# Explainable Liver Segmentation and Volume Assessment Using Parallel Cropping
## 5 Application to 3D Volume Assessment  
The study aims to assess liver volume as efficiently as possible. We propose fast parallel voxel-based 3D cropping for volume assessment. Parallel automatic cropping is implemented as the initial stage, and 3D seeded region growing is applied. The complete process is described below.  
By applying parallel voxel-based cropping before seeded region growing (SRG), we significantly reduce the number of voxels involved in the segmentation process. This reduction lowers memory consumption on the GPU and accelerates the segmentation computation. The cropping ensures that seeded region growing operates within a tightly bounded region of interest (RoI), enhancing efficiency without sacrificing accuracy. This is particularly beneficial in high-resolution CT volumes, where traditional full-volume SRG methods are prohibitively expensive.  
The SRG algorithm is implemented using GPU-based persistent threads with kernel relaunching (KTRL) to enable effective exploration of 3D neighborhoods. After cropping, the seed point is automatically determined within the binary mask, and parallel region growing is used to aggregate connected liver tissue voxels. The volume is computed as the product of labeled voxel count and voxel spacing, yielding precise liver volume estimates directly from CT data. The proposed parallel approach for 3D volume assessment is shown in Figure 4.  
Figure 3: Liver segmentation: Chan-Vese (**left**) and U-Net (**right**).  
The CPU stores the 3D images on the GPU. We apply PT and voxel-based parallel cropping to obtain the necessary RoI on the CT liver image. The 3D volume of the desired organ inside this RoI is assessed using PT and shared memory-based SRG. The parallel implementation of SRG is carried out using kernel termination and relaunch (KTRL) [34]. The SRG algorithm is implemented using GPU-based persistent threads with kernel relaunching (KTRL) to enable effective exploration of 3D neighborhoods. After cropping, the seed point is automatically determined within the binary mask, and parallel region growing is used to aggregate connected liver tissue voxels. Volume is computed as the product of labeled voxel count and voxel spacing, yielding precise liver volume estimates directly from CT data. The proposed parallel approach for 3D volume assessment is shown in Figure 4.  
The CPU transfers the CT liver image to the GPU. The liver image is cropped to obtain the necessary RoI. We apply KTRL-based SRG to the cropped image. The volume of the desired organ is assessed using KTRL-based SRG on the static RoI of the image tiles, and the processed image is stored back on the CPU.  
To demonstrate the generalizability of the proposed cropping method, we evaluated its performance on multiple datasets from the 3D Image Reconstruction for Comparison of Algorithm Database (3 DIRACDb [43]), including vessel, skin, and lung CT volumes. In all cases, the voxel-based cropping consistently accelerated the preprocessing and volume estimation stages when compared to conventional slice-based methods. This shows that our approach is not limited to liver imaging but is broadly applicable to other anatomical structures.  
In the next section, we evaluate the impact of cropping on liver segmentation and volume assessment, discuss the speedup obtained by cropping, and analyze the segmentation accuracy.