Martin Magnusson
The Three-Dimensional Normal-Distributions Transform — an Efficient Representation for Registration, Surface Analysis, and Loop Detection
Doctoral Thesis, Örebro University, December 2009
Abstract:

This dissertation is concerned with three-dimensional (3D) sensing and 3D scan representation. Three-dimensional records are important tools in several disciplines; such as medical imaging, archaeology, and mobile robotics. This dissertation proposes the normal-distributions transform, NDT, as a general 3D surface representation with applications in scan registration, localisation, loop detection, and surface-structure analysis. After applying NDT, the surface is represented by a smooth function with analytic derivatives. This representation has several attractive properties.

The smooth function representation makes it possible to use standard numerical optimisation methods, such as Newton’s method, for 3D registration. This dissertation extends the original two-dimensional NDT registration algorithm of Biber and Straßer to 3D and introduces a number of improvements. The 3D-NDT scan-registration algorithm is compared to current de facto standard registration algorithms. 3D-NDT scan registration with the proposed extensions is shown to be more robust, more accurate, and faster than the popular ICP algorithm. An additional benefit is that 3D-NDT registration provides a confidence measure of the result with little additional effort.

Furthermore, a kernel-based extension to 3D-NDT for registering coloured data is proposed. Approaches based on local visual features typically use only a small fraction of the available 3D points for registration. In contrast, Colour-NDT uses all of the available 3D data. The dissertation proposes to use a combination of local visual features and Colour-NDT for robust registration of coloured 3D scans.

Also building on NDT, a novel approach using 3D laser scans to perform appearance-based loop detection for mobile robots is proposed. Loop detection is an importantproblem in the SLAM (simultaneous localisation and mapping) domain. The proposed approach uses only the appearance of 3D point clouds to detect loops and requires nopose information. It exploits the NDT surface representation to create histograms based on local surface orientation and smoothness. The surface-shape histograms compress the input data by two to three orders of magnitude. Because of the high compression rate, the histograms can be matched efficiently to compare the appearance of two scans. Rotation invariance is achieved by aligning scans with respect to dominant surface orientations. In order to automatically determine the threshold that separates scans at loop closures from nonoverlapping ones, the proposed approach uses expectation maximisation to fit a Gamma mixture model to the output similarity measures.

In order to enable more high-level tasks, it is desirable to extract semantic information from 3D models. One important task where such 3D surface analysis is useful is boulder detection for mining vehicles. This dissertation presents a method, also inspired by NDT, that provides clues as to where the pile is, where the bucket should be placed for loading, and where there are obstacles. The points of 3D point clouds are classified based on the surrounding surface roughness and orientation. Other potential applications include extraction of drivable paths over uneven surfaces.

Errata

Download: Thesis (G5 paper size): [PDF (6.4MB)]
@PHDTHESIS{Magnusson:3D-NDT:2009,
  AUTHOR = {Martin Magnusson},
  TITLE = {The Three-Dimensional Normal-Distributions Transform --- an Efficient Representation for Registration, Surface Analysis, and Loop Detection},
  SCHOOL = {Örebro University},
  NOTE = {Örebro Studies in Technology 36},
  YEAR = 2009,
  MONTH = dec
}