Robust surface segmentation and edge feature lines extraction from fractured fragments of relics

AbstractSurface segmentation and edge feature lines extraction from fractured fragments of relics are essential steps for computer assisted restoration of fragmented relics. As these fragments were heavily eroded, it is a challenging work to segment surface and extract edge feature lines. This paper presents a novel method to segment surface and extract edge feature lines from triangular meshes of irregular fractured fragments. Firstly, a rough surface segmentation is accomplished by using a clustering algorithm based on the vertex normal vector. Secondly, in order to differentiate between original and fracture faces, a novel integral invariant is introduced to compute the surface roughness. Thirdly, an accurate surface segmentation is implemented by merging faces based on face normal vector and roughness. Finally, edge feature lines are extracted based on the surface segmentation. Some experiments are made and analyzed, and the results show that our method can achieve surface segmentation and edge extraction effectively

Recognition of feature curves on 3D shapes using an algebraic approach to Hough transforms

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and meaningful information about a shape. We have first to separate the curves belonging to features from those caused by noise and then to select the lines, which describe non-trivial portions of a surface. The automatic detection of such features is crucial for the identification and/or annotation of relevant parts of a given shape. To do this, the Hough transform (HT) is a feature extraction technique widely used in image analysis, computer vision and digital image processing, while, for 3D shapes, the extraction of salient feature curves is still an open problem. Thanks to algebraic geometry concepts, the HT technique has been recently extended to include a vast class of algebraic curves, thus proving to be a competitive tool for yielding an explicit representation of the diverse feature lines equations. In the paper, for the first time we apply this novel extension of the HT technique to the realm of 3D shapes in order to identify and localize semantic features like patterns, decorations or anatomical details on 3D objects (both complete and fragments), even in the case of features partially damaged or incomplete. The method recognizes various features, possibly compound, and it selects the most suitable feature profiles among families of algebraic curves

Machine learning methods for 3D object classification and segmentation

Field of study: Computer science.Dr. Ye Duan, Thesis Supervisor.Includes vita."July 2018."Object understanding is a fundamental problem in computer vision and it has been extensively researched in recent years thanks to the availability of powerful GPUs and labelled data, especially in the context of images. However, 3D object understanding is still not on par with its 2D domain and deep learning for 3D has not been fully explored yet. In this dissertation, I work on two approaches, both of which advances the state-of-the-art results in 3D classification and segmentation. The first approach, called MVRNN, is based multi-view paradigm. In contrast to MVCNN which does not generate consistent result across different views, by treating the multi-view images as a temporal sequence, our MVRNN correlates the features and generates coherent segmentation across different views. MVRNN demonstrated state-of-the-art performance on the Princeton Segmentation Benchmark dataset. The second approach, called PointGrid, is a hybrid method which combines points and regular grid structure. 3D points can retain fine details but irregular, which is challenge for deep learning methods. Volumetric grid is simple and has regular structure, but does not scale well with data resolution. Our PointGrid, which is simple, allows the fine details to be consumed by normal convolutions under a coarser resolution grid. PointGrid achieved state-of-the-art performance on ModelNet40 and ShapeNet datasets in 3D classification and object part segmentation.Includes bibliographical references (pages 116-140)

Doctor of Philosophy

dissertationThe medial axis of an object is a shape descriptor that intuitively presents the morphology or structure of the object as well as intrinsic geometric properties of the object’s shape. These properties have made the medial axis a vital ingredient for shape analysis applications, and therefore the computation of which is a fundamental problem in computational geometry. This dissertation presents new methods for accurately computing the 2D medial axis of planar objects bounded by B-spline curves, and the 3D medial axis of objects bounded by B-spline surfaces. The proposed methods for the 3D case are the first techniques that automatically compute the complete medial axis along with its topological structure directly from smooth boundary representations. Our approach is based on the eikonal (grassfire) flow where the boundary is offset along the inward normal direction. As the boundary deforms, different regions start intersecting with each other to create the medial axis. In the generic situation, the (self-) intersection set is born at certain creation-type transition points, then grows and undergoes intermediate transitions at special isolated points, and finally ends at annihilation-type transition points. The intersection set evolves smoothly in between transition points. Our approach first computes and classifies all types of transition points. The medial axis is then computed as a time trace of the evolving intersection set of the boundary using theoretically derived evolution vector fields. This dynamic approach enables accurate tracking of elements of the medial axis as they evolve and thus also enables computation of topological structure of the solution. Accurate computation of geometry and topology of 3D medial axes enables a new graph-theoretic method for shape analysis of objects represented with B-spline surfaces. Structural components are computed via the cycle basis of the graph representing the 1-complex of a 3D medial axis. This enables medial axis based surface segmentation, and structure based surface region selection and modification. We also present a new approach for structural analysis of 3D objects based on scalar functions defined on their surfaces. This approach is enabled by accurate computation of geometry and structure of 2D medial axes of level sets of the scalar functions. Edge curves of the 3D medial axis correspond to a subset of ridges on the bounding surfaces. Ridges are extremal curves of principal curvatures on a surface indicating salient intrinsic features of its shape, and hence are of particular interest as tools for shape analysis. This dissertation presents a new algorithm for accurately extracting all ridges directly from B-spline surfaces. The proposed technique is also extended to accurately extract ridges from isosurfaces of volumetric data using smooth implicit B-spline representations. Accurate ridge curves enable new higher-order methods for surface analysis. We present a new definition of salient regions in order to capture geometrically significant surface regions in the neighborhood of ridges as well as to identify salient segments of ridges

Bootstrap Based Surface Reconstruction

Surface reconstruction is one of the main research areas in computer graphics. The goal is to find the best surface representation of the boundary of a real object. The typical input of a surface reconstruction algorithm is a point cloud, possibly obtained by a laser 3D scanner. The raw data from the scanner is usually noisy and contains outliers. Apart from creating models of high visual quality, assuring that a model is as faithful as possible to the original object is also one of the main aims of surface reconstruction. Most surface reconstruction algorithms proposed in the literature assess the reconstructed models either by visual inspection or, in cases where subjective manual input is not possible, by measuring the training error of the model. However, the training error underestimates systematically the test error and encourages overfitting. In this thesis, we provide a method for quantitative assessment in surface reconstruction. We integrate a model averaging method from statistics called bootstrap and define it into our context. Bootstrapping is a resampling procedure that provides statistical parameter. In surface fitting, we obtained error estimate which detect error caused by noise or bad fitting. We also define bootstrap method in context of normal estimation. We obtain variance and error estimates which we use as a quality measure of normal estimates. As application, we provide smoothing algorithm for point clouds and normal smoothing that can handle feature area. We also developed feature detection algorithm

Automatic Landmarking for Non-cooperative 3D Face Recognition

This thesis describes a new framework for 3D surface landmarking and evaluates its performance for feature localisation on human faces. This framework has two main parts that can be designed and optimised independently. The first one is a keypoint detection system that returns positions of interest for a given mesh surface by using a learnt dictionary of local shapes. The second one is a labelling system, using model fitting approaches that establish a one-to-one correspondence between the set of unlabelled input points and a learnt representation of the class of object to detect. Our keypoint detection system returns local maxima over score maps that are generated from an arbitrarily large set of local shape descriptors. The distributions of these descriptors (scalars or histograms) are learnt for known landmark positions on a training dataset in order to generate a model. The similarity between the input descriptor value for a given vertex and a model shape is used as a descriptor-related score. Our labelling system can make use of both hypergraph matching techniques and rigid registration techniques to reduce the ambiguity attached to unlabelled input keypoints for which a list of model landmark candidates have been seeded. The soft matching techniques use multi-attributed hyperedges to reduce ambiguity, while the registration techniques use scale-adapted rigid transformation computed from 3 or more points in order to obtain one-to-one correspondences. Our final system achieves better or comparable (depending on the metric) results than the state-of-the-art while being more generic. It does not require pre-processing such as cropping, spike removal and hole filling and is more robust to occlusion of salient local regions, such as those near the nose tip and inner eye corners. It is also fully pose invariant and can be used with kinds of objects other than faces, provided that labelled training data is available

Skeletonization and segmentation of binary voxel shapes

Preface. This dissertation is the result of research that I conducted between January 2005 and December 2008 in the Visualization research group of the Technische Universiteit Eindhoven. I am pleased to have the opportunity to thank a number of people that made this work possible. I owe my sincere gratitude to Alexandru Telea, my supervisor and first promotor. I did not consider pursuing a PhD until my Master’s project, which he also supervised. Due to our pleasant collaboration from which I learned quite a lot, I became convinced that becoming a doctoral student would be the right thing to do for me. Indeed, I can say it has greatly increased my knowledge and professional skills. Alex, thank you for our interesting discussions and the freedom you gave me in conducting my research. You made these four years a pleasant experience. I am further grateful to Jack vanWijk, my second promotor. Our monthly discussions were insightful, and he continuously encouraged me to take a more formal and scientific stance. I would also like to thank Prof. Jan de Graaf from the department of mathematics for our discussions on some of my conjectures. His mathematical rigor was inspiring. I am greatly indebted to the Netherlands Organisation for Scientific Research (NWO) for funding my PhD project (grant number 612.065.414). I thank Prof. Kaleem Siddiqi, Prof. Mark de Berg, and Dr. Remco Veltkamp for taking part in the core doctoral committee and Prof. Deborah Silver and Prof. Jos Roerdink for participating in the extended committee. Our Visualization group provides a great atmosphere to do research in. In particular, I would like to thank my fellow doctoral students Frank van Ham, Hannes Pretorius, Lucian Voinea, Danny Holten, Koray Duhbaci, Yedendra Shrinivasan, Jing Li, NielsWillems, and Romain Bourqui. They enabled me to take my mind of research from time to time, by discussing political and economical affairs, and more trivial topics. Furthermore, I would like to thank the senior researchers of our group, Huub van de Wetering, Kees Huizing, and Michel Westenberg. In particular, I thank Andrei Jalba for our fruitful collaboration in the last part of my work. On a personal level, I would like to thank my parents and sister for their love and support over the years, my friends for providing distractions outside of the office, and Michelle for her unconditional love and ability to light up my mood when needed