Parameter-Efficient 3D Segmentation of Liver and Liver tumors: Depthwise factorization Scales Better Than Dense Convolution with Spatial Dimensionality

Three-dimensional dense convolutional networks are the strongest performers on volumetric medical image segmentation, but their parameter counts scale poorly: moving a dense k x k convolution to k x k x k multiplies its weights by k. We observe that depthwise separable factorization does not share this penalty. Because the cubic kernel term applies only to the depthwise stage while the pointwise projection, which dominates the parameter count, is unchanged, the same architecture grows by 5 % from 2D to 3D where a dense convolutional U-Net grows by 200 %. We exploit this asymmetry to build a 3D U-Net with 536,990 parameters, 24x fewer than an identical dense 3D U-Net. On MSD Task03 Liver (the Medical Segmentation Decathlon liver task, derived from LiTS), evaluated per case under five-fold cross-validation over all 131 public volumes, the model reaches a tumor Dice of 0.577 (95% CI [0.518, 0.633]) and a liver Dice of 0.947 (95% CI [0.941, 0.952]). Its liver Dice exceeds previously reported performance. Its tumor Dice exceeds their low-resolution configuration (0.4701) by 0.107 and their 2D configuration (0.5394), at approximately one twenty-fourth of the parameters and roughly half the in-plane resolution. Trained under identical conditions on a common held-out split, it exceeds a dense 3D U-Net on liver by +0.031 Dice (paired p = 0.006) and on tumor by +0.041 (95 % CI [+0.005, +0.081], paired p = 0.056), suggesting the factorization also acts as a regularizer in the small-data regime characteristic of medical imaging. We further show, on both LiTS and a 2D endoscopy benchmark, that a large fraction of the network's learnable spatial filters can be replaced by fixed shifts at no cost in accuracy, but that replacing all of them is measurably worse, the placement of spatial capacity matters more than its total amount.