Geometrical Segmentation of Point Cloud Data by Spectral Analysis

A principal step towards solving diverse perception problems is segmentation. Many algorithms benefit from initially partitioning input point clouds into objects and their parts. In accordance with cognitive sciences, segmentation goal may be formulated as to split point clouds into locally smooth convex areas, enclosed by sharp concave boundaries. This goal is based on purely geometrical considerations and does not incorporate any constraints, or semantics, of the scene and objects being segmented, which makes it very general and widely applicable. In this work we perform geometrical segmentation of point cloud data according to the stated goal. The data is mapped onto a graph and the task of graph partitioning is considered. We formulate an objective function and derive a discrete optimization problem based on it. Finding the globally optimal solution is an NP-complete problem; in order to circumvent this, spectral methods are applied. Two algorithms that implement the divisive hierarchical clustering scheme are proposed. They derive graph partition by analyzing the eigenvectors obtained through spectral relaxation. The specifics of our application domain are used to automatically introduce cannot-link constraints in the clustering problem. The algorithms function in completely unsupervised manner and make no assumptions about shapes of objects and structures that they segment. Three publicly available datasets with cluttered real-world scenes and an abundance of box-like, cylindrical, and free-form objects are used to demonstrate convincing performance. Preliminary results of this thesis have been contributed to the International Conference on Autonomous Intelligent Systems (IAS-13)