Scene Recognition on the Semantic Manifold

A new architecture, denoted spatial pyramid matching on the semantic manifold (SPMSM), is proposed for scene recognition. SPMSM is based on a recent image representation on a semantic probability simplex, which is now augmented with a rough encoding of spatial information. A connection between the semantic simplex and a Riemmanian manifold is established, so as to equip the architecture with a similarity measure that respects the manifold structure of the semantic space. It is then argued that the closed-form geodesic distance between two manifold points is a natural measure of similarity between images. This leads to a conditionally positive definite kernel that can be used with any SVM classifier. An approximation of the geodesic distance reveals connections to the well-known Bhattacharyya kernel, and is explored to derive an explicit feature embedding for this kernel, by simple square-rooting. This enables a low-complexity SVM implementation, using a linear SVM on the embedded features. Several experiments are reported, comparing SPMSM to state-of-the-art recognition methods. SPMSM is shown to achieve the best recognition rates in the literature for two large datasets (MIT Indoor and SUN) and rates equivalent or superior to the state-of-the-art on a number of smaller datasets. In all cases, the resulting SVM also has much smaller dimensionality and requires much fewer support vectors than previous classifiers. This guarantees much smaller complexity and suggests improved generalization beyond the datasets considered.