Geometric Ambiguities Research Articles

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. We describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

Res-NeuS: Deep Residuals and Neural Implicit Surface Learning for Multi-View Reconstruction

Surface reconstruction using neural networks has proven effective in reconstructing dense 3D surfaces through image-based neural rendering. Nevertheless, current methods are challenging when dealing with the intricate details of large-scale scenes. The high-fidelity reconstruction performance of neural rendering is constrained by the view sparsity and structural complexity of such scenes. In this paper, we present Res-NeuS, a method combining ResNet-50 and neural surface rendering for dense 3D reconstruction. Specifically, we present appearance embeddings: ResNet-50 is used to extract the appearance depth features of an image to further capture more scene details. We interpolate points near the surface and optimize their weights for the accurate localization of 3D surfaces. We introduce photometric consistency and geometric constraints to optimize 3D surfaces and eliminate geometric ambiguity existing in current methods. Finally, we design a 3D geometry automatic sampling to filter out uninteresting areas and reconstruct complex surface details in a coarse-to-fine manner. Comprehensive experiments demonstrate Res-NeuS’s superior capability in the reconstruction of 3D surfaces in complex, large-scale scenes, and the harmful distance of the reconstructed 3D model is 0.4 times that of general neural rendering 3D reconstruction methods and 0.6 times that of traditional 3D reconstruction methods.

Modelling and inferring fracture curvature from borehole GPR data: A case study from the Bedretto Laboratory, Switzerland

AbstractFracture curvature has been observed from the millimetre to the kilometre scales. Nevertheless, characterizing curvature remains challenging due to data sparsity and geometric ambiguities. As a result, most numerical models often assume planar fractures to ease computations. To address this limitation, we present a novel approach for inferring fracture geometry from travel‐time data of electromagnetic or seismic waves. Our model utilizes co‐kriging interpolation of control points in a three‐dimensional surface mesh to simulate fracture curvature effectively, resulting in an unstructured triangular grid. We then refine the fracture surface into a structured grid with equidistant elements so that both small‐scale heterogeneities and large‐scale curvature can be modelled. To constrain the fracture geometry, we perform a deterministic travel‐time inversion to optimally place these control points. We validate our methodology with synthetic data and address its limitations. Finally, we infer the geometry of a large (more than 200 m) fracture observed in single‐hole ground‐penetrating radar field data. The fracture surface closely agrees with borehole televiewer observations and is also constrained far from the boreholes. Our modelling approach can be trivially adapted to multi‐offset ground‐penetrating radar or active seismic data.

New approach to unimodular relativity

A thorough study and analysis on the conceptual foundations of unimodular gravity shows that this theory is essentially general relativity disguised as unimodular relativity in the literature. The main reason for this dilemma is accepting the Einsteinian paradigm: general relativistic framework, covariant divergence law for matter energy-momentum tensor, and cosmological constant as an integration constant, but introducing the artefact of unimodular description absent in Einstein’s work. A new approach is proposed in this paper in which pure unimodular relativity is defined in terms of equi-projective geodesics with the fundamental metric tensor having determinant unity and the geometric tensors constructed from them. Modification of covariant divergence law for the matter energy-momentum tensor is shown to have two new consequences. In the conventional unimodular gravity an effective cosmological term comprising of two variable scalar fields, namely, the unimodular geometric ambiguity and unimodular matter energy ambiguity, is proposed. A radical departure on the cosmological constant problem is possible assuming differing evolution of the two scalars: the Einstein equations emerge when the two ambiguities cancel each other. Secondly, in the case of pure unimodular relativity the gravitational field equations are proposed consistent with the unimodular space-time structure.

Semantic-guided 3D building reconstruction from triangle meshes

Planar primitives tend to be incorrectly detected or incomplete in complex scenes where adhesions exist between different objects, resulting in topology errors in the reconstructed models. We propose a semantic-guided building reconstruction method known as semantic-guided reconstruction (SGR), which is capable of achieving the independence and integrity of building models in two key stages. In the first stage, the space partition is represented by a 2.5D convex cell complex and is capable of restoring planar primitives that are easily lost and can further infer the potential structural adaptivity. The second stage incorporates semantic information into a graph-cut formulation that can assist in the independent reconstruction of buildings while eliminating interference from the surrounding environment. Our experimental results confirmed that the SGR method can authentically reconstruct weakly observed surfaces. Furthermore, qualitative and quantitative evaluations show that SGR is suitable for reconstructing surfaces from insufficient data with semantic and geometric ambiguity or semantic errors and can obtain watertight models considering fidelity, integrity and time complexity.

Muon trigger with fast Neural Networks on FPGA, a demonstrator

The online reconstruction of muon tracks in High Energy Physics experiments is a highly demanding task, typically performed on reconfigurable digital circuits, such as FPGAs. Complex analytical algorithms are executed in a quasi-real-time environment to identify, select, and reconstruct local tracks in often noise-rich environments. A novel approach to the generation of local triggers based on a hybrid combination of Artificial Neural Networks and analytical methods is proposed, targeting the muon reconstruction for drift tube detectors. The proposed algorithm exploits Neural Networks to solve otherwise computationally expensive analytical tasks for the unique identification of coherent signals and the removal of geometrical ambiguities. The proposed approach is deployed on state-of-the-art FPGA and its performances are evaluated on simulation and on data collected from cosmic rays.

Enhancement of human 3D pose estimation using a novel concept of depth prediction with pose alignment from a single 2D image

2D poses are insufficient to estimate human activities under the geometric ambiguities, occlusion, diverse appearance, and viewpoints inside the image. As a result, 3D posing has emerged as an attractive research area in recent decades due to its ability to distinguish human activities effectively. Human skeletal 3D posture is the foundation for 3D avatar creation, the construction of human 3D meshes, recognition of human actions or activities, augmented reality, etc. Therefore, estimating the correct human 3D skeleton or pose with minimum errors is an essential task. This research paper proposes a depth predictor module; an innovative and creative approach of depth prediction for evaluating the human 3D pose from a single 2D image. However, no predicted 3D pose is entirely free from errors. Therefore, it needs to reduce the inaccuracy after predicting the 3D pose. For this purpose, an enhancement approach, pose alignment, is used to reduce the positioning inaccuracies of the anticipated 3D pose. The specialty of the proposed model is that it does not require any training dataset, and it effectively estimates 3D poses under any scale variations. This proposed method is evaluated on different datasets: Human3.6M, HumanEva-I, NTU RGB + D, MPII, UAV-human and the Articulated Free Fall dataset. In terms of errors, the proposed approach achieves the minimum 3D pose error compared to the existing 3D pose estimation techniques. The proposed depth prediction approach reduces the average MPJPE value to 48.30, and the pose alignment module further reduces it to 40.61. In addition, the proposed model takes an inference time of 1.806 s per frame for a single person.

DTM extraction from DSM using a multi-scale DTM fusion strategy based on deep learning

Extraction of digital terrain model (DTM) from Digital Surface Model (DSM) still faces many problems in a complex scene with geometric ambiguities such as steep slope forested environments and contiguous non-ground regions. In this paper, an approach based on deep learning is proposed to generate DTM directly from DSM without applying filtering methods for eliminating non-ground pixels. In this regard, first, in the preprocessing step, the data is prepared for entering into the proposed deep network. Then, a hybrid deep convolutional neural network (HDCNN) is proposed which is a combination of the U-net architecture and residual networks. In this network, effective features are generate4d in different scales during the downsampling process from the input DSM and the DTM is extracted during the upsampling process. To rectify the results, a multi-scale fusion strategy is proposed to produce the final DTM by fusing the generated DTMs at different scales and with different spatial shifts. The performance of the proposed approach is analyzed by implementing four different evaluation scenarios in five different datasets. The evaluation results demonstrated significant performance and high generalizability of the proposed approach. The proposed network also outperforms the deep learning-based filtering methods and two reference DTM extraction algorithms especially in challenging regions.

MULTILATERATION UNDER FLIP AMBIGUITY FOR UAV POSITIONING USING ULTRAWIDE-BAND

Abstract. Ultrawide-band (UWB) ranging technology and multilateration techniques have recently been emerging solutions for positioning unmanned aerial vehicles (UAVs) in GNSS-denied environments. This solution offers cm-level ranging accuracy and considerable robustness to multipath receptions. UWB modules are commonly used in an anchor-based configuration; i.e., one UWB tag is mounted on the UAV, and several UWB anchors are installed on the ground. In real-world operational conditions, anchors can form a planar or a near-planar surface. This causes a geometric ambiguity, called flip ambiguity, in position estimation. Flip ambiguity can lead to considerable errors in the estimated position by multilateration. In this paper, we present a multilateration approach, which automatically resolves the flip ambiguity for UAV-positioning using UWB ranging. The proposed multilateration method first computes an algebraic solution through recursive least squares. If the initially estimated position is found to be flipped, then it is corrected by a symmetric reflection with respect to the anchor plane. Finally, the estimated position is refined by non-linear optimization. Extensive experiments in a real environment show that the proposed algorithm can effectively tackle the issue of flip ambiguity in multilateration, leading to a significant improvement in positioning accuracy.

3D Human Pose Machines with Self-Supervised Learning.

Driven by recent computer vision and robotic applications, recovering 3D human poses has become increasingly important and attracted growing interests. In fact, completing this task is quite challenging due to the diverse appearances, viewpoints, occlusions and inherently geometric ambiguities inside monocular images. Most of the existing methods focus on designing some elaborate priors /constraints to directly regress 3D human poses based on the corresponding 2D human pose-aware features or 2D pose predictions. However, due to the insufficient 3D pose data for training and the domain gap between 2D space and 3D space, these methods have limited scalabilities for all practical scenarios (e.g., outdoor scene). Attempt to address this issue, this paper proposes a simple yet effective self-supervised correction mechanism to learn all intrinsic structures of human poses from abundant images. Specifically, the proposed mechanism involves two dual learning tasks, i.e., the 2D-to-3D pose transformation and 3D-to-2D pose projection, to serve as a bridge between 3D and 2D human poses in a type of "free" self-supervision for accurate 3D human pose estimation. The 2D-to-3D pose implies to sequentially regress intermediate 3D poses by transforming the pose representation from the 2D domain to the 3D domain under the sequence-dependent temporal context, while the 3D-to-2D pose projection contributes to refining the intermediate 3D poses by maintaining geometric consistency between the 2D projections of 3D poses and the estimated 2D poses. Therefore, these two dual learning tasks enable our model to adaptively learn from 3D human pose data and external large-scale 2D human pose data. We further apply our self-supervised correction mechanism to develop a 3D human pose machine, which jointly integrates the 2D spatial relationship, temporal smoothness of predictions and 3D geometric knowledge. Extensive evaluations on the Human3.6M and HumanEva-I benchmarks demonstrate the superior performance and efficiency of our framework over all the compared competing methods.

A deep learning approach to DTM extraction from imagery using rule-based training labels

Existing algorithms for Digital Terrain Model (DTM) extraction still face difficulties due to data outliers and geometric ambiguities in the scene such as contiguous off-ground areas or sloped environments. We postulate that in such challenging cases, the radiometric information contained in aerial imagery may be leveraged to distinguish between ground and off-ground objects. We propose a method for DTM extraction from imagery which first applies morphological filters to the Digital Surface Model to obtain candidate ground and off-ground training samples. These samples are used to train a Fully Convolutional Network (FCN) in the second step, which can then be used to identify ground samples for the entire dataset. The proposed method harnesses the power of state-of-the-art deep learning methods, while showing how they can be adapted to the application of DTM extraction by (i) automatically selecting and labelling dataset-specific samples which can be used to train the network, and (ii) adapting the network architecture to consider a larger surface area without unnecessarily increasing the computational burden. The method is successfully tested on four datasets, indicating that the automatic labelling strategy can achieve an accuracy which is comparable to the use of manually labelled training samples. Furthermore, we demonstrate that the proposed method outperforms two reference DTM extraction algorithms in challenging areas.

Lattice-Support repetitive local feature detection for visual search

Repetitive patterns such as building facades, floor tiles, vegetation, and wallpapers are commonly found in sceneries and images. The presence of such repetitive patterns in images often leads to visual burstiness and geometric ambiguity, which poses challenge for state-of-the-art visual search technologies. To alleviate these problems, we propose a new lattice-support repetitive local feature detection method to detect repetitive patterns, estimate the underlying lattice structure, and enhance descriptors used for subsequent visual image search. Existing methods for repetitive pattern detection are commonly based on determining the underlying lattice structures. However, these structures do not correspond directly to robust features that are scale- and rotation-invariant. This paper proposes a new lattice-support repetitive local feature (LS-RLF) detection method that aims to integrate lattice information into repeated local feature detection and extraction. The advantage of the proposed method is that the detected features can be directly used by current visual search technologies. The LS-RLF method estimates the undetected repeated features in the lattice structure using Hough transform-based feature estimation. Further, in order to handle the visual burstiness issue, a new LS-RLF based image retrieval framework is developed. Experiments performed on benchmark datasets show that the proposed method outperforms the state-of-the-art methods by mean Average Precisions (mAP) of 4.5%, 5.5% and 3.2% on Oxford, Paris, and INRIA holidays datasets respectively. This demonstrates the effectiveness of the proposed method in performing visual search for images which contain wide range of repeated patterns.

Environmental Geometry Aligns the Hippocampal Map during Spatial Reorientation

When a navigator's internal sense of direction is disrupted, she must rely on external cues to regain her bearings, a process termed spatial reorientation. Extensive research has demonstrated that the geometric shape of the environment exerts powerful control over reorientation behavior, but the neural and cognitive mechanisms underlying this phenomenon are not well understood. Whereas some theories claim that geometry controls behavior through an allocentric mechanism potentially tied to the hippocampus, others postulate that disoriented navigators reach their goals by using an egocentric view-matching strategy. To resolve this debate, we characterized hippocampal representations during reorientation. We first recorded from CA1 cells as disoriented mice foraged in chambers of various shapes. We found that the alignment of the recovered hippocampal map was determined by the geometry of the chamber, but not by nongeometric cues, even when these cues could be used to disambiguate geometric ambiguities. We then recorded hippocampal activity as disoriented mice performed a classical goal-directed spatial memory task in a rectangular chamber. Again, we found that the recovered hippocampal map aligned solely to the chamber geometry. Critically, we also found a strong correspondence between the hippocampal map alignment and the animal's behavior, making it possible to predict the search location of the animal from neural responses on a trial-by-trial basis. Together, these results demonstrate that spatial reorientation involves the alignment of the hippocampal map to local geometry. We hypothesize that geometry may be an especially salient cue for reorientation because it is an inherently stable aspect of the environment.

A table of geometrical ambiguities in powder indexing obtained by exhaustive search.

Geometrical ambiguity means the cases in which more than one powder indexing solution exists. Using a new function implemented in the powder indexing software CONOGRAPH, unit cells that involve geometrical ambiguity are exhaustively searched. As a result, many unknown cases are obtained, although the number of such unit cells is still rather limited. It is also proven that the number of solutions in powder auto-indexing is not always unique, but generally finite.

Method to generate all the geometrical ambiguities of powder indexing solutions

A new algorithm is reported that returns all the lattices with the same set ofdspacings as that of a given lattice. The algorithm is useful for quickly checking lattice parameters obtained for a considered powder diffraction pattern and assessing the reliability of the results of powder indexing. The proposed algorithm was implemented as a new function in the powder indexing softwareConograph(http://sourceforge.jp/projects/conograph/; http://research.kek.jp/people/rtomi/ConographGUI/web_page.html). Examples of real cases are reported to explain how the algorithm can be used.

A method to obtain all geometric ambiguities in powder indexing

It is known that different unit cells can have the same computed lines in some cases (Figure). The phenomenon was first called geometrical ambiguity and studied in [1]. In all the high-symmetric cases provided in [1], such unit cells correspond to derivative lattices of each other. Although this is not true in general for 3-dimensional lattices, this has been assumed in methods to search for geometrical ambiguities (e.g., [2]). Thus, a method to obtain all the geometrical ambiguities in very short time for a given unit cell parameters is provided. Because such a method has not been used for powder indexing, it will have impact in the following sense: firstly, it is useful for checking powder indexing solutions promptly. Some powder auto-indexing methods cannot obtain all the geometrical ambiguities. Even for the software including Conograph which can gain all the ambiguities, it is not straightforward to search for them from many indexing solutions using the figures of merit which are sometimes not reliable [3]. Secondly, the new method indicates that powder indexing has only finitely many solutions at least if peak search succeeds in obtaining all (but a few) diffraction peaks with q-values smaller than some calculated value. (Note that infinitely many solutions may exist for lattices of dimension more than 4.) The result seems to provide a foundation of automatic powder crystal structure analysis, because it is possible to obtain all the ambiguities by computation. The introduced method was implemented in the newest version of Conograph, which will be distributed on the web (http://research.kek.jp/people/rtomi/ConographGUI/web_page.html) by IUCr2014. ACKNOWLEDGEMENT: this research was partly supported by a JSPS KAKENHI grant (No.22740077) and by Ibaraki Prefecture (J-PARC-23D06).

Water-tight membranes from neuronal morphology files

We present an algorithm to form watertight 3D surfaces consistent with the point-and-diameter based neuronal morphology descriptions widely used with spatial electrophysiology simulators. Such morphology descriptions are readily available online and may come from light-microscopy tracings or from an artificial cell grown algorithmically. These files contain only limited information about a neuron's full three-dimensional shape, as they consist mostly of a list of points and diameters with connectivity data. This representation is well-suited for electrophysiology simulations, where the space constants are larger than geometric ambiguities. However, the simple interpretations used for pure electrophysiological simulation produce geometries unsuitable for multi-scale models that also involve three-dimensional reaction–diffusion, as such models have smaller space constants. Although one cannot exactly reproduce an original neuron's full shape from point-and-diameter data, our new constructive tessellated neuronal geometry (CTNG) algorithm uses constructive solid geometry to define a plausible reconstruction without gaps or cul-de-sacs. CTNG then uses “constructive cubes” to produce a watertight triangular mesh of the neuron surface, suitable for use in reaction–diffusion simulations. CTNG provides the correspondence between internal voxels and surface triangles, needed to make connections between cytoplasmic and membrane mechanisms. Optimization of the underlying marching cubes algorithm and distance calculations enhanced the performance of constructive cubes for a neuronal geometry, where a large number of small objects sparsely occupy a large volume.

A constrained genetic algorithm for line labelling of line drawings with shadows and table-lines

Line drawings are well known to exhibit geometric ambiguities, resulting in, drawings that can have multiple interpretations. However, drawings are used to present design concepts to peers in fields such as engineering design, where it is imperative that the observer interprets the drawing in the same way as the designer for effective communication. Designers therefore use cues, prompting the observer to resolve the geometric ambiguities and achieve the desired interpretation. In this paper, we identify the cues introduced in drawings and focus on two cues, namely table-lines (which convey information about the position of the object in space) and shadows (which convey information about the geometry of the object). These cues can be used in a line-labelling context to allow a line-labelling algorithm to overcome the geometric ambiguities of the drawing. For this purpose, we propose a cue-constrained genetic algorithm that takes the vectorized line drawing and the identified cues attached to each edge, and uses these cues as constraints on the edge labels, thus distinguishing between different object-background interactions. We show that the proposed algorithm can be used to successfully label intentionally ambiguous line drawings according to some desired interpretation as specified by the additional cues present in the drawing.

RANSAC-based Or thogonal Vanishing Point Estimation in the Equirectangular Images

In this paper, we present an algorithm that quickly and effectively estimates orthogonal vanishing points in equirectangular images of urban environment. Our algorithm is based on the RANSAC (RANdom Sample Consensus) algorithm and on the characteristics of the line segment in the spherical panorama image of the 360˚ longitude and 180˚ latitude field of view. These characteristics can be used to reduce the geometric ambiguity in the line segment classification as well as to improve the robustness of vanishing point estimation. The proposed algorithm is validated experimentally on a wide set of images. The results show that our algorithm provides excellent levels of accuracy for the vanishing point estimation as well as line segment classification.

An Onboard Monocular Vision System for Autonomous Takeoff, Hovering and Landing of a Micro Aerial Vehicle

In this paper, we present an onboard monocular vision system for autonomous takeoff, hovering and landing of a Micro Aerial Vehicle (MAV). Since pose information with metric scale is critical for autonomous flight of a MAV, we present a novel solution to six degrees of freedom (DOF) pose estimation. It is based on a single image of a typical landing pad which consists of the letter H surrounded by a circle. A vision algorithm for robust and real-time landing pad recognition is implemented. Then the 5 DOF pose is estimated from the elliptic projection of the circle by using projective geometry. The remaining geometric ambiguity is resolved by incorporating the gravity vector estimated by the inertial measurement unit (IMU). The last degree of freedom pose, yaw angle of the MAV, is estimated from the ellipse fitted from the letter H. The efficiency of the presented vision system is demonstrated comprehensively by comparing it to ground truth data provided by a tracking system and by using its pose estimates as control inputs to autonomous flights of a quadrotor.