Phillip N. Azariadis

Retrieval of 3D articulated objects using a graph-based representation

Most of the approaches which address the problem of 3D object retrieval, use global descriptors of the objects which fail to consistently compensate for the intra-class variability of articulated objects. In this paper, a retrieval methodology is presented which is based upon a graph-based object representation. This is composed of a meaningful new mesh segmentation along with a graph matching between the graph of the query object and each of the graphs that correspond to the objects of the 3D object database. The graph matching algorithm is based on the Earth Movers Distance (EMD) similarity measure which is calculated using a new ground distance assignment. The superior performance of the proposed methodology is shown after an extensive experimentation comprising alternative descriptors for the constituent components of the 3D object as well as comparison with state of the art retrieval algorithms.

Obstacle representation by Bump-surfaces for optimal motion-planning

Abstract This paper introduces a new method for global, near optimal, motion-planning of a robot (either mobile or redundant manipulator) moving in an environment cluttered with a priori known prohibited areas which have arbitrary shape, size and location. The proposed method is based on the novel notion of Bump-surfaces (or B-surfaces) which represent the entire robot environment through a single mathematical entity. The motion-planning solution is searched on a higher-dimension B-surface in such a way that its inverse image into the robot environment satisfies the given objectives and constraints. The computed solution for a mobile robot consists of a smooth curve without self-loops which connects the starting and destination points with the shortest possible path. The same approach is also used for nth degree-of-freedom manipulators where the end-effector reaches the destination position following a smooth short path avoiding the prohibited areas. For clarity reasons the proposed method is introduced in this paper for the case of a two-dimensional (2D) planar terrain with static obstacles, while a generalization to motion-planning problems on curved terrains is also discussed. Extensive experiments are presented and discussed to illustrate the efficiency and effectiveness of the proposed motion-planning method in a variety of complex environments.

Parameterization of clouds of unorganized points using dynamic base surfaces

In this paper a new method for parameterizing clouds of unorganized points is presented. The proposed method introduces the notion of dynamic base surfaces (DBS) which are dynamically adapted to the three-dimensional shape implied by the clouds of points. The only assumption regarding the cloud of points is the existence of a boundary defined by a closed path of four curves. The proposed method is based on an iterative procedure where a DBS is gradually improved approximating more faithfully the fundamental geometry of the cloud of points. Parameterization is achieved by orthogonally projecting the cloud of points onto the DBS. An application of the introduced parameterization method to the well-known surface least-squares fitting is presented which illustrates the effectiveness and the efficiency of the proposed approach.

Mission design for a group of autonomous guided vehicles

In this paper, a generic approach for the integration of vehicle routing and scheduling and motion planning for a group of autonomous guided vehicles (AGVs) is proposed. The AGVs are requested to serve all the work stations in a two-dimensional environment while taking into account kinematics constraints and the environments geometry during their motion. The problem objective is the simultaneous determination of time-optimum and collision-free paths for all AGVs. The proposed method is investigated and discussed through a number of simulated experiments using a variety of environments and different initial conditions.

Drawing curves onto a cloud of points for point-based modelling

Point-based geometric models are gaining popularity in both the computer graphics and CAD fields. A related design/modelling problem is the focus of the reported research: drawing curves onto digital surfaces represented by clouds of points. The problem is analyzed and solved, and a set of ‘design tools’ are proposed which allow the user/designer to efficiently perform ‘product development’ (alternative name: ‘detail design’) tasks which require efficient processing of a ‘digital surface’. The primary tool is a robust and efficient point projection algorithm combined with a smoothing technique for producing smooth ‘digital curves’ lying onto the cloud surface. The new design tools are tested on a real-life industrial example with very satisfactory results, which are thoroughly presented in the paper. q 2004 Elsevier Ltd. All rights reserved.

3D articulated object retrieval using a graph-based representation

In this paper, a retrieval methodology for 3D articulated objects is presented that relies upon a graph-based object representation. The methodology is composed of a mesh segmentation stage which creates the Attributed Relation Graph (ARG) of the object along with a graph matching algorithm which matches two ARGs. The graph matching algorithm is based on the Earth Movers Distance (EMD) similarity measure calculated with a new ground distance assignment. The superior performance of the proposed retrieval methodology against state-of-the-art approaches is shown by extensive experimentation that comprise the application of various geometric descriptors representing the components of the 3D objects that become the node attributes of the ARGs as well as alternative mesh segmentation approaches for the extraction of the object parts. The performance evaluation is addressed in both qualitative and quantitative terms.

Planar development of free-form surfaces: quality evaluation and visual inspection

Surface flattening is a crucial problem for many applications as indicated by the steady flow of new methods appearing in related publications. Quality control of these methods, by means of “accuracy criteria” independent of particular flattening methodologies, has not been addressed yet by researchers. This is exactly the subject of this paper: a detailed analysis of flattening is presented leading to geometric and physics-based criteria. These are implemented in intuitively-acceptable visualization techniques, which are applied to practical examples.

Two-dimensional motion-planning for nonholonomic robots using the bump-surfaces concept

In this paper, a new method is introduced for finding a near-optimal path of a nonholonomic robot moving in a 2D environment cluttered with static obstacles. The method is based on the Bump-Surfaces concept and is able to deal with robots represented by a translating and rotating rigid body. The proposed approach is applied to car-like robots.

A parametric feature-based approach to reconstructing traditional filigree jewelry

This paper presents a novel approach to reconstructing traditional filigree jewelry. Our method aims at producing an editable CAD representation that can accurately capture the original design and be capable of re-parameterization and modification prior to manufacturing (for example to insert custom designs and abide to free-form artistic alterations). To achieve this, we have developed robust and accurate representations of patterns, used in the design of such jewelry, based on spirals, circular and elliptic arcs, curve segments and braids of various types; all optimized by fairness criteria for aesthetic purposes. We have also built a library of parametric, constraint-based, manufacturable solid patterns that occur frequently in filigree jewelry. For the purposes of this work, a suite of software tools called ReJCAD has been developed, that is able to process a highly accurate point cloud of jewelry pieces and to detect features which are fitted by the primitives of the pattern library through user interaction. The point cloud, in the current framework, guides the assembling of all patterns into one robust manufacturable solid piece. We demonstrate the unique capabilities of ReJCAD by reconstructing a filigree brooch part commonly used in late 19th century in northwestern Greece.

Parametric-based reconstruction of 3D mesh models; towards the generation of a parametric human foot biomodel

In this work a new reconstruction technique is presented based on Parametric-Based Deformation. The new method uses a template 3D mesh model which is deformed according to user-defined semantic parameters in order to derive a new 3D object. The proposed methodology is divided in three stages: template construction (production of a template mesh model), regression (the template model is deformed to match sample models) and prediction (new instance mesh models are derived based on user parameters). The proposed method has been successfully applied for the reconstruction of human and animal skeletal models. A practical and novel reconstruction methodology has been developed and implemented for the reconstruction of the human foot given a bi-planar X-ray. The purpose of this methodology is to support the parametric generation of human foot biomodels in an automated way. The generated biomodels are employed by simulation tools based on Finite Element Analysis to test the stress factors that the foot is undertaking during its contact with the ground or a footwear sole structure.