Implicit modelling is a powerful technique to design geometric shapes, where a geometric object is described by a real function. In general, the real functions used in implicit modelling are unbounded and can take any values in space R. In general, the shapes described by different level sets of an unbounded implicit function can be varied significantly and are very unpredictable. In addition, ...

Alpha shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for the shape of a given point set V . For a given point set V in 2 or 3 dimensions, we show that the knowledge of pairwise distances between pairs of points which are closer than a certain distance is sufficient to compute the alpha shape. We also show that the alpha shapes c...

We combine classical concepts from different disciplines — those of α-hull and α-shape from computational geometry, splitting data into training and test sets from artificial intelligence, density-based spatial clustering from data mining, and moving average from time series analysis — to develop a robust algorithm for reconstructing the shape of a curve from noisy samples. The novelty of our a...

This paper considers a new kind of knowledge discovery among spatial objects|namely that of partial boundary shape matching. Our focus is on mining spatial data, whereby many objects called features (represented as polygons) are compared with one or more point sets called clusters. The research described has practical application in such domains as Geographic Information Systems, in which a clu...

LiDAR (Light Detection and Ranging) technology has been used to obtain geometrical attributes of tree crops in small field plots, sometimes using manual steps in data processing. The objective of this study was to develop a method for estimating canopy volume and height based on a mobile terrestrial laser scanner suited for large commercial orange groves. A 2D LiDAR sensor and a GNSS (Global Na...

In this paper a framework for defining scale-spaces, based on the computational geometry concepts of α-shapes, is proposed. In this approach, objects (curves or surfaces) of increasing convexity are computed by selective sub-sampling, from the original shape to its convex hull. The relationships with the Empirical Mode Decomposition (EMD), the curvature motion-based scale-space and some operato...

Multi-scale geometrical and topological analyses of point clouds can reveal their rich structures. Because conformal alpha shapes of point clouds are hierarchical shapes under different mesh resolution or internal alpha values, their surface curvature estimations are one of the multi-scale geometrical analyses. We present a robust method for computing surface curvature of conformal alpha shapes...

We study the problem of segmenting, reconstructing, and analyzing the structure growth of thrombi (clots) in blood vessels in vivo based on 2-photon microscopic image data. First, we develop an algorithm for segmenting clots in 3D microscopic images based on density-based clustering and methods for dealing with imaging artifacts. Next, we apply the union-of-balls (or alpha-shape) algorithm to r...

Filtration techniques are useful tools of analysing roundness profiles. The 2RC filter and Gaussian filter are commonly used to assess peripheral undulations of the roundness data. However they cannot do every aspect of functional prediction. Morphological filters are employed to characterise roundness profiles for functional assessment. Traditional computation methods for morphological filters...

Shape optimization is the design process to obtain an optimal structure under specific conditions, such structure must have the minimum weight without exceeding the maximum allowed Von Mises stress and displacement. In our procedure, the analyzed structure is defined by a set of control points, we apply the α-shape method to them in order to get the contour of the shape. To search for optimal s...