Narrow Results

We introduce a modeling framework that can be applied to cases of multiple converging fronts during episodes of population expansion and innovation diffusion, referring to two prehistoric case studies known archaeologically (the spread of pottery-making in Europe, and the spread of farming in southern Africa). We model front propagation using Fast Marching methods, drawing on the analogy with crystallization processes to build compoundly-weighted Voronoi diagrams of a spatially partitioned surface in which the zones of influence of each competing spreading process are determined by their respective front initiation times and propagation rates. We analyze the phase space for the general two-source case, and illustrate the potential of this approach by modeling the evolving interface for the archaeological case studies.

This paper investigates the simulation of a modified Hamilton–Jacobi equation in order to provide a classical wavefront-based formulation of reaction dynamics. Here, the wavefront is interpreted as minimizing a particular action functional. The method is rooted in the geometric optics and an eikonal equation is typically used for describing the light wave propagation. We have introduced a general formulation for reaction force surface (RFS) and a host of several force-based properties, which offer a reinvigorated understanding of the occurrence of a reaction event at molecular level. The calculation is performed on a model potential energy surface representing the hydrogen transfer reaction in malonaldehyde.

In this paper, a new method is proposed that integrates the 3D terrain information, ditch geometry, and biped dynamics for motion planning of a 14-DOF biped robot on 3D terrain containing a 3D ditch. The path planning is modeled as a wavefront propagation in Non-uniform medium represented by the Eikonal equation. A speed function expresses the inhomogeneity of uneven terrain. The Eikonal equation is solved by the Fast marching method (FMM) to obtain the global path. Ten Footstep variables (FSVs) characterize one step of walk on a 3D uneven terrain surface. The hip and foot trajectory parameters (HFTPs) are used to construct cubic spline-based hip and foot trajectories of the biped robot. The optimal value of HFTPs is obtained by a Genetic algorithm by minimization of energy and satisfying the constraint of dynamic balance. A walk-dataset is created that contains the optimal trajectories for different FSVs. The generated walk-dataset was used to train the biped to walk on rough terrain using a feed-forward Neural network for making a real-time estimate of optimal HFTPs. Simulation results validate the effectiveness of the proposed method of ditch crossing on different uneven terrains.

3D facial reconstruction systems create 3D facial computer models of individuals from their 2D photographic images or video sequences. Currently, published face recognition systems are mostly based on large training sets of 2D facial images although there has been an increase in interest in using 3D data input instead. An intermediate approach is to synthesize a 3D face making use of a single 2D image. In this paper, we present such a method that does not require complicated optimization steps or user-defined parameters, which distinguishes it from existing 3D face reconstruction methods. The method has been used in 2D face recognition experiments to generate a 3D Morphological Model (3DMM) from a single facial training image.

Given a single 2D facial image, a small set of morphological feature points are selected. Their corresponding three-dimensional indices in the morphological model are obtained using the so-called Fast Marching Method. Shape alignment between the 2D input image and the 3D morphological model is achieved using Newton's Method to solve a single nonlinear equation to obtain a scalar parameter. This yields all of the shape parameters of the 3DMM. Texture recovery for the model involves bridging the 2D image representation of the 3DMM using the so-called UV space as an intermediary. Thus the advantage of the proposed method over others in the literature is that a computationally complex geometric problem is simplified and transformed to a 2D-to-3D warping problem. This enhances both the efficiency and accuracy of texture recovery.

We also introduce a quantitative shape measure based on the Bending Invariant Canonical Form to determine the quality of the 3D reconstruction. This is shown to produce a reconstruction error of 5% over the database of 100 stored 3D faces. In addition, the reconstructed 3D faces at various head poses have been used to create 2D images of faces that form the training set for face recognition experiments reported elsewhere.