Deploying high-performance convolutional neural network (CNN) models on low-earth orbit (LEO) satellites for rapid remote sensing image processing has attracted significant interest from industry and academia. However, the limited resources available on LEO satellites contrast with the demands of resource-intensive CNN models, necessitating the adoption of ground-station server assistance for training and updating these models. Existing approaches often require large floating-point operations (FLOPs) and substantial model parameter transmissions, presenting considerable challenges. To address these issues, this paper introduces a ground-station server-assisted framework. With the proposed framework, each layer of the CNN model contains only one learnable feature map (called the seed feature map) from which other feature maps are generated based on specific rules. The hyperparameters of these rules are randomly generated instead of being trained, thus enabling the generation of multiple feature maps from the seed feature map and significantly reducing FLOPs. Furthermore, since the random hyperparameters can be saved using a few random seeds, the ground station server assistance can be facilitated in updating the CNN model deployed on the LEO satellite. Experimental results on the ISPRS Vaihingen, ISPRS Potsdam, UAVid, and LoveDA datasets for semantic segmentation services demonstrate that the proposed framework outperforms existing state-of-the-art approaches. In particular, the SineFM-based model achieves a higher mIoU than the UNetFormer on the UAVid dataset, with 3.3$\times$ fewer parameters and 2.2$\times$ fewer FLOPs.