Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures

This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison

Analysing and Enhancing the Coarse Registration Pipeline

The current and continual development of sensors and imaging systems capable of acquiring three-dimensional data provides a novel form in which the world can be expressed and examined. The acquisition process, however, is often limited by imaging systems only being able to view a portion of a scene or object from a single pose at a given time. A full representation can still be produced by shifting the system and registering subsequent acquisitions together. While many solutions to the registration problem have been proposed, there is no quintessential approach appropriate for all situations. This dissertation aims to coarsely register range images or point-clouds of a priori unknown pose by matching their overlapping regions. Using spherical harmonics to correlate normals in a coarse registration pipeline has been shown previously to be an effective means for registering partially overlapping point-clouds. The advantage of normals is their translation invariance, which permits the rotation and translation to be decoupled and determined separately. Examining each step of this pipeline in depth allows its registration capability to be quantified and identifies aspects which can be enhanced to further improve registration performance. The pipeline consists of three primary steps: identifying the rotation using spherical harmonics, identifying the translation in the Fourier domain, and automatically verifying if alignment is correct. Having achieved coarse registration, a fine registration algorithm can be used to refine and complete the alignment. Major contributions to knowledge are provided by this dissertation at each step of the pipeline. Point-clouds with known ground-truth are used to examine the pipeline's capability, allowing its limitations to be determined; an analysis which has not been performed previously. This examination allowed modifications to individual components to be introduced and measured, establishing their provided benefit. The rotation step received the greatest attention as it is the primary weakness of the pipeline, especially as the nature of the overlap between point-clouds is unknown. Examining three schemes for binning normals found that equiangular binning, when appropriately normalised, only had a marginal decrease in accuracy with respect to the icosahedron and the introduced Fibonacci schemes. Overall, equiangular binning was the most appropriate due to its natural affinity for fast spherical-harmonic conversion. Weighting normals was found to provide the greatest benefit to registration performance. The introduction of a straightforward method of combining two different weighting schemes using the orthogonality of complex values increased correct alignments by approximately 80% with respect to the next best scheme; additionally, point-cloud pairs with overlap as low as 5% were able to be brought into correct alignment. Transform transitivity, one of two introduced verification strategies, correctly classified almost 100% of point-cloud pair registrations when there are sufficient correct alignments. The enhancements made to the coarse registration pipeline throughout this dissertation provide significant improvements to its performance. The result is a pipeline with state-of-the-art capabilities that allow it to register point-cloud with minimal overlap and correct for alignments that are classified as misaligned. Even with its exceptional performance, it is unlikely that this pipeline has yet reached its pinnacle, as the introduced enhancements have the potential for further development