Ralph Robert Martin

Reverse engineering of geometric models—an introduction

In many areas of industry, it is desirable to create geometric models of existing objects for which no such model is available. This paper reviews the process of reverse engineering of shapes. After identifying the purpose of reverse engineering and the main application areas, the most important algorithmic steps are outlined and various reconstruction strategies are presented. Pros and cons of various data acquisition techniques are described with related problems of boundary representation model construction. Specific issues addressed include characterization of geometric models and related surface representations, segmentation and surface fitting for simple and free-form shapes, multiple view combination and creating consistent and accurate B-rep models. The limitations of currently known solutions are also described, and we point out areas in which further work is required before reverse engineering of shape becomes a practical, widely-available engineering tool.

A sequential niche technique for multimodal function optimization

A technique is described that allows unimodal function optimization methods to be extended to locate all optima of multimodal problems efficiently. We describe an algorithm based on a traditional genetic algorithm (GA). This technique involves iterating the GA but uses knowledge gained during one iteration to avoid re-searching, on subsequent iterations, regions of problem space where solutions have already been found. This gain is achieved by applying a fitness derating function to the raw fitness function, so that fitness values are depressed in the regions of the problem space where solutions have already been found. Consequently, the likelihood of discovering a new solution on each iteration is dramatically increased. The technique may be used with various styles of GAs or with other optimization methods, such as simulated annealing. The effectiveness of the algorithm is demonstrated on a number of multimodal test functions. The technique is at least as fast as fitness sharing methods. It provides an acceleration of between 1 and l0p on a problem with p optima, depending on the value of p and the convergence time complexity.

Merging and splitting eigenspace models

We present new deterministic methods that, given two eigenspace models-each representing a set of n-dimensional observations-will: 1) merge the models to yield a representation of the union of the sets and 2) split one model from another to represent the difference between the sets. As this is done, we accurately keep track of the mean. Here, we give a theoretical derivation of the methods, empirical results relating to the efficiency and accuracy of the techniques, and three general applications, including the construction of Gaussian mixture models that are dynamically updateable.

Incremental Eigenanalysis for Classification

Eigenspace models are a convenient way to represent sets of observations with widespread applications, including classification. In this paper we describe a new constructive method for incrementally adding observations to an eigenspace model. Our contribution is to explicitly account for a change in origin as well as a change in the number of eigenvectors needed in the basis set. No other method we have seen considers change of origin, yet both are needed if an eigenspace model is to be used for classification purposes. We empirically compare our incremental method with two alternatives from the literature and show our method is the more useful for classification because it computes the smaller eigenspace model representing the observations.

Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid

Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization. Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends.

A Shape‐Preserving Approach to Image Resizing

We present a novel image resizing method which attempts to ensure that important local regions undergo a geometric similarity transformation, and at the same time, to preserve image edge structure. To accomplish this, we define handles to describe both local regions and image edges, and assign a weight for each handle based on an importance map for the source image. Inspired by conformal energy, which is widely used in geometry processing, we construct a novel quadratic distortion energy to measure the shape distortion for each handle. The resizing result is obtained by minimizing the weighted sum of the quadratic distortion energies of all handles. Compared to previous methods, our method allows distortion to be diffused better in all directions, and important image edges are well‐preserved. The method is efficient, and offers a closed form solution.

Constrained fitting in reverse engineering

This paper considers simultaneous fitting of multiple curves and surfaces to 3D measured data captured as part of a reverse engineering process, where constraints exist between the parameters of the curves or surfaces. Enforcing such constraints may be necessary (i) to produce models to sufficiently accurate tolerances for import into a CAD system, and (ii) to produce models which successfully reproduce regularities and symmetries required by engineering applications.The constraints to be satisfied may be determined manually, or more likely, by an automatic process. In the latter case, typically many more constraints are generated than can all be simultaneously satisfied. We present a new numerical method able to resolve conflicts between constraints.Secondly, reverse engineering generates large amounts of data. Constrained fitting methods are iterative in nature, and so an efficient method needs to restrict the amount of computation performed on each iteration. Our method achieves this through carefully constructed representations for objects and constraints, and approximations to distance functions.This paper describes our approach to constrained fitting, and illustrates its usefulness with some 2D and 3D examples taken from reverse engineering.

Fast and Effective Feature-Preserving Mesh Denoising

We present a simple and fast mesh denoising method, which can remove noise effectively while preserving mesh features such as sharp edges and corners. The method consists of two stages. First, noisy face normals are filtered iteratively by weighted averaging of neighboring face normals. Second, vertex positions are iteratively updated to agree with the denoised face normals. The weight function used during normal filtering is much simpler than that used in previous similar approaches, being simply a trimmed quadratic. This makes the algorithm both fast and simple to implement. Vertex position updating is based on the integration of surface normals using a least-squares error criterion. Like previous algorithms, we solve the least-squares problem by gradient descent; whereas previous methods needed user input to determine the iteration step size, we determine it automatically. In addition, we prove the convergence of the vertex position updating approach. Analysis and experiments show the advantages of our proposed method over various earlier surface denoising methods.

Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation

This paper addresses a problem arising in the reverse engineering of solid models from depth-maps. We wish to identify and fit surfaces of known type wherever these are a good fit. This paper presents a set of methods for the least-squares fitting of spheres, cylinders, cones and tori to three-dimensional point data. Least-squares fitting of surfaces other planes, even of simple geometric type, has been little studied.

Algorithms for reverse engineering boundary representation models

Abstract A procedure for reconstructing solid models of conventional engineering objects from a multiple-view, 3D point cloud is described. (Conventional means bounded by simple analytical surfaces, swept surfaces and blends.) Emphasis is put on producing accurate and topologically consistent boundary representation models, ready to be used in computer aided design and manufacture. The basic phases of our approach to reverse engineering are summarised, and related computational difficulties are analysed. Four key algorithmic components are presented in more detail: efficiently segmenting point data into regions; creating linear extrusions and surfaces of revolution with smooth, constrained profiles; creating the topology of B-rep models; and finally adding blends. The application of these algorithms in an integrated system is illustrated by means of various examples, including a well-known reverse engineering benchmark.