Beyond Linear Convolutional Representations: Manifold-Aware Neighborhood Feature Learning for PolSAR Ship Detection

Abstract

Classical polarimetric synthetic aperture radar (PolSAR) ship detectors can be unified into a quadratic form of polarimetric scattering vectors, offering clear physical interpretability. To further exploit spatial information, the neighborhood polarimetric covariance matrix (NPCM) was introduced to characterize inter-pixel polarimetric coherences. However, NPCM-based approaches fundamentally rely on single-look complex data and suffer from high computational complexity, limiting their applicability in large-scale multilook scenarios. Conversely, convolutional neural networks have become a dominant paradigm but are often treated as “black boxes” operating in Euclidean space. A fundamental theoretical gap remains: for the pre-activation, single-layer linear convolutional representation analyzed in this article, the corresponding function class is a strict subset of the NPCM function class. This result shows that such linear convolutional aggregation cannot represent the off-diagonal inter-pixel correlation terms captured by NPCM, especially when phase information is absent. To bridge this gap, a manifold-aware neighborhood feature learning framework is proposed. Instead of treating polarimetric matrices as flat vectors in Euclidean space, the Riemannian geometric structure of polarimetric covariance matrices is explicitly embedded into the network representation. By constructing a neighborhood quadratic embedding, nonlinear inter-pixel polarimetric interactions are effectively learned from incoherent multilook data, acting as a proxy for the missing phase information. Experiments on both simulated and measured datasets demonstrate that the proposed method outperforms standard linear convolutional representations.