基 于 调 和 函 数 理 论 的 二 阶 段 遥 感 目 标 实 例 分 割 算 法

Remote-sensing instance segmentation often suffers from ambiguous object boundaries and cluttered backgrounds， while adding heavy mask heads can increase computational cost and reduce deployment flexibility. This paper aims to develop a fast，accurate，and detector-agnostic mask-generation scheme that can be integrated into existing detection pipelines with minimal engineering overhead and without extra training. We propose a two-stage framework that couples a replaceable object detector（e.g.，YOLOv10 or DINO） with a plug-and-play harmonic background modelling （HBM） module. For each detected bounding box，HBM treats the local background as a harmonic function and reconstructs it by least-squares fitting of a truncated harmonic-polynomial basis. Boundary constraints are formed by sampling pixel values along the bounding-box boundary，and the coefficients are solved efficiently via the Moore-Penrose pseudoinverse. The foreground mask is then derived from the channel-wise residual between the original image and the reconstructed background，followed by a contrast-enhancing nonlinearity，Otsu thresholding，and connected-component filtering to suppress spurious fragments. The overall pipeline is fully decoupled from the detector：the detector is not modified or retrained，and the additional computation mainly comes from solving a small least-squares problem per proposal rather than processing full-resolution feature maps with a learned segmentation head. Extensive experiments on NWPU VHR-10 and iSAID-mini datasets demonstrate consistent gains in both box and mask metrics， while maintaining high throughput. With DINO as the proposal generator，DINO+HBM achieves AP-Box and AP-Mask of 69.3% and 66.3% on NWPU VHR-10 and reaches AP-Mask-50 of 92.1%，improving the previous best result by 2.5 percentage points. On iSAID-mini，DINO+HBM obtains AP-Box and AP-Mask of 55.3% and 42.3% with AP-Mask-50 and AP-Mask-75 of 72.1% and 53.3%，showing clear benefits under more complex scenes. Ablation studies further verify the roles of truncation order，constraint-point number，and sampling strategy，and indicate that bounding-box boundary sampling is more stable than random sampling for background regression and mask extraction without sacrificing speed. The proposed training-free harmonic background suppression provides an efficient way to obtain boundary-faithful instance masks in remote-sensing images and offers a practical，modular add-on to detector-based pipelines when rapid inference and easy deployment are required. Highlights: 1.A training-free, plug-and-play harmonic background modelling (HBM) module is introduced to generate instance masks from detector proposals without modifying the detector. 2. Local background reconstruction is cast as a Dirichlet-type harmonic regression problem and solved efficiently via a truncated harmonic-polynomial basis and least-squares fitting under boundary constraints.