Geometric Primitives Research Articles

Dexterous Manipulation Based on Object Recognition and Accurate Pose Estimation Using RGB-D Data.

This study presents an integrated system for object recognition, six-degrees-of-freedom pose estimation, and dexterous manipulation using a JACO robotic arm with an Intel RealSense D435 camera. This system is designed to automate the manipulation of industrial valves by capturing point clouds (PCs) from multiple perspectives to improve the accuracy of pose estimation. The object recognition module includes scene segmentation, geometric primitives recognition, model recognition, and a color-based clustering and integration approach enhanced by a dynamic cluster merging algorithm. Pose estimation is achieved using the random sample consensus algorithm, which predicts position and orientation. The system was tested within a 60° field of view, which extended in all directions in front of the object. The experimental results show that the system performs reliably within acceptable error thresholds for both position and orientation when the objects are within a ±15° range of the camera's direct view. However, errors increased with more extreme object orientations and distances, particularly when estimating the orientation of ball valves. A zone-based dexterous manipulation strategy was developed to overcome these challenges, where the system adjusts the camera position for optimal conditions. This approach mitigates larger errors in difficult scenarios, enhancing overall system reliability. The key contributions of this research include a novel method for improving object recognition and pose estimation, a technique for increasing the accuracy of pose estimation, and the development of a robot motion model for dexterous manipulation in industrial settings.

Neural radiance fields as a complementary method to photogrammetry for forensic 3D documentation: Initial comparative insights

ObjectivesPhotogrammetry is widely used in forensic practice to create 3D models of crime scenes, bodies, living individuals, and objects. However, it has limitations in accurately capturing transparent, reflective, and low-texture surfaces, which can hinder forensic investigations. Neural Radiance Fields (NeRFs), a recently developed method, offer a potential solution by creating more accurate and detailed 3D models in these challenging contexts. This study aims to evaluate whether NeRFs can serve as effective alternatives to structure-from-motion (SfM) photogrammetry for recording forensic autopsies. Materials and MethodsPhotogrammetric scans were performed on a variety of forensic subjects, including a cadaver with skin discoloration and epidermal exfoliation, a metal trashcan, a vehicle, and a mock crime scene. The scans were processed using traditional photogrammetry software (Meshroom) and compared with NeRF-based visualizations generate using instant neural graphics primitives. ResultsNeRF-based models provided more lifelike and detailed visualizations than photogrammetry, particularly when documenting transparent, reflective, or featureless surfaces. NeRF demonstrated superior capability in capturing complex details that photogrammetry struggled with. ConclusionNeRF technology shows considerable promise for improving the documentation of forensic autopsies, offering enhanced visual fidelity for challenging surfaces such as transparent or reflective materials. While the method presents challenges related to editing, software compatibility, and high computational demands, its potential benefits in forensic investigations are evident and merit further exploration.

A geometry projection method for designing and optimizing additively manufactured variable-stiffness composite laminates

A method for designing laminates is presented using geometry projection to optimize the layout of additively manufactured variable-stiffness composite laminates. By considering fiberreinforced bars as geometric primitives, the geometry projection methodology is extended to include optimizing regions with intersecting load paths. This is achieved by utilizing a dual representation of bars, which considers the geometric parameters and the element-wise density field representation. The dual representation enables the combining and overlapping of bars, resulting in a localized orthotropic material response at overlapping regions that mitigates the transverse compliant response of fiberreinforced components. The proposed method’s effectiveness is demonstrated through minimizing the compliance of the Messerschmitt-Bölkow-Blohm beam problem, a well-known benchmark problem in topology optimization.

Investigation of compressive strength of primitive geometries printed through the fused deposition modeling technique with different path patterns

Fused Deposition Modeling (FDM) is a material-extrusion-based technique used primarily for rapid prototyping and sometimes for an actual servicing part. In the FDM technique, input parent materials are commercial polymers. FDM also has some manufacturing parameters, and the raster pattern significantly affects the mechanical performance of the FDM products. Due to its intrinsic nature, Acrylonitrile Butadiene Styrene (ABS) is widely used in many industries, such as automobiles, medicine, etc. Producing the primitive geometry and selecting the proper infill pattern is challenging. Therefore, the current research paper investigates the effects of various infill patterns on the compressive performance of the three geometries (sphere, 3-side, and 4-side pyramids) printed through the FDM technique out of ABS material. The compressive experiments were conducted on the printed samples and load-displacement curves were evaluated. The results reveal that the concentrate path pattern in the sphere samples has the highest compressive failure load (40127 N). Also, the compressive failure loads in the 3-side and 4-side pyramids fabricated with a 45°/−45° raster pattern are 30444 N and 44396 N, respectively. Finally, comprehensive discussions about the obtained results are stated.

Extraction of complex pipeline features from incomplete point clouds

Abstract Control point detection in industrial pipelines, characterized by flanges
and multiple passes, is critical for accurate virtual simulations and quality assessments
in manufacturing. This paper introduces an innovative method for detecting control
points in complex pipelines using incomplete point clouds, significantly streamlining
the process. Our approach uniquely requires only straight sections and end-plane
localizations as inputs, markedly reducing both data acquisition and processing times.
We develop a robust feature descriptor to align the CAD model with incomplete
point clouds, facilitating semantic automatic segmentation despite the lack of explicit
semantic information. Following this, geometric primitives are fitted to the segmented
clouds, and a cylindrical fitting algorithm tailored for incomplete data is introduced.
The control points are computed based on the relative positions and geometric
parameters of these primitives. Our method has been validated through experiments
on several real-world industrial complex pipelines. The results confirm that our
approach achieves a high measurement accuracy of 0.067 mm, even with point cloud
incompleteness of up to 50%. These findings highlight the effectiveness of our method in
accurately determining the geometric parameters of complex pipelines and suggesting its
considerable potential for practical applications.

Discretisation of the Hough parameter space for fitting and recognising geometric primitives in 3D point clouds

Research in recognising and fitting simple geometric shapes has been ongoing since the 1970s, with various approaches proposed, including stochastic methods, parameter methods, primitive-based registration techniques, and more recently, deep learning. The Hough transform is a method of interest due to its demonstrated robustness to noise and outliers, ability to handle missing data, and support for multiple model instances. Unfortunately, one of the main limitations of the Hough transform is how to properly discretise its parameter space, as increasing their number or decreasing the sampling frequency can make it computationally expensive.The relationship between the approximation accuracy and the parameter space’s discretisation is investigated to address this. We present two distinct discretisations to illustrate how the fitting and recognition quality can be improved by selecting an appropriate parameter discretisation. Our parameter-driven space discretisation is shown to significantly improve the parameter recognition quality over the classical method and reduce computational time and space by decreasing the discretisation’s dimension, as demonstrated by an extensive validation on a benchmark of geometric primitives. Preliminary experiments are also presented on segmenting datasets from urban buildings and CAD objects.

A case study of preliminary damage detection of two heritage vaults through geometric deformation analysis on 3D point clouds

Masonry vaults are common structural elements in heritage buildings that, given their long lifespan, are susceptible to the accumulation of damages and deformations from diverse actions such as overloads, support movements, seismic action, etc. The use of 3D point clouds from terrestrial laser scanners and structure from motion photogrammetry survey to investigate these deformations can offer valuable information for structural assessment and conservation, particularly when historical information is limited. The analysis of the deviation measured between the surveyed as-built point cloud of a vault and a reference geometry could reveal deformation patterns. Those, compared with recurring damage mechanisms discussed in literature, can provide a preliminary identification of the damage mechanisms affecting a structure, and the evaluation guide the recognition of the underlying action. The aim of this paper is to investigate how to generate different reference geometries and the impacts of their choice as reference geometry for the identification and quantification of different deformations. Deviation analyses were performed on the main vaults of two different churches with different reference geometries (i.e., geometries derived from the survey and geometrical primitives fitted on point-cloud), and the results were discussed by comparing the deviation maps obtained with the crack pattern and the already known deformations of the buildings.

The shading isophotes: Model and methods for Lambertian planes and a point light

Structure-from-Motion (SfM) and Shape-from-Shading (SfS) are complementary classical approaches to 3D vision. Broadly speaking, SfM exploits geometric primitives from textured surfaces and SfS exploits pixel intensity from the shading image. We propose an approach that exploits virtual geometric primitives extracted from the shading image, namely the level-sets, which we name shading isophotes. Our approach thus combines the strength of geometric reasoning with the rich shading information. We focus on the case of untextured Lambertian planes of unknown albedo lit by an unknown Point Light Source (PLS) of unknown intensity. We derive a comprehensive geometric model showing that the unknown scene parameters are in general all recoverable from a single image of at least two planes. We propose computational methods to detect the isophotes, to reconstruct the scene parameters in closed-form and to refine the results densely using pixel intensity. Our methods thus estimate light source, plane pose and camera pose parameters for untextured planes, which cannot be achieved by the existing approaches. We evaluate our model and methods on synthetic and real images.

A Hierarchical Neural Network for Point Cloud Segmentation and Geometric Primitive Fitting.

Automated generation of geometric models from point cloud data holds significant importance in the field of computer vision and has expansive applications, such as shape modeling and object recognition. However, prevalent methods exhibit accuracy issues. In this study, we introduce a novel hierarchical neural network that utilizes recursive PointConv operations on nested subdivisions of point sets. This network effectively extracts features, segments point clouds, and accurately identifies and computes parameters of regular geometric primitives with notable resilience to noise. On fine-grained primitive detection, our approach outperforms Supervised Primitive Fitting Network (SPFN) by 18.5% and Cascaded Primitive Fitting Network (CPFN) by 11.2%. Additionally, our approach consistently maintains low absolute errors in parameter prediction across varying noise levels in the point cloud data. Our experiments validate the robustness of our proposed method and establish its superiority relative to other methodologies in the extant literature.

Hybrid Resonant Metasurfaces with Configurable Structural Colors

AbstractMetasurfaces are sub‐wavelength nanostructures with the potential to overcome the limitations of traditional optics. Existing dielectric metasurfaces, however, are often limited to geometric primitives, which hamper their application in emergent hybrid metasurfaces. Here, a simple fabrication scheme for non‐primitive metasurfaces that addresses this limitation is introduced. Due to their broken out‐of‐plane symmetry, these nanostructures provide a new dimension in the design space. Taking inspiration from bio‐photonic systems in nature, using these elements complex hybrid metasurfaces are designed that encompass an ordered and a disordered phase. The capabilities of this hybrid optical systems are illustrated by generating configurable structural colors with extra ordinary resolution. Furthermore, the local control of light over a broad bandwidth is demonstrated and a maximum coupling efficiency of more than 97% is achieved.

Regiomontanus angle maximization for catadioptric sensors with paraboloidal mirrors

Dioptric cameras with conventional perspective projection have well established analytical properties. However, they suffer from perspective distortions and only have a limited field of view. Catadioptric cameras offer panoramic imaging. Their extensive field of view together with projection specific image analysis, can simplify many computer vision tasks. Several properties of catadioptric projection for geometric primitives such as points and lines have been addressed and have also been used for calibration. However, higher order geometric properties are yet to be investigated. Such analysis is complicated by the specifics of the warping of the scene by catadioptric projection. One such property, that is the subject of this work, is the Regiomontanus angle maximization relative to the effective viewpoint of the sensor. This work considers catadioptric sensors with paraboloidal mirrors, that is, paracatadioptric sensors. Analytical ray tracing of a simplified 1D world object gives its projection in the image and an expression for its length. The optimization of the length of the projection results in a third degree equation for the Regiomontanus distance that can be solved explicitly. The Khayyam geometric solution of this equation provides the Regiomontanus distance of maximum subtended projection for these cameras. Applications of these results in various contexts are presented and discussed.

Origami single-end capacitive sensing for continuous shape estimation of morphing structures

In this work, we propose a novel single-end morphing capacitive sensing method for shape tracking, FxC, by combining Folding origami structures and Capacitive sensing to detect the morphing structural motions using state-of-the-art sensing circuits and deep learning. It was observed through embedding areas of origami structures with conductive materials as single-end capacitive sensing patches, that the sensor signals change coherently with the motion of the structure. Different from other origami capacitors where the origami structures are used in adjusting the thickness of the dielectric layer of double-plate capacitors, FxC uses only a single conductive plate per channel, and the origami structure directly changes the geometry of the conductive plate. We examined the operation principle of morphing single-end capacitors through 3D geometry simulation combined with physics theoretical deduction, which deduced similar behavior as observed in experimentation. Then a software pipeline was developed to use the sensor signals to reconstruct the dynamic structural geometry through data-driven deep neural network regression of geometric primitives extracted from vision tracking. We created multiple folding patterns to validate our approach, based on folding patterns including Accordion, Chevron, Sunray and V-Fold patterns with different layouts of capacitive sensors using paper-based and textile-based materials. Experimentation results show that the geometry primitives predicted from the capacitive signals have a strong correlation with the visual ground truth with R-squared value of up to 95% and tracking error of 6.5 mm for patches. The simulation and machine learning constitute two-way information exchange between the sensing signals and structural geometry. By embedding part of the origami surface with morphing single-end capacitive sensors, FxC presents a unique solution that leverages both the mechanical properties of origami and sensing properties of capacitive sensing.

Variational Feature Extraction in Scientific Visualization

Across many scientific disciplines, the pursuit of even higher grid resolutions leads to a severe scalability problem in scientific computing. Feature extraction is a commonly chosen approach to reduce the amount of information from dense fields down to geometric primitives that further enable a quantitative analysis. Examples of common features are isolines, extremal lines, or vortex corelines. Due to the rising complexity of the observed phenomena, or in the event of discretization issues with the data, a straightforward application of textbook feature definitions is unfortunately insufficient. Thus, feature extraction from spatial data often requires substantial pre- or post-processing to either clean up the results or to include additional domain knowledge about the feature in question. Such a separate pre- or post-processing of features not only leads to suboptimal and incomparable solutions, it also results in many specialized feature extraction algorithms arising in the different application domains. In this paper, we establish a mathematical language that not only encompasses commonly used feature definitions, it also provides a set of regularizers that can be applied across the bounds of individual application domains. By using the language of variational calculus, we treat features as variational minimizers, which can be combined and regularized as needed. Our formulation not only encompasses existing feature definitions as special case, it also opens the path to novel feature definitions. This work lays the foundations for many new research directions regarding formal definitions, data representations, and numerical extraction algorithms.

3D reconstruction of building structures incorporating neural radiation fields and geometric constraints

Neural Radiance Fields (NeRF) techniques demonstrate potential for reconstructing complex architectural scenes in three dimensions. However, applying NeRF poses challenges, such as prolonged training processes and limited detailed characterization. To address these issues, this paper introduces NeRFusion by integrating Mipmapped Neural Radiance Fields (Mip-NeRF) and Instant Neural Graphics Primitives (iNGP). NeRFusion enhances training efficiency, rendering quality, and reduces jaggedness through multisampling, weight reduction, and loss function optimization. Geometric constraints—normal consistency, plane fitting, and vertical/horizontal constraints—improve 3D reconstruction accuracy. Using the Manhattan World Model (MWM), NeRFusion accurately extracts primary building components and dimensions. Experimental results show NeRFusion achieved a Peak Signal-to-Noise Ratio (PSNR) of 36.23 dB and completed training in 50 min. Structural Similarity Index Measure (SSIM) improved by 13.41% over Mip-NeRF and 50.00% over iNGP, with PSNR increasing by 10.45% and 25.10%. NeRFusion significantly reduces training time by a factor of 15 compared to the original NeRF.

Optimization‐based motion planning for autonomous agricultural vehicles turning in constrained headlands

AbstractHeadland maneuvering is a crucial part of the field operations performed by autonomous agricultural vehicles (AAVs). While motion planning for headland turning in open fields has been extensively studied and integrated into commercial autoguidance systems, the existing methods primarily address scenarios with ample headland space and thus may not work in more constrained headland geometries. Commercial orchards often contain narrow and irregularly shaped headlands, which may include static obstacles, rendering the task of planning a smooth and collision‐free turning trajectory difficult. To address this challenge, we propose an optimization‐based motion planning algorithm for headland turning under geometrical constraints imposed by headland geometry and obstacles. Our method models the headland and the AAV using convex polytopes as geometric primitives, and calculates optimal and collision‐free turning trajectories in two stages. In the first stage, a coarse path is generated using either a classical pattern‐based turning method or a directional graph‐guided hybrid A* algorithm, depending on the complexity of the headland geometry. The second stage refines this coarse path by feeding it into a numerical optimizer, which considers the vehicle's kinematic, control, and collision‐avoidance constraints to produce a feasible and smooth trajectory. We demonstrate the effectiveness of our algorithm by comparing it to the classical pattern‐based method in various types of headlands. The results show that our optimization‐based planner outperforms the classical planner in generating collision‐free turning trajectories inside constrained headland spaces. Additionally, the trajectories generated by our planner respect the kinematic and control limits of the vehicle and, hence, are easier for a path‐tracking controller to follow. In conclusion, our proposed approach successfully addresses complex motion planning problems in constrained headlands, making it a valuable contribution to the autonomous operation of AAVs, particularly in real‐world orchard environments.

MODELING THE DYNAMICS OF DEFORMABLE OBJECTS BASED ON VOLUMETRIC PATCHES OF FREE FORMS

A method for solving nonlinear implicit numerical integration problems based on volumetric patches of free forms for modeling deformable objects with high-speed dynamics is proposed. This method improves the accuracy, consistency and controllability of deformation modeling and animation. The method is characterized by speed, accuracy, stability and uses optimization with region decomposition. The method is well suited for modeling deformable bodies with a large time step, in a wide range of deformation dynamics. We propose decomposed optimization, an optimization method based on free-form patches with region decomposition to minimize incremental potentials at each time step. The method uses quadratic matrix decomposition to combine non-overlapping subregions. The Hessian is evaluated once at the beginning of the time step. The advantages of the method are as follows. Geometric primitives and their mathematical models are proposed, which allow the reasonable application of these primitives to solve problems of volume-oriented modeling. Such requirements are met by volumetric patches of free forms based on analytical perturbation functions relative to the base triangles. The decomposed Hessian is constructed for each subregion and calculated using a set of vertices taken from a complete non-decomposed grid. The weights add the missing second-order Hessian data to the vertices of the subregions from the neighbors along the decomposition boundaries. Thanks to this, the descent is performed along the grid coordinates. There is no need to add gradients. During the descent, the gradient is determined. The Hessians under the region are calculated and factorized in parallel once per time step. They are used as an initializer at each iteration. Then the results are mixed together. This ensures stable and continuous high-quality modeling. An automated and reliable optimization method adapted for modeling nonlinear materials, high-speed dynamics and large deformations is proposed.

Advancing Fine Branch Biomass Estimation with Lidar and Structural Models.

Lidar is a promising tool for fast and accurate measurements of trees. There are several approaches to estimate aboveground woody biomass using lidar point clouds. One of the most widely used methods involves fitting geometric primitives (e.g. cylinders) to the point cloud, thereby reconstructing both the geometry and topology of the tree. However, current algorithms are not suited for accurate estimation of the volume of finer branches, because of the unreliable point dispersions from e.g. beam footprint compared to the structure diameter. We propose a new method that couples point cloud-based skeletonization and multi-linear statistical modelling based on structural data to make a model (structural model) that accurately estimates the aboveground woody biomass of trees from high-quality lidar point clouds, including finer branches. The structural model was tested at segment, axis, and branch level, and compared to a cylinder fitting algorithm and to the pipe model theory. The model accurately predicted the biomass with 1.6% nRMSE at the segment scale from a k-fold cross-validation. It also gave satisfactory results when up-scaled to the branch level with a significantly lower error (13% nRMSE) and bias (-5%) compared to conventional cylinder fitting to the point cloud (nRMSE: 92%, bias: 82%), or using the pipe model theory (nRMSE: 31%, bias: -27%).The model was then applied to the whole-tree scale and showed that the sampled trees had more than 1.7km of structures on average and that 96% of that length was coming from the twigs (i.e. <5cm diameter). Our results showed that neglecting twigs can lead to a significant underestimation of tree aboveground woody biomass (-21%). The structural model approach is an effective method that allows a more accurate estimation of the volumes of smaller branches from lidar point clouds. This method is versatile but requires manual measurements on branches for calibration. Nevertheless, once the model is calibrated, it can provide unbiased and large-scale estimations of tree structure volumes, making it an excellent choice for accurate 3D reconstruction of trees and estimating standing biomass.

Interactive reverse engineering of CAD models

Reverse engineering Computer-Aided Design (CAD) models based on the original geometry is a valuable and challenging research problem that has numerous applications across various tasks. However, previous approaches have often relied on excessive manual interaction, leading to limitations in reconstruction speed. To mitigate this issue, in this study, we approach the reconstruction of a CAD model by sequentially constructing geometric primitives (such as vertices, edges, loops, and faces) and performing Boolean operations on the generated CAD modules. We address the complex reconstruction problem in four main steps. Firstly, we use a plane to cut the input mesh model and attain a loop cutting line, ensuring accurate normals. Secondly, the cutting line is automatically fitted to edges using primitive information and connected to form a primitive loop. This eliminates the need for time-consuming manual selection of each endpoint and significantly accelerates the reconstruction process. Subsequently, we construct the loop of primitives as a chunked CAD model through a series of CAD procedural operations, including extruding, lofting, revolving, and sweeping. Our approach incorporates an automatic height detection mechanism to minimize errors that may arise from manual designation of the extrusion height. Finally, by merging Boolean operations, these CAD models are assembled together to closely approximate the target geometry. We conduct a comprehensive evaluation of our algorithm using a diverse range of CAD models from both the Thingi10K dataset and real-world scans. The results validate that our method consistently delivers accurate, efficient, and robust reconstruction outcomes while minimizing the need for manual interactions. Furthermore, our approach demonstrates superior performance compared to competing methods, especially when applied to intricate geometries.

Lattice-Based Generation of Euclidean Geometry Figures

We present a user-guided method to generate geometry figures appropriate for high school Euclidean geometry courses: a useful starting point for an intelligent tutoring system to provide meaningful, realistic figures for study. We first establish that a two-dimensional geometry figure can be represented abstractly using a complete, lattice we call a geometry figure lattice (GFL). As input, we take a user-defined vector of primitive geometry shapes and convert each into a GFL. We then exhaustively combine each these ‘primitive’ GFLs into a set of complex GFLs using a process we call gluing. We mitigate redundancy in GFLs by introducing a polynomial-time algorithm for determining if two GFLs are isomorphic. These lattices act as a template for the second step: instantiating GFLs into a sequence of concrete geometry figures. To identify figures that are structurally similar to textbook problems, we use a discriminator model trained on a corpus of textbook geometry figures.

Robust tracking of deformable anatomical structures with severe occlusions using deformable geometrical primitives

Background and objective:Surgical robotics tends to develop cognitive control architectures to provide certain degree of autonomy to improve patient safety and surgery outcomes, while decreasing the required surgeons’ cognitive load dedicated to low level decisions. Cognition needs workspace perception, which is an essential step towards automatic decision-making and task planning capabilities. Robust and accurate detection and tracking in minimally invasive surgery suffers from limited visibility, occlusions, anatomy deformations and camera movements. Method:This paper develops a robust methodology to detect and track anatomical structures in real time to be used in automatic control of robotic systems and augmented reality. The work focuses on the experimental validation in highly challenging surgery: fetoscopic repair of Open Spina Bifida. The proposed method is based on two sequential steps: first, selection of relevant points (contour) using a Convolutional Neural Network and, second, reconstruction of the anatomical shape by means of deformable geometric primitives. Results:The methodology performance was validated with different scenarios. Synthetic scenario tests, designed for extreme validation conditions, demonstrate the safety margin offered by the methodology with respect to the nominal conditions during surgery. Real scenario experiments have demonstrated the validity of the method in terms of accuracy, robustness and computational efficiency. Conclusions:This paper presents a robust anatomical structure detection in present of abrupt camera movements, severe occlusions and deformations. Even though the paper focuses on a case study, Open Spina Bifida, the methodology is applicable in all anatomies which contours can be approximated by geometric primitives. The methodology is designed to provide effective inputs to cognitive robotic control and augmented reality systems that require accurate tracking of sensitive anatomies.