Shape-from-image via cross-sections

International Conference on Pattern Recognition (ICPR), 2000, Barcelona (España)Using structural geometry, Whiteley (1991) showed that a line drawing is a correct projection of a spherical polyhedron if and only if it has a cross-section compatible with it. We extend the class of drawings to which this test applies, including those of polyhedral disks. Our proof is constructive, showing how to derive all spatial interpretations; it relies on elementary synthetic geometric arguments, and, as a by-product, it yields a simpler and shorter proof of Whiteley's result. Moreover, important properties of line drawings are visually derived as corollaries: realizability is independent of the adopted projection, it is an invariant projective property, and for trihedral drawings it can be checked with a pencil and an unmarked ruler alone.Peer Reviewe

Shape-from-Image via Cross-Sections

Abstrac

The interpretations of line drawings with contrast failure and shadows

Abstract. In line drawings derived from real images, lines may be missing due to contrast failure and objects with curved surfaces may cast shadows from multiple light sources. This paper shows that it is the presence of shadows, rather than contrast failure, that renders the line drawing labelling problem NP-complete. However, shadows are a valuable visual cue, since their presence is formally shown to reduce the average ambiguity of drawings. This is especially true when constraints concerning shadow formation are employed to differentiate shadow and non-shadow lines. The extended junction constraint, concerning straight lines colinear with junctions, compensates the loss of information caused by contrast failure. In fact, we observe the contrast failure paradox: a drawing is sometimes less ambiguous when lines are partly missing due to contrast failure. It is known that the coplanarity of sets of object vertices can be deduced from the presence of straight lines in the drawing. This paper shows that these coplanarity constraints are robust to the presence of contrast failure

Recovering 3D geometry from single line drawings.

Xue, Tianfan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 52-55).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Previous Approaches on Face Identification --- p.3Chapter 1.1.1 --- Face Identification --- p.3Chapter 1.1.2 --- General Objects --- p.4Chapter 1.1.3 --- Manifold Objects --- p.7Chapter 1.2 --- Previous Approaches on 3D Reconstruction --- p.9Chapter 1.3 --- Our approach for Face Identification --- p.11Chapter 1.4 --- Our approach for 3D Reconstruction --- p.13Chapter 2 --- Face Detection --- p.14Chapter 2.1 --- GAFI and its Face Identification Results --- p.15Chapter 2.2 --- Our Face Identification Approach --- p.17Chapter 2.2.1 --- Real Face Detection --- p.18Chapter 2.2.2 --- The Weak Face Adjacency Theorem --- p.20Chapter 2.2.3 --- Searching for Type 1 Lost Faces --- p.22Chapter 2.2.4 --- Searching for Type 2 Lost Faces --- p.23Chapter 2.3 --- Experimental Results --- p.25Chapter 3 3 --- D Reconstruction --- p.30Chapter 3.1 --- Assumption and Terminology --- p.30Chapter 3.2 --- Finding Cuts from a Line Drawing --- p.34Chapter 3.2.1 --- Propositions for Finding Cuts --- p.34Chapter 3.2.2 --- Searching for Good Cuts --- p.35Chapter 3.3 --- Separation of a Line Drawing from Cuts --- p.38Chapter 3.4 3 --- D Reconstruction from a Line Drawing --- p.45Chapter 3.5 --- Experiments --- p.45Chapter 4 --- Conclusion --- p.5

3D object reconstruction from line drawings.

Cao Liangliang.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 64-69).Abstracts in English and Chinese.Chapter 1 --- Introduction and Related Work --- p.1Chapter 1.1 --- Reconstruction from Single Line Drawings and the Applications --- p.1Chapter 1.2 --- Optimization-based Reconstruction --- p.2Chapter 1.3 --- Other Reconstruction Methods --- p.2Chapter 1.3.1 --- Line Labeling and Algebraic Methods --- p.2Chapter 1.3.2 --- CAD Reconstruction --- p.3Chapter 1.3.3 --- Modelling from Images --- p.3Chapter 1.4 --- Finding Faces of Line Drawings --- p.4Chapter 1.5 --- Generalized Cylinder --- p.4Chapter 1.6 --- Research Problems and Our Contribution --- p.5Chapter 1.6.1 --- A New Criteria --- p.5Chapter 1.6.2 --- Recover Objects from Line Drawings without Hidden Lines --- p.6Chapter 1.6.3 --- Reconstruction of Curved Objects --- p.6Chapter 1.6.4 --- Planar Limbs Assumption and the Derived Models --- p.6Chapter 2 --- A New Criteria for Reconstruction --- p.8Chapter 2.1 --- Introduction --- p.8Chapter 2.2 --- Human Visual Perception and the Symmetry Measure --- p.10Chapter 2.3 --- Reconstruction Based on Symmetry and Planarity --- p.11Chapter 2.3.1 --- Finding Faces --- p.11Chapter 2.3.2 --- Constraint of Planarity --- p.11Chapter 2.3.3 --- Objective Function --- p.12Chapter 2.3.4 --- Reconstruction Algorithm --- p.13Chapter 2.4 --- Experimental Results --- p.13Chapter 2.5 --- Summary --- p.18Chapter 3 --- Line Drawings without Hidden Lines: Inference and Reconstruction --- p.19Chapter 3.1 --- Introduction --- p.19Chapter 3.2 --- Terminology --- p.20Chapter 3.3 --- Theoretical Inference of the Hidden Topological Structure --- p.21Chapter 3.3.1 --- Assumptions --- p.21Chapter 3.3.2 --- Finding the Degrees and Ranks --- p.22Chapter 3.3.3 --- Constraints for the Inference --- p.23Chapter 3.4 --- An Algorithm to Recover the Hidden Topological Structure --- p.25Chapter 3.4.1 --- Outline of the Algorithm --- p.26Chapter 3.4.2 --- Constructing the Initial Hidden Structure --- p.26Chapter 3.4.3 --- Reducing Initial Hidden Structure --- p.27Chapter 3.4.4 --- Selecting the Most Plausible Structure --- p.28Chapter 3.5 --- Reconstruction of 3D Objects --- p.29Chapter 3.6 --- Experimental Results --- p.32Chapter 3.7 --- Summary --- p.32Chapter 4 --- Curved Objects Reconstruction from 2D Line Drawings --- p.35Chapter 4.1 --- Introduction --- p.35Chapter 4.2 --- Related Work --- p.36Chapter 4.2.1 --- Face Identification --- p.36Chapter 4.2.2 --- 3D Reconstruction of planar objects --- p.37Chapter 4.3 --- Reconstruction of Curved Objects --- p.37Chapter 4.3.1 --- Transformation of Line Drawings --- p.37Chapter 4.3.2 --- Finding 3D Bezier Curves --- p.39Chapter 4.3.3 --- Bezier Surface Patches and Boundaries --- p.40Chapter 4.3.4 --- Generating Bezier Surface Patches --- p.41Chapter 4.4 --- Results --- p.43Chapter 4.5 --- Summary --- p.45Chapter 5 --- Planar Limbs and Degen Generalized Cylinders --- p.47Chapter 5.1 --- Introduction --- p.47Chapter 5.2 --- Planar Limbs and View Directions --- p.49Chapter 5.3 --- DGCs in Homogeneous Coordinates --- p.53Chapter 5.3.1 --- Homogeneous Coordinates --- p.53Chapter 5.3.2 --- Degen Surfaces --- p.54Chapter 5.3.3 --- DGCs --- p.54Chapter 5.4 --- Properties of DGCs --- p.56Chapter 5.5 --- Potential Applications --- p.59Chapter 5.5.1 --- Recovery of DGC Descriptions --- p.59Chapter 5.5.2 --- Deformable DGCs --- p.60Chapter 5.6 --- Summary --- p.61Chapter 6 --- Conclusion and Future Work --- p.62Bibliography --- p.6

3D object reconstruction from 2D and 3D line drawings.

Chen, Yu.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 78-85).Abstracts in English and Chinese.Chapter 1 --- Introduction and Related Work --- p.1Chapter 1.1 --- Reconstruction from 2D Line Drawings and the Applications --- p.2Chapter 1.2 --- Previous Work on 3D Reconstruction from Single 2D Line Drawings --- p.4Chapter 1.3 --- Other Related Work on Interpretation of 2D Line Drawings --- p.5Chapter 1.3.1 --- Line Labeling and Superstrictness Problem --- p.6Chapter 1.3.2 --- CAD Reconstruction --- p.6Chapter 1.3.3 --- Modeling from Images --- p.6Chapter 1.3.4 --- Identifying Faces in the Line Drawings --- p.7Chapter 1.4 --- 3D Modeling Systems --- p.8Chapter 1.5 --- Research Problems and Our Contributions --- p.10Chapter 1.5.1 --- Recovering Complex Manifold Objects from Line Drawings --- p.10Chapter 1.5.2 --- The Vision-based Sketching System --- p.11Chapter 2 --- Reconstruction from Complex Line Drawings --- p.13Chapter 2.1 --- Introduction --- p.13Chapter 2.2 --- Assumptions and Terminology --- p.15Chapter 2.3 --- Separation of a Line Drawing --- p.17Chapter 2.3.1 --- Classification of Internal Faces --- p.18Chapter 2.3.2 --- Separating a Line Drawing along Internal Faces of Type 1 --- p.19Chapter 2.3.3 --- Detecting Internal Faces of Type 2 --- p.20Chapter 2.3.4 --- Separating a Line Drawing along Internal Faces of Type 2 --- p.28Chapter 2.4 --- 3D Reconstruction --- p.44Chapter 2.4.1 --- 3D Reconstruction from a Line Drawing --- p.44Chapter 2.4.2 --- Merging 3D Manifolds --- p.45Chapter 2.4.3 --- The Complete 3D Reconstruction Algorithm --- p.47Chapter 2.5 --- Experimental Results --- p.47Chapter 2.6 --- Summary --- p.52Chapter 3 --- A Vision-Based Sketching System for 3D Object Design --- p.54Chapter 3.1 --- Introduction --- p.54Chapter 3.2 --- The Sketching System --- p.55Chapter 3.3 --- 3D Geometry of the System --- p.56Chapter 3.3.1 --- Locating the Wand --- p.57Chapter 3.3.2 --- Calibration --- p.59Chapter 3.3.3 --- Working Space --- p.60Chapter 3.4 --- Wireframe Input and Object Editing --- p.62Chapter 3.5 --- Surface Generation --- p.63Chapter 3.5.1 --- Face Identification --- p.64Chapter 3.5.2 --- Planar Surface Generation --- p.65Chapter 3.5.3 --- Smooth Curved Surface Generation --- p.67Chapter 3.6 --- Experiments --- p.70Chapter 3.7 --- Summary --- p.72Chapter 4 --- Conclusion and Future Work --- p.74Chapter 4.1 --- Conclusion --- p.74Chapter 4.2 --- Future Work --- p.75Chapter 4.2.1 --- Learning-Based Line Drawing Reconstruction --- p.75Chapter 4.2.2 --- New Query Interface for 3D Object Retrieval --- p.75Chapter 4.2.3 --- Curved Object Reconstruction --- p.76Chapter 4.2.4 --- Improving the 3D Sketch System --- p.77Chapter 4.2.5 --- Other Directions --- p.77Bibliography --- p.7

3D Reconstruction of Indoor Corridor Models Using Single Imagery and Video Sequences

In recent years, 3D indoor modeling has gained more attention due to its role in decision-making process of maintaining the status and managing the security of building indoor spaces. In this thesis, the problem of continuous indoor corridor space modeling has been tackled through two approaches. The first approach develops a modeling method based on middle-level perceptual organization. The second approach develops a visual Simultaneous Localisation and Mapping (SLAM) system with model-based loop closure. In the first approach, the image space was searched for a corridor layout that can be converted into a geometrically accurate 3D model. Manhattan rule assumption was adopted, and indoor corridor layout hypotheses were generated through a random rule-based intersection of image physical line segments and virtual rays of orthogonal vanishing points. Volumetric reasoning, correspondences to physical edges, orientation map and geometric context of an image are all considered for scoring layout hypotheses. This approach provides physically plausible solutions while facing objects or occlusions in a corridor scene. In the second approach, Layout SLAM is introduced. Layout SLAM performs camera localization while maps layout corners and normal point features in 3D space. Here, a new feature matching cost function was proposed considering both local and global context information. In addition, a rotation compensation variable makes Layout SLAM robust against cameras orientation errors accumulations. Moreover, layout model matching of keyframes insures accurate loop closures that prevent miss-association of newly visited landmarks to previously visited scene parts. The comparison of generated single image-based 3D models to ground truth models showed that average ratio differences in widths, heights and lengths were 1.8%, 3.7% and 19.2% respectively. Moreover, Layout SLAM performed with the maximum absolute trajectory error of 2.4m in position and 8.2 degree in orientation for approximately 318m path on RAWSEEDS data set. Loop closing was strongly performed for Layout SLAM and provided 3D indoor corridor layouts with less than 1.05m displacement errors in length and less than 20cm in width and height for approximately 315m path on York University data set. The proposed methods can successfully generate 3D indoor corridor models compared to their major counterpart

Reconstruction of Orthogonal Polyhedra

In this thesis I study reconstruction of orthogonal polyhedral surfaces and orthogonal polyhedra from partial information about their boundaries. There are three main questions for which I provide novel results. The first question is "Given the dual graph, facial angles and edge lengths of an orthogonal polyhedral surface or polyhedron, is it possible to reconstruct the dihedral angles?" The second question is "Given the dual graph, dihedral angles and edge lengths of an orthogonal polyhedral surface or polyhedron, is it possible to reconstruct the facial angles?" The third question is "Given the vertex coordinates of an orthogonal polyhedral surface or polyhedron, is it possible to reconstruct the edges and faces, possibly after rotating?" For the first two questions, I show that the answer is "yes" for genus-0 orthogonal polyhedra and polyhedral surfaces under some restrictions, and provide linear time algorithms. For the third question, I provide results and algorithms for orthogonally convex polyhedra. Many related problems are studied as well