Image tangent space is actually high-level semantic space learned from low-level feature space by modified local tangent space alignment which was originally proposed for nonlinear manifold learning. Under the assumption that a data point in image space can be linearly approximated by some nearest neighbors in its local neighborhood, we develop a lazy learning method to locally approximate the optimal mapping function between image space and image tangent space. That is, the semantics of a new query image in image space can be inferred by the local approximation in its corresponding image tangent space. While Euclidean distance induced by the ambient space is often used to represent the difference between images, clearly, their natural distance is possibly different from Euclidean distance. Here, we compare three distance metrics: Chebyshev, Manhattan and Euclidean distances, and find that Chebyshev distance outperforms the other two in measuring the semantic similarity during retrieval. Experimental results show that our approach is effective in improving the performance of image retrieval systems.