We present OCRA, an Object-Centric framework for video-based human-to-Robot Action transfer that learns directly from human demonstration videos to enable robust manipulation. Object-centric learning emphasizes task-relevant objects and their interactions while filtering out irrelevant background, providing a natural and scalable way to teach robots. OCRA leverages multi-view RGB videos, the state-of-the-art 3D foundation model VGGT, and advanced detection and segmentation models to reconstruct object-centric 3D point clouds, capturing rich interactions between objects. To handle properties not easily perceived by vision alone, we incorporate tactile priors via a large-scale dataset of over one million tactile images. These 3D and tactile priors are fused through a multimodal module (ResFiLM) and fed into a Diffusion Policy to generate robust manipulation actions. Extensive experiments on both vision-only and visuo-tactile tasks show that OCRA significantly outperforms existing baselines and ablations, demonstrating its effectiveness for learning from human demonstration videos.