Solid reconstruction using recognition of quadric surfaces from orthographic views

International audienceThe reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided

Estimation of Epipolar Geometry via the Radon Transform

One of the key problems in computer vision is the recovery of epipolar geometry constraints between different camera views. The majority of existing techniques rely on point correspondences, which are typically perturbed by mismatches and noise, hence limiting the accuracy of these techniques. To overcome these limitations, we propose a novel approach that estimates epipolar geometry constraints based on a statistical model in the Radon domain. The method requires no correspondences, explicit constraints on the data or assumptions regarding the scene structure. Results are presented on both synthetic and real data that show the method's robustness to noise and outliers

Calibration of a Telecentric Structured-light Device for Micrometric 3D Reconstruction

Structured-light 3D reconstruction techniques are employed in a wide range of applications for industrial inspection. In particular, some tasks require micrometric precision for the identification of microscopic surface irregularities. We propose a novel calibration technique for structured-light systems adopting telecentric lenses for both camera and projector. The device exploits a fixed light pattern (striped-based) to perform accurate microscopic surface reconstruction and measurements. Our method employs a sphere with a known radius as calibration target and takes advantage of the orthographic projection model of the telecentric lenses to recover the bundle of planes originated by the projector. Once the sheaf of parallel planes is properly described in the camera reference frame, the triangulation of the surface’s object hit by the light stripes is immediate. Moreover, we tested our technique in a real-world scenario for industrial surface inspection by implementing a complete pipeline to recover the intersections between the projected planes and the surface. Experimental analysis shows the robustness of the proposed approach against synthetic and real-world test data

Intersecting Architectural Surfaces Between Graphic and Analytic Representations

Since 2014, we have been dealing with Geometry as a common and shared language between Architecture and Mathematics. In this contribution we focus, from that point of view, on the relationship between the architectural object and its theoretical model by mean of analyzing its Geometry, also bearing in mind the context of first year Bachelor’s in Architecture, with the wider goal of improving spatial thinking and visualization abilities. In fact, in architects’ training when it comes to analyzing built shapes, there occurs the need to abstract their geometric essences from the real world. It is then important to provide students with instruments to derivate the theoretical object from its built counterpart. We have been focusing on particular architectural/geometric realities such as compound vaults generated by intersecting surfaces and on the analysis of a variety of approaches for representing them: from the analytical one, which allows rigorous and unambiguous outcomes, to graphical ones, which are consequences of choices (of tools and constructive sequences) leading to only partially rigorous results. To analyze a groin vault with our students, we consider graphical representations of portions of intersecting cones, as outcome of a critical process of data discretization. We compare graphic solutions (obtained via descriptive geometry by CAAD-AutoCAD) and their different levels of approximation with a mathematical formalization (obtained via analytical geometry) and the use of a DGS (GeoGebra), reasoning about subjectivity and objectivity of the respective representations. We chose to use these tools because our students are at their very first year of academic studies, thus they are not comfortable with highly specialized software, with which they will be trained in more advanced courses. There are possible learning difficulties of epistemological nature related to the recognition of geometric objects in space, which involve understanding of concepts, symbols, procedures and different types of representations; even only from a mathematical point of view, indeed, a geometric object can be described by Cartesian equations, or by parametric equations, or even considering it as a set of points that verify the same property; then, students need adequate flexibility to switch from one register to another (in the sense of Duval). Thus we need them to experiment with simple tasks, avoiding possible issues with difficulties in spatial prefiguration capabilities they have might not already developed during their high schools studies. Students are provided with some testing and verification tool: on one side a DGS makes Mathematics accessible to experimentation; on the other side Monge himself, in his 1798 treatise Géométrie descriptive, suggested that one of the purposes of this science is to allow a graphic verification of objects’ geometric properties and to suggest new previously unknown features. This remark reveals an aspect of Representation as an experimental science, where reasoning proceeds by adding other entities to the figure or by imagining operations that also have a physical model, such as plane sections. We propose analytical tools to critically verify students’ geometric intuitions about built architecture, with the further possibility to highlight relationships between graphic representation sought and analytical properties of surfaces and resulting vaults. Such activities, in the spirit of visual thinking, allow them to visualize relations between surfaces in a more dynamic, manageable and intuitive way and to compare results obtained with a variety of architectural and mathematical tools, by means of implementing the use of the same theoretical concepts using the interdisciplinary language of Geometry

Single shot three-dimensional imaging of dilute atomic clouds

Light field microscopy methods together with three dimensional (3D) deconvolution can be used to obtain single shot 3D images of atomic clouds. We demonstrate the method using a test setup which extracts three dimensional images from a fluorescent $^{87}$Rb atomic vapor.Comment: 10 pages, 5 figure

3D Automatic Target Recognition for Future LIDAR Missiles

We present a real-time three-dimensional automatic target recognition approach appropriate for future light detection and ranging-based missiles. Our technique extends the speeded-up robust features method into the third dimension by solving multiple two-dimensional problems and performs template matching based on the extreme case of a single pose per target. Evaluation on military targets shows higher recognition rates under various transformations and perturbations at lower processing time compared to state-of-the-art approaches

Relating vanishing points to catadioptric camera calibration

This paper presents the analysis and derivation of the geometric relation between vanishing points and camera parameters of central catadioptric camera systems. These vanishing points correspond to the three mutually orthogonal directions of 3D real world coordinate system (i.e. X, Y and Z axes). Compared to vanishing points (VPs) in the perspective projection, the advantages of VPs under central catadioptric projection are that there are normally two vanishing points for each set of parallel lines, since lines are projected to conics in the catadioptric image plane. Also, their vanishing points are usually located inside the image frame. We show that knowledge of the VPs corresponding to XYZ axes from a single image can lead to simple derivation of both intrinsic and extrinsic parameters of the central catadioptric system. This derived novel theory is demonstrated and tested on both synthetic and real data with respect to noise sensitivity

Current State of the Art Historic Building Information Modelling

In an extensive review of existing literature a number of observations were made in relation to the current approaches for recording and modelling existing buildings and environments: Data collection and pre-processing techniques are becoming increasingly automated to allow for near real-time data capture and fast processing of this data for later modelling applications. Current BIM software is almost completely focused on new buildings and has very limited tools and pre-defined libraries for modelling existing and historic buildings. The development of reusable parametric library objects for existing and historic buildings supports modelling with high levels of detail while decreasing the modelling time. Mapping these parametric objects to survey data, however, is still a time-consuming task that requires further research. Promising developments have been made towards automatic object recognition and feature extraction from point clouds for as-built BIM. However, results are currently limited to simple and planar features. Further work is required for automatic accurate and reliable reconstruction of complex geometries from point cloud data. Procedural modelling can provide an automated solution for generating 3D geometries but lacks the detail and accuracy required for most as-built applications in AEC and heritage fields