \right\} \cap \left\{ i|s_{i}^{g}>\lambda _{o2m}^{g} \right\} 
+        \varOmega _{o2o}^{pos}\equiv \left\{ i|\tilde{s}_{i}^{g}>\lambda _{o2o}^{s} \right\} \cap \left\{ i|s_{i}^{g}>\lambda _{o2m}^{s} \right\} 
 \end{align}
 where the $\varOmega _{o2o}^{pos}$ denoted the final set of the non-redundant predictions with the two types of confidences both statisfy the above conditions with dual confidence thresholds. The selection principle for non-redundant predictions is called dual confidence selection.