Point cloud completion is a fundamental yet not well-solved problem in 3D vision. Current approaches often rely on 3D coordinate information and/or additional data (e.g., images and scanning viewpoints) to fill in missing parts. Unlike these methods, we explore self-structure augmentation and propose PointSea for global-to-local point cloud completion. In the global stage, consider how we inspect a defective region of a physical object, we may observe it from various perspectives for a better understanding. Inspired by this, PointSea augments data representation by leveraging self-projected depth images from multiple views. To reconstruct a compact global shape from the cross-modal input, we incorporate a feature fusion module to fuse features at both intra-view and inter-view levels. In the local stage, to reveal highly detailed structures, we introduce a point generator called the self-structure dual-generator. This generator integrates both learned shape priors and geometric self-similarities for shape refinement. Unlike existing efforts that apply a unified strategy for all points, our dual-path design adapts refinement strategies conditioned on the structural type of each point, addressing the specific incompleteness of each point. Comprehensive experiments on widely-used benchmarks demonstrate that PointSea effectively understands global shapes and generates local details from incomplete input, showing clear improvements over existing methods.