Latent Embedded Graphs for Image and Shape Interpolation

Abstract

In this paper, we introduce latent embedded graphs, a simple approach for shape and image interpolation using generative neural network models. A latent embedded graph is defined as a topological structure constructed over a set of lower-dimensional embedding (latent space) of points in a high-dimensional dataset learnt by a generative model. Given two samples in the original dataset, the problem of interpolation can simply be re-formulated as traversing through this embedded graph along the minimal path. This deceptively simple method is based on the fundamental observation that a low-dimensional space induced by a given sample is typically non-Euclidean and in some cases may even represent a multi-manifold. Therefore, simply performing linear interpolation of the encoded data may not necessarily lead to plausible interpolation in the original space. Latent embedded graphs address this issue by capturing the topological structure within the spatial distribution of the data in the latent space, thereby allowing for approximate geodesic computations in a robust and effective manner. We demonstrate our approach through variational autoencoder (VAE) as the method for learning the latent space and generating the topological structure using k-nearest-neighbor graph. We then present a systematic study of our approach by applying it to 2D curves (superformulae), image (Fashion-MNIST), and voxel (ShapeNet) datasets. We further demonstrate that our approach performs better than the linear case in preserving geometric and topological variations during interpolation.