A variational approach to 3D geometry reconstruction from two or multiple views

[EN] In the last years we have developed some methods for 3D reconstruction. First we began with the problem of reconstructing a 3D scene from a stereoscopic pair of images. We developed some methods based on energy functionals which produce dense disparity maps by preserving discontinuities from image boundaries. Then we passed to the problem of reconstructing a 3D scene from multiple views (more than 2). The method for multiple view reconstruction relies on the method for stereoscopic reconstruction. For every pair of consecutive images we estimate a disparity map and then we apply a robust method that searches for good correspondences through the sequence of images. Recently we have proposed several methods for 3D surface regularization. This is a postprocessing step necessary for smoothing the final surface, which could be afected by noise or mismatch correspondences. These regularization methods are interesting because they use the information from the reconstructing process and not only from the 3D surface. We have tackled all these problems from an energy minimization approach. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method.

3D geometry of growth strata in a fault-propagation fold: insights into space–time evolution of the Crevillente Fault (Abanilla-Alicante sector), Betic Cordillera, Spain

This work presents a 3D geometric model of growth strata cropping out in a fault-propagation fold associated with the Crevillente Fault (Abanilla-Alicante sector) from the Bajo Segura Basin (eastern Betic Cordillera, southern Spain). The analysis of this 3D model enables us to unravel the along-strike and along-section variations of the growth strata, providing constraints to assess the fold development, and hence, the fault kinematic evolution in space and time. We postulate that the observed along-strike dip variations are related to lateral variation in fault displacement. Along-section variations of the progressive unconformity opening angles indicate greater fault slip in the upper Tortonian–Messinian time span; from the Messinian on, quantitative analysis of the unconformity indicate a constant or lower tectonic activity of the Crevillente Fault (Abanilla-Alicante sector); the minor abundance of striated pebbles in the Pliocene-Quaternary units could be interpreted as a decrease in the stress magnitude and consequently in the tectonic activity of the fault. At a regional scale, comparison of the growth successions cropping out in the northern and southern limits of the Bajo Segura Basin points to a southward migration of deformation in the basin. This means that the Bajo Segura Fault became active after the Crevillente Fault (Abanilla-Alicante sector), for which activity on the latter was probably decreasing according to our data. Consequently, we propose that the seismic hazard at the northern limit of the Bajo Segura Basin should be lower than at the southern limit.

Three primary school students’ cognition about 3D rotation in a virtual reality learning environment

This paper reports on three primary school students’ explorations of 3D rotation in a virtual reality learning environment (VRLE) named VRMath. When asked to investigate if you would face the same direction when you turn right 45 degrees first then roll up 45 degrees, or when you roll up 45 degrees first then turn right 45 degrees, the students found that the different order of the two turns ended up with different directions in the VRLE. This was contrary to the students’ prior predictions based on using pen, paper and body movements. The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements.

Constructing a frame of cube : connecting 3D shapes with direction, location and movement

With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about 3D shapes with direction, location and movement, and how young children can mentally and visually construct virtual 3D shapes using movements in both egocentric and fixed frames of reference (FOR). Findings suggest that year 4 (aged 9) children can develop the capacity to construct a cube using egocentric FOR only, fixed FOR only or a combination of both FOR. However, these young participants were unable to articulate the effect of individual or combined FOR movements. Directions for future research are proposed.

Rectilinear Path Following in 3D Space

This paper addresses the problem of determining an optimal (shortest) path in three dimensional space for a constant speed and turn-rate constrained aerial vehicle, that would enable the vehicle to converge to a rectilinear path, starting from any arbitrary initial position and orientation. Based on 3D geometry, we propose an optimal and also a suboptimal path planning approach. Unlike the existing numerical methods which are computationally intensive, this optimal geometrical method generates an optimal solution in lesser time. The suboptimal solution approach is comparatively more efficient and gives a solution that is very close to the optimal one. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a straight line with a prescribed orientation as required in several applications. But, if the distance between the initial point and the straight line to be followed along the vertical axis is high, then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we resort to a numerical method for obtaining the optimal solution. The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.

3D face computational photography using PCA spaces

In this paper, we present a 3D face photography system based on a facial expression training dataset, composed of both facial range images (3D geometry) and facial texture (2D photography). The proposed system allows one to obtain a 3D geometry representation of a given face provided as a 2D photography, which undergoes a series of transformations through the texture and geometry spaces estimated. In the training phase of the system, the facial landmarks are obtained by an active shape model (ASM) extracted from the 2D gray-level photography. Principal components analysis (PCA) is then used to represent the face dataset, thus defining an orthonormal basis of texture and another of geometry. In the reconstruction phase, an input is given by a face image to which the ASM is matched. The extracted facial landmarks and the face image are fed to the PCA basis transform, and a 3D version of the 2D input image is built. Experimental tests using a new dataset of 70 facial expressions belonging to ten subjects as training set show rapid reconstructed 3D faces which maintain spatial coherence similar to the human perception, thus corroborating the efficiency and the applicability of the proposed system.

Cell force measurements in 3D microfabricated environments based on compliant cantilevers.

We report the fabrication, functionalization and testing of microdevices for cell culture and cell traction force measurements in three-dimensions (3D). The devices are composed of bent cantilevers patterned with cell-adhesive spots not lying on the same plane, and thus suspending cells in 3D. The cantilevers are soft enough to undergo micrometric deflections when cells pull on them, allowing cell forces to be measured by means of optical microscopy. Since individual cantilevers are mechanically independent of each other, cell traction forces are determined directly from cantilever deflections. This proves the potential of these new devices as a tool for the quantification of cell mechanics in a system with well-defined 3D geometry and mechanical properties.

3D Porous Architecture of Stacks of β-TCP Granules Compared with That of Trabecular Bone: A microCT, Vector Analysis, and Compression Study

International audience

Porosity imaged by a vector projection algorithm correlates with fractal dimension measured on 3D models obtained by microCT

International audience

A hierarchical evolutionary algorithmic design (HEAD) system for generating and evolving building design models

This thesis develops a detailed conceptual design method and a system software architecture defined with a parametric and generative evolutionary design system to support an integrated interdisciplinary building design approach. The research recognises the need to shift design efforts toward the earliest phases of the design process to support crucial design decisions that have a substantial cost implication on the overall project budget. The overall motivation of the research is to improve the quality of designs produced at the author's employer, the General Directorate of Major Works (GDMW) of the Saudi Arabian Armed Forces. GDMW produces many buildings that have standard requirements, across a wide range of environmental and social circumstances. A rapid means of customising designs for local circumstances would have significant benefits. The research considers the use of evolutionary genetic algorithms in the design process and the ability to generate and assess a wider range of potential design solutions than a human could manage. This wider ranging assessment, during the early stages of the design process, means that the generated solutions will be more appropriate for the defined design problem. The research work proposes a design method and system that promotes a collaborative relationship between human creativity and the computer capability. The tectonic design approach is adopted as a process oriented design that values the process of design as much as the product. The aim is to connect the evolutionary systems to performance assessment applications, which are used as prioritised fitness functions. This will produce design solutions that respond to their environmental and function requirements. This integrated, interdisciplinary approach to design will produce solutions through a design process that considers and balances the requirements of all aspects of the design. Since this thesis covers a wide area of research material, 'methodological pluralism' approach was used, incorporating both prescriptive and descriptive research methods. Multiple models of research were combined and the overall research was undertaken following three main stages, conceptualisation, developmental and evaluation. The first two stages lay the foundations for the specification of the proposed system where key aspects of the system that have not previously been proven in the literature, were implemented to test the feasibility of the system. As a result of combining the existing knowledge in the area with the newlyverified key aspects of the proposed system, this research can form the base for a future software development project. The evaluation stage, which includes building the prototype system to test and evaluate the system performance based on the criteria defined in the earlier stage, is not within the scope this thesis. The research results in a conceptual design method and a proposed system software architecture. The proposed system is called the 'Hierarchical Evolutionary Algorithmic Design (HEAD) System'. The HEAD system has shown to be feasible through the initial illustrative paper-based simulation. The HEAD system consists of the two main components - 'Design Schema' and the 'Synthesis Algorithms'. The HEAD system reflects the major research contribution in the way it is conceptualised, while secondary contributions are achieved within the system components. The design schema provides constraints on the generation of designs, thus enabling the designer to create a wide range of potential designs that can then be analysed for desirable characteristics. The design schema supports the digital representation of the human creativity of designers into a dynamic design framework that can be encoded and then executed through the use of evolutionary genetic algorithms. The design schema incorporates 2D and 3D geometry and graph theory for space layout planning and building formation using the Lowest Common Design Denominator (LCDD) of a parameterised 2D module and a 3D structural module. This provides a bridge between the standard adjacency requirements and the evolutionary system. The use of graphs as an input to the evolutionary algorithm supports the introduction of constraints in a way that is not supported by standard evolutionary techniques. The process of design synthesis is guided as a higher level description of the building that supports geometrical constraints. The Synthesis Algorithms component analyses designs at four levels, 'Room', 'Layout', 'Building' and 'Optimisation'. At each level multiple fitness functions are embedded into the genetic algorithm to target the specific requirements of the relevant decomposed part of the design problem. Decomposing the design problem to allow for the design requirements of each level to be dealt with separately and then reassembling them in a bottom up approach reduces the generation of non-viable solutions through constraining the options available at the next higher level. The iterative approach, in exploring the range of design solutions through modification of the design schema as the understanding of the design problem improves, assists in identifying conflicts in the design requirements. Additionally, the hierarchical set-up allows the embedding of multiple fitness functions into the genetic algorithm, each relevant to a specific level. This supports an integrated multi-level, multi-disciplinary approach. The HEAD system promotes a collaborative relationship between human creativity and the computer capability. The design schema component, as the input to the procedural algorithms, enables the encoding of certain aspects of the designer's subjective creativity. By focusing on finding solutions for the relevant sub-problems at the appropriate levels of detail, the hierarchical nature of the system assist in the design decision-making process.

Open design of high pressure ratio radial-inflow turbine for academic validation

Computational Fluid Dynamics (CFD) simulations are widely used in mechanical engineering. Although achieving a high level of confidence in numerical modelling is of crucial importance in the field of turbomachinery, verification and validation of CFD simulations are very tricky especially for complex flows encountered in radial turbines. Comprehensive studies of radial machines are available in the literature. Unfortunately, none of them include enough detailed geometric data to be properly reproduced and so cannot be considered for academic research and validation purposes. As a consequence, design improvements of such configurations are difficult. Moreover, it seems that well-developed analyses of radial turbines are used in commercial software but are not available in the open literature especially at high pressure ratios. It is the purpose of this paper to provide a fully open set of data to reproduce the exact geometry of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multipurpose Small Power Unit. First, preliminary one-dimensional meanline design and analysis are performed using the commercial software RITAL from Concepts-NREC in order to establish a complete reference test case available for turbomachinery code validation. The proposed design of the existing turbine is then carefully and successfully checked against the geometrical and experimental data partially published in the literature. Then, three-dimensional Reynolds-Averaged Navier-Stokes simulations are conducted by means of the Axcent-PushButton CFDR CFD software. The effect of the tip clearance gap is investigated in detail for a wide range of operating conditions. The results confirm that the 3D geometry is correctly reproduced. It also reveals that the turbine is shocked while designed to give a high-subsonic flow and highlight the importance of the diffuser.

Computational fluid dynamics simulation and turbomachinery code validation of a high pressure ratio radial-inflow turbine

The present study explores reproducing the closest geometry of a high pressure ratio single stage radial-inflow turbine applied in the Sundstrans Power Systems T-100 Multipurpose Small Power Unit. The commercial software ANSYS-Vista RTD along with a built in module, BladeGen, is used to conduct a meanline design and create 3D geometry of one flow passage. Carefully examining the proposed design against the geometrical and experimental data, ANSYS-TurboGrid is applied to generate computational mesh. CFD simulations are performed with ANSYS-CFX in which three-dimensional Reynolds-Averaged Navier-Stokes equations are solved subject to appropriate boundary conditions. Results are compared with numerical and experimental data published in the literature in order to generate the exact geometry of the existing turbine and validate the numerical results against the experimental ones.

Long-term experiments with an adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In this work, we introduce a method to update the reference views in a hybrid metrictopological map so that a mobile robot can continue to localize itself in a changing environment. The updating mechanism, based on the multi-store model of human memory, incorporates a spherical metric representation of the observed visual features for each node in the map, which enables the robot to estimate its heading and navigate using multi-view geometry, as well as representing the local 3D geometry of the environment. A series of experiments demonstrate the persistence performance of the proposed system in real changing environments, including analysis of the long-term stability.

Hydrostratigraphic analysis of the MADE site with full-resolution GPR and direct-push hydraulic profiling

Full-resolution 3D Ground-Penetrating Radar (GPR) data were combined with high-resolution hydraulic conductivity (K) data from vertical Direct-Push (DP) profiles to characterize a portion of the highly heterogeneous MAcro Dispersion Experiment (MADE) site. This is an important first step to better understand the influence of aquifer heterogeneities on observed anomalous transport. Statistical evaluation of DP data indicates non-normal distributions that have much higher similarity within each GPR facies than between facies. The analysis of GPR and DP data provides high-resolution estimates of the 3D geometry of hydrostratigraphic zones, which can then be populated with stochastic K fields. The lack of such estimates has been a significant limitation for testing and parameterizing a range of novel transport theories at sites where the traditional advection-dispersion model has proven inadequate.

On Using Projective Relations for Calibration and Estimation in a Structured-Light Scanner

For structured-light scanners, the projective geometry between a projector-camera pair is identical to that of a camera-camera pair. Consequently, in conjunction with calibration, a variety of geometric relations are available for three-dimensional Euclidean reconstruction. In this paper, we use projector-camera epipolar properties and the projective invariance of the cross-ratio to solve for 3D geometry. A key contribution of our approach is the use of homographies induced by reference planes, along with a calibrated camera, resulting in a simple parametric representation for projector and system calibration. Compared to existing solutions that require an elaborate calibration process, our method is simple while ensuring geometric consistency. Our formulation using the invariance of the cross-ratio is also extensible to multiple estimates of 3D geometry that can be analysed in a statistical sense. The performance of our system is demonstrated on some cultural artifacts and geometric surfaces.