Autoencoder-Aided Visualization of Collections of Morse Complexes

Jixian Li, Dan Van Boxel, Joshua Levine

View presentation:2022-10-17T20:45:00ZGMT-0600Change your timezone on the schedule page
2022-10-17T20:45:00Z
Exemplar figure, described by caption below
From a collection of scalar fields, we first compute the arcs of their Morse complexes. Then we convert the arcs of Morse complexes into image-based encoding to obtain a set of images of arcs. Next, we train an autoencoder to reconstruct those images. The autoencoder learns latent representations of those images of arcs. We use those latent representations as a proxy for the geometry of Morse complexes. Projecting those latent representations into a visual space helps us study the collection of Morse complexes.

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Keywords

Morse complex, Dimensionality reduction, Autoencoders

Abstract

Though analyzing a single scalar field using Morse complexes is well studied, there are few techniques for visualizing a collection of Morse complexes. We focus on analyses that are enabled by looking at a Morse complex as an embedded domain decomposition. Specifically, we target 2D scalar fields, and we encode the Morse complex through binary images of the boundaries of decomposition. Then we use image-based autoencoders to create a feature space for the Morse complexes. We apply additional dimensionality reduction methods to construct a scatterplot as a visual interface of the feature space. This allows us to investigate individual Morse complexes, as they relate to the collection, through interaction with the scatterplot. We demonstrate our approach using a synthetic data set, microscopy images, and time-varying vorticity magnitude fields of flow. Through these, we show that our method can produce insights about structures within the collection of Morse complexes.