Exploration of Latent Spaces of 3D Shapes via Isomap and Inverse Mapping

We introduce a deep neural network based 3D shape latent space exploration method where exploration is performed through 2D embedding navigation. It is based on a combination of Isomap dimensionality reduction and an inverse mapping function. For a shape dataset, we train an autoencoder network to learn the latent representation. Then, we reduce the dimensionality of the latent space to two dimensions with the Isomap method. This makes navigation and new point sampling easy in the 2D latent space embedding. Our method then translates the sampled points back to latent vectors with an inverse mapping function, while the latent vectors are decoded by the neural network into 3D shapes that can be inspected by the user. The inverse mapping poses it as a radial basis function (RBF) scattered interpolation problem. The qualitative and quantitative experiments show the performance of the exploration method, along with the comparative advantages, and meaningful outcomes.