Gaussian Process Modeling of Large Scale Terrain

This talk will focus on the problem of large scale multi-sensor multi-data-set sensor based perception and sensor fusion. The application context of this study is large scale terrain modeling for mining automation.

Building a model of large scale terrain (5 sq km) that can adequately handle uncertainty and incompleteness of sensor data in a statistically sound way is a challenging problem. Most contemporary representations are not equipped to model spatially correlated data and typically treat data as being statistically independent. To obtain a comprehensive model of such terrain, typically, multiple sensory modalities as well as multiple data sets are required. This necessitates sensor fusion.

In order to address these issues, this work proposed the use of Gaussian processes (GP's) as models of large scale terrain. The model naturally provided a multi-resolution representation of space, incorporated and handled uncertainties aptly and coped with incompleteness of sensory information. Gaussian process regression techniques were applied to estimate and interpolate (to fill gaps in occluded areas) elevation information across the field. A single non-stationary (neural network) Gaussian process was shown to be powerful enough to model large and complex terrain, effectively handling issues relating to discontinuous data.

Experiments were performed on large scale 3D data sets taken using GPS and laser scanners from a mining scenario. Extensive statistical performance evaluation of the technique was performed through cross validation experiments on the aforementioned data sets. These experiments also compared the proposed modeling approach with most other well known interpolation and representation methods. The outcome of these comparison and benchmarking experiments was that the proposed approach will perform as well as grid based techniques or triangulated irregular networks (TIN's) for dense, relatively flat laser scanner data sets, however, for complex and/or sparse data sets, the proposed Gaussian process modeling approach will significantly outperform grid based approaches using most standard interpolation techniques as well as TIN's using triangle based interpolation techniques.

This work then proposed two approaches to data fusion using Gaussian processes - one based on Heteroscedastic GP's and the other based on Dependent GP's. The approach based on heteroscedastic GP's modeled the different data sets as different noisy samples of a common underlying terrain. Dependent GP based data fusion modeled each data set using a separate GP and learnt spatial correlation information between different GP's through auto and cross correlations. A key novelty of this work was the derivation and use of non-stationary kernels for multi-task problems with dependent Gaussian processes. The work based on dependent GP's has also successfully demonstrated the simultaneous modeling/prediction of multiple properties of the terrain (terrain elevation and color).

To enable the approach to cope with multiple large-scale data sets, GP approximations were developed for both the learning and inference stages. A local approximation method based on a "moving window" methodology and implemented using KD-Trees was proposed for both GP learning and inference. Further, a block learning approach to GP learning was proposed which guaranteed the successful use of this approach in resource constrained systems. These approximation methods enabled the approach to handle large data sets, thereby addressing its scalability issues.

ABOUT THE SPEAKER:

Dr Shrihari Vasudevan has a BE in Computer Science and Engineering from the University of Madras (2002), an MS in Computer Science / Intelligent Robotics from the University of Southern California, USA (2004) and a DSc in Intelligent Robotics from the Swiss Federal Institute of Technology Zurich (2008). He is currently a research fellow / lecturer at the Australian Centre for Field Robotics, The University of Sydney. His research interests may be summarized as the modeling and mining of sensor data. Specifically, he is interested in sensor based perception, sensor fusion, machine learning and pattern recognition towards developing intelligent robots and systems.