## 1 Introduction
Recent advancements in neural networks have significantly transformed the field of image segmentation [17; 18; 19; 20; 21]. [PERSON] et al. [22] proposed an efficient medical image segmentation network based on an alternating mixture of a CNN and Transformer tandem, which is called Eff-CTNet, which achieved better performance with less computation sources. [PERSON] et al. [23] proposed a graph model initialized by a fully convolutional network (FCN) named Graph-FCN for image semantic segmentation. H-DenseUNet [24] extracted the intra-slice features efficiently and used the 3-D counterpart  
Figure 1: System interface. (**a**) Clinical shooting of thoracoscopic surgery system. (**b**) Target region indication of a specific frame. with hierarchically aggregating volumetric contexts for liver and tumor segmentation. [PERSON] et al. [25] highlighted the convolution with upsampled filters, atrous spatial pyramid pooling (ASPP), and combining methods from DCNNs as well as probabilistic graphical models for better segmentation performance. Mask R-CNN [15], which served as the base model for this paper, has been widely applied for medical image segmentation and achieves accurate and fast performance by adding a branch for predicting the object mask. Mask R-CNN is still one of the most representative segmentation models and is widely applied in clinical contexts; its variations [26; 27; 28; 29] provide stable foundations for medical image segmentation. However, the proposed channel R-CNN distinguishes itself by employing a novel multi-channel architecture; by integrating DenseNet as a base model, it processes feature maps through two parallel channels: one for instance segmentation using Mask R-CNN and another for generating surgical cutting curves. This dual-channel approach not only enhances segmentation accuracy but also provides real-time surgical guidance, setting it apart from traditional single-task models. Cutting indication. An improper cutting curve not only makes the surgery difficult but may also lead to the injury of other tissues; therefore, cutting curve indication is a difficult and critical challenge in medical applications [30]. [PERSON] et al. [31] applied the CNN model for the assessment of unconstrained surgical cuttings in VR; different cutting trajectories were distinguished and selected for optimization. Fast and efficient fluid dynamic visualizations for the heart surgery simulation were proposed by [PERSON] et al. [32]; comparison of the frame rates for the surgery simulation proved the effectiveness of their approaches. [PERSON] et al. [33] presented the meshless total Lagrangian adaptive dynamic relaxation (MTLADR) algorithm to address the shortcomings, including high computational cost and the need for re-meshing in clinical surgical cutting. [PERSON] et al. [34] designed a hybrid CNN-Transformer network to capture both the local and global information and performed experiments on two datasets to demonstrate its superior capability. A periactabular tumor resection was simulated using a pelvic bone model by [PERSON] et al. [35], by which the location of the cut planes with respect to the target planes was significantly improved. However, the existing methods still face limitations with real-time requirements and are not able to handle the cutting curve indication in thoracoscopic surgery; high computation costs and a complex operation background add difficulties to their clinical applications. Despite these advancements, existing methods face limitations in real-time applications and complex surgical environments. The channel R-CNN overcomes these challenges by incorporating a Thorax Network Head (TNH) that generates rough cutting curves, specifically designed for thoracoscopic surgery. This integration allows for real-time navigation and precise cutting path planning, addressing the high computational demands and operational complexities of current methods. Computer-aided surgery navigation system.