Kendall Shape-VAE : Learning Shapes in a Generative Framework

Learning an interpretable representation of data without supervision is an important precursor for the development of artificial intelligence. In this work, we introduce \textit{Kendall Shape}-VAE, a novel Variational Autoencoder framework for learning shapes as it disentangles the latent space by compressing information to simpler geometric symbols. In \textit{Kendall Shape}-VAE, we modify the Hyperspherical Variational Autoencoder such that it results in an exactly rotationally equivariant network using the notion of landmarks in the Kendall shape space. We show the exact equivariance of the model through experiments on rotated MNIST.