Geometry Processing as Inference

Introduction

Geometry Processing is concerned with algorithms and data structures for representing and processing three-dimensional shapes. Techniques in geometry processing have been developed over the last three decades and are now driving real-world applications in various industries.

Algorithms and Applications

Geometry processing algorithms may be interpreted as components of digital signal processing or machine learning, solving inference problems. Given an incomplete description of the geometry, commonly based on point samples, the concept or process underlying the observations - the surface - is recovered (unsupervised feature learning).

These algorithms can then be applied to:

1. Smooth the surface (filtering)
2. Segment the surface (clustering)
3. Interactively modify the surface (semi-supervised learning)

To facilitate these operations, the surface representation is adjusted through transcoding and resampling.

Challenges in Higher Dimensions

However, using the algorithms and data structures in geometry processing for data living in higher-dimensional spaces requires fundamentally new methods in geometric computing.

Emerge Research Program

Emerge presents a research program aiming at making geometry processing methods available as a set of tools in data science. Emerge will introduce fundamentally new concepts for surface representations and computational methods for surface interrogation in dimensions beyond three, providing useful tools in various science and engineering disciplines.

Thesis and Impact

The thesis of Emerge is that the resulting extensions and generalizations of geometry processing techniques will be fruitfully complementing and adding to the state of the art in processing large amounts of data.

Any progress in this direction will have a profound impact, as the proliferation of sensors and data processing has led to most of the current societal challenges, including:

• Climate change
• Global biological risks
• Population growth
• Global policy making
• Energy

These challenges come with enormous amounts of unstructured quantitative data to be analyzed.