Manifold Traversal Using Density Ridges

In this work we present two examples of how a manifold learning model can represent the complexity of shape variation in images. Manifold learning techniques for image manifolds can be used to model data in sparse manifold regions. Additionally, they can be used as generative models as they can often better represent or learn structure in the data. We propose a method of estimating the underlying manifold using the ridges of a kernel density estimate as well as tangent space operations that allows interpolation between images along the manifold and offers a novel approach to analyzing the image manifold.