## 1 Introduction
In this paper, instead of modifying the network's overall architecture to circumvent the trade-off between model size and its representational power, we address this dilemma by looking into the very basic unit of 3D CNNs: 3D convolutional kernels, and propose replacing them with a compact module that possesses better parameter efficiency and stronger nonlinear representational power. We named the proposed module 3D Dense Separated Convolution (3D-DSC), and Figure 1 illustrates its layout schematically. The 3D-DSC module was constructed by a series of densely connected 1D filters. Decomposing 3D kernels into 1D filters alleviated the risk of overfitting by removing the redundancy within 3D kernels in a topologically constrained manner, while providing the infrastructure for deepening the network. The nonlinear layers inserted between 1D filters were responsible for the boosting of the block's nonlinearity, as well as its representational power. The dense connections between 1D filters ensured efficient propagation of information and gradient flow, thus facilitating the training of deepened network. Finally, the 1 \(\times\) 1 \(\times\) 1 convolution attached at the end of the block acted as a bottleneck layer to reduce the number of output feature volumes. Compared with direct 3D convolutions, the introduction of 3D-DSC not only effectively deepened the network, thus improving its representational power, but also considerably reduced the number of learnable parameters. This feature is especially useful when training data are limited. In addition, since 3D-DSC did not change the number of input and output feature maps of the convolutional layers, it could be directly used to replace 3D convolutions to boost the network's performance without modifying its overall architecture. We evaluated the effectiveness and efficiency of 3D-DSC on volumetric image classification and segmentation, which are two challenging tasks often encountered in biomedical image computing. The results on both tasks showed that significant performance improvements could be consistently obtained with comparable or even fewer parameters than the original 3D convolution version. Our main contributions are summarized as follows. (1) We propose an effective strategy for alleviating the overfitting problem while enabling the effective training of a much deeper network in volumetric image analysis, especially for the cases with limited training samples. It is demonstrated that a significant accuracy improvement can be achieved in both classification and segmentation tasks with a similar number of parameters. (2) The dense connections are introduced between 1D filters in our work to facilitate the training of the deeper network, while it is impractical to introduce dense connections for paralleled 2D and 1D filters. In addition, with nonlinear layers inserted, the effective depth of the network, as well as its representational power can be considerably increased without increasing the number of parameters. (3) The proposed 3D-DSC is not limited to any specific architecture or application, and it can be used to boost the performance by directly substituting the original 3D convolutional kernels.