In this paper, we propose a novel Patch Geodesic Distance (PGD) to transform the texture map of an object through its shape data for robust 2.5D object recognition. Local geodesic paths within patches and global geodesic paths for patches are combined in a coarse to fine hierarchical computation of PGD for each surface point to tackle the missing data problem in 2.5D images. Shape adjusted texture patches are encoded into local patterns for similarity measurement between two 2.5D images with different viewing angles and/or shape deformations. An extensive experimental investigation is conducted on 2.5 face images using the publicly available BU-3DFE and Bosphorus databases covering face recognition under expression and pose changes. The performance of the proposed method is compared with that of three benchmark approaches. The experimental results demonstrate that the proposed method provides a very encouraging new solution for 2.5D object recognition.