Camouflaged object detection (COD) aims to identify object pixels visually embedded in the background environment. Existing deep learning methods fail to utilize the context information around different pixels adequately and efficiently. In order to solve this problem, a novel pixel-centric context perception network (PCPNet) is proposed, the core of which is to customize the personalized context of each pixel based on the automatic estimation of its surroundings. Specifically, PCPNet first employs an elegant encoder equipped with the designed vital component generation (VCG) module to obtain a set of compact features rich in low-level spatial and high-level semantic information across multiple subspaces. Then, we present a parameter-free pixel importance estimation (PIE) function based on multiwindow information fusion. Object pixels with complex backgrounds will be assigned with higher PIE values. Subsequently, PIE is utilized to regularize the optimization loss. In this way, the network can pay more attention to those pixels with higher PIE values in the decoding stage. Finally, a local continuity refinement module (LCRM) is used to refine the detection results. Extensive experiments on four COD benchmarks, five salient object detection (SOD) benchmarks, and five polyp segmentation benchmarks demonstrate the superiority of PCPNet with respect to other state-of-the-art methods.