We propose a new framework for image-based three-dimensional (3D) model retrieval.We first model the query image as a Euclidean point.Then we model all projected views of a 3D model as a symmetric positive definite (SPD) matrix,which is a point on a Riemannian manifold.Thus,the image-based 3D model retrieval is reduced to a problem of Euclid-to-Riemann metric leaing.To solve this heterogeneous matching problem,we map the Euclidean space and SPD Riemannian manifold to the same high-dimensional Hilbert space,thus shrinking the great gap between them.Finally,we design an optimization algorithm to lea a metric in this Hilbert space using a keel trick.Any new image descriptors,such as the features from deep leaing,can be easily embedded in our framework.Experimental results show the advantages of our approach over the state-of-the-art methods for image-based 3D model retrieval.