3D perception of object shapes from RGB image input is fundamental towards semantic scene understanding, grounding image-based perception in our spatially 3-dimensional real-world environments. To achieve a mapping between image views of objects and 3D shapes, we leverage CAD model priors from existing large-scale databases, and propose a novel approach towards constructing a joint embedding space between 2D images and 3D CAD models in a patch-wise fashion – establishing correspondences between patches of an image view of an object and patches of CAD geometry. This enables part similarity reasoning for retrieving similar CADs to a new image view without exact matches in the database. Our patch embedding provides more robust CAD retrieval for shape estimation in our end-to-end estimation of CAD model shape and pose for detected objects in a single input image. Experiments on in-the-wild, complex imagery from ScanNet show that our approach is more robust than state of the art in real-world scenarios without any exact CAD matches.