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.