We describe a method of constructing a B-rep solid model from a single hidden-line removed sketch view of a 3D object. The main steps of our approach are as follows. The sketch is first tidied in 2D (to remove digitisation errors). Line labelling is used to deduce the initial topology of the object and to locate hidden faces. Constraints are then produced from the line labelling and features in the drawing (such as probable symmetry) involving the unknown face coefficients and point depths. A least squares solution is found to the linear system and any grossly incompatible equations are rejected. Vertices are recalculated as the intersections of the faces to ensure we have a reconstructible solid. Any incomplete faces are then completed as far as possible from neighbouring faces, producing a solid model from the initial sketch, if successful. The current software works for polyhedral objects with trihedral vertices.

Abstract—This paper presents an effective jump-diffusion method for segmenting a range image and its associated reflectance image in the Bayesian framework. The algorithm works on complex real-world scenes (indoor and outdoor), which consist of an unknown number of objects (or surfaces) of various sizes and types, such as planes, conics, smooth surfaces, and cluttered objects (like trees and bushes). Formulated in the Bayesian framework, the posterior probability is distributed over a solution space with a countable number of subspaces of varying dimensions. The algorithm simulates Markov chains with both reversible jumps and stochastic diffusions to traverse the solution space. The reversible jumps realize the moves between subspaces of different dimensions, such as switching surface models and changing the number of objects. The stochastic Langevin equation realizes diffusions within each subspace. To achieve effective computation, the algorithm precomputes some importance proposal probabilities over multiple scales through Hough transforms, edge detection, and data clustering. The latter are used by the Markov chains for fast mixing. The algorithm is tested on 100 1D simulated data sets for performance analysis on both accuracy and speed. Then, the algorithm is applied to three data sets of range images under the same parameter setting. The results are satisfactory in comparison with manual segmentations.

This thesis presents methods for the automatic creation of boundary-representation models of polyhedral objects from single line drawings depicting the objects. This topic is important in that automated interpretation of freehand sketches would remove a bottleneck in current engineering design methods. The thesis does not consider conversion of freehand sketches to line drawings or methods which require manual intervention or multiple drawings. Thge thesis contains a number of...

... line drawing of an engineering object (with hidden lines removed) as a B-rep model. As part of this process, we seek to deduce a frontal geometry of the object, a 3D geometric realisation of that part of the object visible in the drawing. Inflation takes a drawing in which all lines have been line-labelled, and creates the frontal geometry by adding a z-coordinate to the x- and y-coordinates of each junction. This depth information comes from compliance functions, interpretations of drawing features expressed as equations in junction z-coordinates. We examine several compliance functions, and assessing their use in interpretation of engineering objects. We also describe a compliance function based on junction labels, and remove its previous restriction to trihedral vertices. We give a

sketch with hidden lines removed of a single polyhedral object into a boundary representation solid model.

Mechanical design and manufacturing information for 3-D solid objects has been effectively conveyed through a set of annotated orthographic projections and optional cross-sections. This forms the basis of engineering drawings, which solve the problem of unambiguously representing a 3-D object on a 2-D plane. In this paper we address the inverse problem: given an engineering drawing of an object, construct the object's 3-D representation. To enable automatic recognition, the paper line drawings are initially scanned, and yield images which are inherently noisy. The 3-D objects themselves can have surfaces that are planar, spherical, or cylindrical. We examine the stages of drawing generation and formulate the drawing interpretation problem. Most 3-D reconstruction algorithms have assumed that the vertex coordinates and line and arc endpoint coordinates are known accurately and without error, and that no annotation exists in the drawing. In practice, however, scanned drawings are noisy a...

Optimization is one of the most promising geometrical reconstruction approaches. In this approach, the 2D vertices of the given figure maintain their plane coordinates (X,Y), while a set of Z coordinates (orthogonal to the plane) is computed to obtain a 3D configuration that matches the "implicit spatial information" contained in the departure drawing. In other words, Z coordinates are the variables, and image regularities are used to define both the Objective Function and the Constraints. Some authors have introduced and tested the approach. Nevertheless, further improvements are needed. Mainly because in this problem only global optimum is acceptable in order to ensure the "psychologically plausible" model is always the one to be obtained. In this paper, some key aspects of the strategy proposed by the authors to convey the optimization process towards the psychologically plausible solution are discussed. Keywords: geometrical reconstruction, optimization. 1 This work wa...

A new algorithm is presented for interpreting two-dimensional (2D) line drawings as threedimensional (3D) objects without models. Even though no explicit models or additional heuristics are included, the algorithm tends to reach the same 3D interpretations of 2D line drawings that humans do. The algorithm explicitly calculates the partial derivatives of Marill's Minimum Standard Deviation of Angles (MSDA) with respect to all adjustable parameters, and follows this gradient to minimize SDA. For an image with lines meeting at m points forming n angles, the gradient descent algorithm requires O(n) time to adjust all the points, while Marill’s method required O(mn) time to do so. Experimental results on various line drawing objects show that this gradient descent algorithm running on a Macintosh II is one to two orders of magnitude faster than the MSDA algorithm running on a Symbolics, while still giving comparable results.

A tool which can quickly interpret line drawings (with hidden lines removed) of engineering objects as boundary representation CAD models would be of significant benefit in the process of engineering design. Inflation of the drawing to produce a frontal geometry, a geometric realisation of that part of the object visible in the drawing, is an important stage of this process. Previous

Current user interfaces of CAD systems are still not suited to the initial stages of product development, where freehand drawings are used by engineers and designers to express their visual thinking. In order to exploit these sketching skills, we present a sketch based modeling system, which provides a reduced instruction set calligraphic interface to create orthogonal polyhedra, and an extension of them we named quasi-normalons. Our system allows users to draw lines on free-hand axonometric-like drawings, which are automatically tidied and beautified. These line drawings are then converted into a threedimensional model in real time because we implemented a fast reconstruction process, suited for quasi-normalon objects and so-called axonometric inflation method, providing in this way an innovative integrated 2D sketching and 3D view visualization work environment.