Metric learning with two-dimensional smoothness for visual analysis

In recent years, metric learning methods based on pairwise side information have attracted considerable interests, and lots of efforts have been devoted to utilize these methods for visual analysis like content based image retrieval and face identification. When applied to image analysis, these methods merely look on an n₁ × n₂ image as a vector in R^n1×n2 space and the pixels of the image are considered as independent. They fail to consider the fact that an image represented in the plane is intrinsically a matrix, and pixels spatially close to each other may probably be correlated. Even though we have n₁ × n₂ pixels per image, this spatial correlation suggests the real number of freedom is far less. In this paper, we introduce a regularized metric learning framework, Two-Dimensional Smooth Metric Learning (2DSML), which uses a discretized Laplacian penalty to restrict the coefficients to be two-dimensional smooth. Many existing metric learning algorithms can fit into this framework and learn a spatially smooth metric which is better for image applications than their original version. Recognition, clustering and retrieval can be then performed based on the learned metric. Experimental results on benchmark image datasets demonstrate the effectiveness of our method.