Geometry Processing as Inference

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.

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) and then may be smoothed (filtering), segmented (clustering), or interactively modified (semi-supervised learning).

To facilitate these operations the surface representation is adjusted (transcoding, resampling).

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 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 dimension beyond three -- providing useful tools in various science and engineering disciplines.

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 profound impact, as the proliferation of sensors and data processing has led to most of the current societal challenges (climate change, global biological risks, population growth, global policy making, energy) coming with enormous amounts of unstructured quantitative data to be analyzed.