The alpha model, a parametrized family of probabilities on cladograms (rooted binary leaf labeled trees), is introduced. This model is Markovian self-similar, deletion-stable (sampling consistent), and passes through the Yule, Uniform and Comb models. An explicit formula is given to calculate the probability of any cladogram or tree shape under the alpha model. Sackin's and Colless' index are s...

In contrast to the mean-line based filters, morphological filters are function oriented and more suitable for the functional prediction of component performance. This paper presents a novel morphological method based on the alpha shape for the extraction of topographical features from engineering surfaces. Compared to the traditional implementation of morphological filters, the alpha shape meth...

Morphological filters are useful tools as they are commonly employed in surface metrology and dimensional metrology, serving for surface texture analysis and data smoothing respectively. Compared to the mean-line filtering techniques, such as the Gaussian filter, morphological filters have the merits of compact support, no need to remove form, and being relevant to geometrical properties of sur...

We design a probabilistic trajectory synthesis algorithm for generating time-varying sequences of geometric configuration data. The algorithm takes a set of observed samples (each may come from a different trajectory) and simulates the dynamic evolution of the patterns in O(n logn) time. To synthesize geometric configurations with indistinct identities, we use the pair correlation function to s...

Reconstruction of a real tree from scattered scanned points is a new challenge in virtual reality. Although many progresses are made on main branch structures and overall shape of a tree, reconstructions are still not satisfactory in terms of silhouette and details. We do think that 3D reconstruction of the tree crown shapes may help to constrain accurate reconstruction of complete real tree ge...

Extracting ground surface from high-density point clouds collected by Mobile Laser Scanning (MLS) systems is of vital importance in urban planning and digital city mapping. This article proposes a novel approach for automated extraction of ground surface along urban roads from MLS point clouds. The approach, which was designed to handle both ordered and unordered MLS point clouds, consists of t...