Decoupled pixel-wise correction for abdominal multi-organ segmentation

The attention mechanism has emerged as a crucial component in medical image segmentation. Attention-based deep neural networks (ADNNs) fundamentally engage in the iterative computation of gradients for both input layers and weight parameters. Our research reveals a remarkable similarity between the optimization trajectory of ADNN and non-negative matrix factorization (NMF), where the latter involves the alternate adjustment of the base and coefficient matrices. This similarity implies that the alternating optimization strategy—characterized by the adjustment of input features by the attention mechanism and the adjustment of network weights—is central to the efficacy of attention mechanisms in ADNNs. Drawing an analogy to the NMF approach, we advocate for a pixel-wise adjustment of the input layer within ADNNs. Furthermore, to reduce the computational burden, we have developed a decoupled pixel-wise attention module (DPAM) and a self-attention module (DPSM). These modules are designed to counteract the challenges posed by the high inter-class similarity among different organs when performing multi-organ segmentation. The integration of our DPAM and DPSM into traditional network architectures facilitates the creation of an NMF-inspired ADNN framework, known as the DPC-Net, which comes in two variants: DPCA-Net for attention and DPCS-Net for self-attention. Our extensive experiments on the Synapse and FLARE22 datasets demonstrate that the DPC-Net achieves satisfactory performance and visualization results with lower computational cost. Specifically, the DPC-Net achieved a Dice score of 77.98% on the Synapse dataset and 87.04% on the FLARE22 dataset, while possessing merely 14.991 million parameters. Notably, our findings indicate that DPC-Net, when equipped with convolutional attention, surpasses those networks utilizing Transformer attention mechanisms on multi-organ segmentation tasks. Our code is available at https://github.com/605671435/DPC-Net.