A grid map generated from ground-based 3D LIDAR point clouds is a critical component for facilitating autonomous system navigation without crashing into obstacles and also to generate a road map for a large local area. This paper proposes a novel approach to generate an occupancy grid map along with object classification in real-time for autonomous ground robot applications. Based on geometric analysis of the raster-scanned LIDAR data, we formulate criteria to distinguish 3D points directly from coordinate values and generate three grid maps; occupancy, ground, and scatter maps which directly correspond to hypotheses on object type. Then 2D and 3D shape analysis are carried out to verify the object hypotheses. Our experimental results show that the new method performs well providing an autonomous system with surrounding 3D information and object classification.

A watershed transform and a graph partitioning are studied on statistical manifold. Statistical manifold is a 2D Riemannian manifold which is statistically defined by maps that transform a parameter domain onto a set of probability density functions (PDFs). Due to high dimensionality of PDFs, it is hard and computationally expensive to produce segmentation on statistical manifold. In this paper, we propose a method that generates super-pixels using watershed transform. Finding capturing basins on statistical manifold is not straightforward. Here, we create a local distance map using metric tensor defined on statistical manifold. Watershed transform is performed on this local distance map and provides super-pixels that significantly reduce the number of data points and thus make efficient clustering algorithms such as normalized cut (Ncut) feasible to work on. Experimental results show superiority of the proposed method over principal component analysis (PCA) based dimensionality reduction method.

Dimensionality reduction and clustering on statistical manifolds is presented. Statistical manifold [16] is a 2D Riemannian manifold which is statistically defined by maps that transform a parameter domain onto a set of probability density functions. Principal component analysis (PCA) based dimensionality reduction is performed on the manifold, and therefore, estimation of a mean and a variance of the set of probability distributions are needed. First, the probability distributions are transformed by an isometric transform that maps the distributions onto a surface of hyper-sphere. The sphere constructs a Riemannian manifold with a simple geodesic distance measure. Then, a Frechet mean is estimated on the Riemannian manifold to perform the PCA on a tangent plane to the mean. Experimental results show that clustering on the Riemannian space produce more accurate and stable classification than the one on Euclidean space.

This paper introduces a new representation for planar curves. From the well-known Dirichlet problem for a disk, the harmonic function embedded in a circular disk is solely dependent on specified boundary values and can be obtained from Poisson’s integral formula. We derive a discrete version of Poisson’s formula and assess its harmonic properties. Various shape signatures can be used as boundary values, whereas only the corresponding Fourier descriptors are needed for the framework. The proposed approach is similar to a scale space representation but exhibits greater generality by accommodating using any type of shape signature. In addition, it is robust to noise and computationally efficient, and it is guaranteed to have a unique solution. In this paper, we demonstrate that the approach has strong potential for shape representation and matching applications.

This paper presents a new diffusion scheme on statistical manifolds for the detection of texture boundaries. The technique derives from our previous work, in which 2-dimensional Riemannian manifolds were statistically defined by maps that transform a parameter domain onto a set of probability density functions. In the earlier approach, a modified Kullback-Leibler divergence, measuring dissimilarity between two density distributions, was added to the statistical manifolds so that a geometric interpretation of the manifolds becomes possible. Although the previous framework produced good segmentation results, the approach led to offsets in texture boundaries for some situations. This paper introduces a diffusion scheme on statistical manifolds that leads to substantially improved localization accuracy in segmentation of textured images.

A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2-dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto a set of probability density functions. In this novel framework, color or texture features are measured at each image point and their statistical characteristics are estimated. This is different from statistical representation of bounded regions. A modified Kullback-Leibler divergence, that measures dissimilarity between two density distributions, is added to the statistical manifolds so that a geometric interpretation of the manifolds becomes possible. With this framework, we can formulate a metric tensor on the statistical manifolds. Then, a geodesic active contour is evolved with the aid of the metric tensor. We show that the statistical manifold framework provides more robust and accurate texture segmentation results.