Multiple Geometric Constraints Research Articles

Binocular camera-based visual localization with optimized keypoint selection and multi-epipolar constraints

In recent years, visual localization has gained significant attention as a key technology for indoor navigation due to its outstanding accuracy and low deployment costs. However, it still encounters two primary challenges: the requirement for multiple database images to match the query image and the potential degradation of localization precision resulting from the keypoints clustering and mismatches. In this research, a novel visual localization framework based on a binocular camera is proposed to estimate the absolute positions of the query camera. The framework integrates three core methods: the multi-epipolar constraints-based localization (MELoc) method, the Optimal keypoint selection (OKS) method, and a robust measurement method. MELoc constructs multiple geometric constraints to enable absolute position estimation with only a single database image, while OKS and the robust measurement method further enhance localization accuracy by refining the precision of these geometric constraints. Experimental results demonstrate that the proposed system consistently outperforms existing visual localization systems across various scene scales, database sampling intervals, and lighting conditions

OMS-SLAM: dynamic scene visual SLAM based on object detection with multiple geometric feature constraints and statistical threshold segmentation

Abstract SLAM technology is crucial to robot navigation. Despite the good performance of traditional SLAM algorithms in static environments, dynamic objects typically exist in realistic operating environments. These objects can lead to misassociated features, which in turn considerably impact the system’s localization accuracy and robustness. To better address this challenge, we have proposed the OMS-SLAM. In OMS-SLAM, we adopted the YOLOv8 target detection network to extract object information from environment and designed a dynamic probability propagation model that is coupled with target detection and multiple geometric constrains to determine the dynamic objects in the environment. For the identified dynamic objects, we have designed a foreground image segmentation algorithm based on depth image histogram statistics to extract the object contours and eliminate the feature points within these contours. We then use the GMS (Grid-based Motion Statistics) matching pair as the filtering strategy to enhance the quality of the feature points and use the enhanced feature points for tracking. This combined method can accurately identify dynamic objects and extract related feature points, significantly reducing its interference and consequently enhancing the system's robustness and localization accuracy. We also built static dense point cloud maps to support advanced tasks of robots. Finally, through testing on the high-speed dataset of TUM RGB-D, it was found that the root mean square error of the Absolute Trajectory Error (ATE) in this study decreased by an average of 97.10%, compared to ORB-SLAM2. Moreover, tests in real-world scenarios also confirmed the effectiveness of the OMS-SLAM algorithm in dynamic environments.

Accurate Monocular SLAM Initialization via Structural Line Tracking.

In this paper, we present a novel monocular simultaneous localization and mapping (SLAM) initialization algorithm that relies on structural features by tracking structural lines. This approach addresses the limitations of the traditional method, which can fail to account for a lack of features or their uneven distribution. Our proposed method utilizes a sliding window approach to guarantee the quality and stability of the initial pose estimation. We incorporate multiple geometric constraints, orthogonal dominant directions, and coplanar structural lines to construct an efficient pose optimization strategy. Experimental evaluations conducted on both the collected chessboard datasets and real scene datasets show that our approach provides superior results in terms of accuracy and real-time performance compared to the well-tuned baseline methods. Notably, our algorithm achieves these improvements while being computationally lightweight, without the need for matrix decomposition.

Research on Calibration Method of Line-Structured Light Based on Multiple Geometric Constraints

Line-structured light calibration is an important step in the process of the visual measurement of structured light, and in the calibration process, the light plane equation is fitted by the camera coordinates of the data points on the light plane. There is error in solving the spatial coordinates of the data points, and the existing methods generally cannot effectively find the deviation points in the fitted data points, which leads to deviation when solving the parameters of the light plane equation. To correct the error caused by the deviation point in the calibration, this paper established a calibration method based on geometric constraints. In the method, the first constraint was that all fit points involved in the fitting had a certain consistency, and a part of the error points could be filtered by the distance from the data point to the light plane. In order to further improve the calibration accuracy, the laser was moved on a linear guide, the optimized objective function was established by the second geometric constraint, and the constraint was the relationship that the light plane at each position was parallel. In the experiment, a high-precision gauge block was used as the measured object, and the measurement results could be obtained. The calibration method can improve the calibration accuracy according to the experimental results.

Tool path generation for 5-axis flank milling of ruled surfaces with optimal cutter locations considering multiple geometric constraints

Ruled surfaces found in engineering parts are often blended with a constraint surface, like the blade surface and hub surface of a centrifugal impeller. It is significant to accurately machine these ruled surfaces in flank milling with interference-free and fairing tool path, while current models in fulfilling these goals are complex and rare. In this paper, a tool path planning method with optimal cutter locations (CLs) is proposed for 5-axis flank milling of ruled surfaces under multiple geometric constraints. To be specific, a concise three-point contact tool positioning model is firstly developed for a cylindrical cutter. Different tool orientations arise when varying the three contact positions and a tool orientation pool with acceptable cutter-surface deviation is constructed using a meta-heuristic algorithm. Fairing angular curves are derived from candidates in this pool, and then curve registration for cutter tip point on each determined tool axis is performed in respect of interference avoidance and geometric smoothness. On this basis, an adaptive interval determination model is developed for deviation control of interpolated cutter locations. This model is designed to be independent of the CL optimization process so that multiple CLs can be planned simultaneously with parallel computing technique. Finally, tests are performed on representative surfaces and the results show the method has advantages over previous meta-heuristic tool path planning approaches in both machining accuracy and computation time, and receives the best comprehensive performance compared to other multi-constrained methods when machining an impeller.

DGM-VINS: Visual–Inertial SLAM for Complex Dynamic Environments With Joint Geometry Feature Extraction and Multiple Object Tracking

Most current state-of-the-art simultaneous localization and mapping (SLAM) algorithms perform well in static environments. However, their applications in real-world scenarios are limited by the assumption that environments are static because their performance becomes unstable in complex dynamic environments. To enhance system stability and localization accuracy in complex dynamic scenes, this article presents a novel visual-inertial SLAM system called DGM-VINS. In DGM-VINS, a joint geometric dynamic feature extraction module (JGDFE) is designed that can combine the advantages of multiple geometric constraints and effectively reduce the limitations of a single geometric constraint in the application process. In addition, a temporal instance segmentation module (TISM) is presented to establish the temporal correlation of instance objects in consecutive frames, which effectively addresses the instance segmentation issue in complex environments. The inertial measurement unit (IMU) is utilized for motion prediction and consistency detection to improve localization accuracy in challenging environments with weak textures. The proposed methodology is tested in various public datasets and actual scenarios, and the results demonstrate superior accuracy and robustness than existing methods in complex dynamic scenarios.

Genetic Algorithm Based Model for Optimal Selection of Open Channel Design Parameters

Open channels are one of the most used water conveyance systems for delivering water for different purposes. Existing models for the design of open channels mainly assume uniform flow, focus on cross-section sizing, and generally decouple cross-section sizing from the selection of channel alignment and profile. In this study, we developed an optimization model for a comprehensive design of transmission channels. The model minimizes the sum of costs for earthwork, lining, water losses, and land acquisition; accounts for non-uniform, mixed-regime flow; and considers multiple geometric and hydraulic constraints. The model was validated using several idealized scenarios. The model potential in minimizing the cost of real open channel projects was demonstrated through application to an existing irrigation water transmission canal in Egypt (the Sheikh Zayed Canal). The results of validation scenarios matched the anticipated outcomes for channel profile and alignment and reproduced analytical solutions given in the literature for channel cross-section design. Application of the model to the Sheikh Zayed Canal gave a more optimal design; the OCCD model produced a design alternative with ~27% less cost than the constructed alternative.

Exterior orientation estimation of oblique aerial images using SfM-based robust bundle adjustment

ABSTRACT In this article, a structure from motion (SfM) framework for oblique aerial images of man-made environments is proposed, covering the issues of determining overlapping images, feature extraction, image matching, rejection of erroneous correspondences, feature tracking, automatic transfer of ground control points (GCPs), and bundle block adjustment. One of the challenges that it is intended to solve is the reduction of the required manual work concerning the measurement of GCPs, in order to increase the degree of automation of the exterior orientation estimation process, through the usage of geometric constraints automatically imposed. Yet another challenge is the difficulty in matching correctly feature points among multiple oblique views that depict scenes with repetitive patterns and homogeneous textures. The proposed algorithm solves this by eliminating all erroneous tie points through the combination of multiple checks and geometric constraints imposed during the image matching procedure and a robust iterative bundle adjustment framework. The proposed SfM methodology is applied in different configurations of oblique images under non-ideal aerial triangulation scenarios characterized by lack of well-distributed GCPs as well as minimum manual image measurements. The results are analysed, focusing on the improvement of the accuracy of the exterior orientation parameters thanks to the proposed robust outlier removal technique as well as on the impact of the proposed scale-based weighting strategy for bundle adjustment of oblique images on the exterior orientation results. The proposed SfM framework proves to be a good alternative solution to existing commercial SfM methods.

A Novel Loop Closure Detection Approach Using Simplified Structure for Low-Cost LiDAR.

Reducing the cumulative error is a crucial task in simultaneous localization and mapping (SLAM). Usually, Loop Closure Detection (LCD) is exploited to accomplish this work for SLAM and robot navigation. With a fast and accurate loop detection, it can significantly improve global localization stability and reduce mapping errors. However, the LCD task based on point cloud still has some problems, such as over-reliance on high-resolution sensors, and poor detection efficiency and accuracy. Therefore, in this paper, we propose a novel and fast global LCD method using a low-cost 16 beam Lidar based on “Simplified Structure”. Firstly, we extract the “Simplified Structure” from the indoor point cloud, classify them into two levels, and manage the “Simplified Structure” hierarchically according to its structure salience. The “Simplified Structure” has simple feature geometry and can be exploited to capture the indoor stable structures. Secondly, we analyze the point cloud registration suitability with a pre-match, and present a hierarchical matching strategy with multiple geometric constraints in Euclidean Space to match two scans. Finally, we construct a multi-state loop evaluation model for a multi-level structure to determine whether the two candidate scans are a loop. In fact, our method also provides a transformation for point cloud registration with “Simplified Structure” when a loop is detected successfully. Experiments are carried out on three types of indoor environment. A 16 beam Lidar is used to collect data. The experimental results demonstrate that our method can detect global loop closures efficiently and accurately. The average global LCD precision, accuracy and negative are approximately 0.90, 0.96, and 0.97, respectively.

Real-time editing of man-made mesh models under geometric constraints

Editing man-made mesh models under multiple geometric constraints is a crucial need for product design to facilitate design exploration and iterative optimization. However, the presence of multiple geometric constraints (e.g. the radius of a cylindrical shape, distance from a point to a plane) as well as the high dimensionality of the discrete mesh representation of man-made models make it difficult to solve this constraint system in real-time. In this paper, we propose an approach based on subspace decomposition to achieve this goal. When a set of variables are edited by the user, the proposed method minimizes the residual of the constraint system in a least square sense to derive a new shape. The resulting shape shall comply with the assigned (extrinsic) constraints while maintaining the original (intrinsic) constraints analyzed from the given mesh model. In particular, we extract a meaningful subspace of the entire solution space based on the user’s edits to reduce the order of the problem, and solve the constraint system globally in real-time. Finally, we project the approximate solution back to the original solution space to obtain the editing result.

Robust Precise Dynamic Point Reconstruction From Multi-View

Reconstructing precise dynamic points with multiple camera systems (MCSs) is a pivotal work in many computer vision applications, such as motion capture. However, the deviation of 2-D position leads to frequent mismatch when searching for correspondence from multi-view. This paper puts forward a two-stage framework based on passive optical motion capture system to reconstruct precise dynamic points with MCSs. Our proposed method improves the performance of calibration and matching simultaneously. In the calibration stage, the extrinsic parameters of numerous cameras are calibrated synchronously via an L-shaped frame, where the position of four reference points is optimized with multiple geometric constraints. Bundle adjustment occurs after calibration. In the reconstruction stage, we propose a novel sparse multi-view matching method called cyclical voting, which includes multiple pairs of global voting and in-group voting. Point residual method is proposed to exclude outliers in matching groups further. The experiments show that our proposed method can decrease mismatching significantly and achieve commendable reconstruction results compared with Cortex (one of the most successful commercial motion analysis software).

Fast Ellipse Detection via Gradient Information for Robotic Manipulation of Cylindrical Objects

Robotic manipulation of objects requires a fast recognition from image stream. For many cylindrical object (e.g., cans, cups, pipes, bottles, etc.) this is possible through detection of ellipse depicting the circular top of the cylinder. Growing industrial and warehouse applications of robots drive the demand for fast and reliable detection of ellipses, while state-of-the-art methods are lacking in either speed or accuracy strength. We present a novel algorithm to perform fast and robust ellipse detection. First, the method utilizes the information of edge curvature to split curves into arcs. Next, the arc convexity–concavity is used to classify arcs into different quadrants of ellipses. Then, based on multiple geometric constraints the arcs can be grouped at low computational cost. Our method is compared with six state-of-the-art methods using three public image datasets. The comparison results show that the proposed algorithm outperforms other methods with high detection accuracy and fast detection speed. Lastly, the algorithm is applied to identifying cylindrical objects in real-time for arranging and tracking purposes.

多几何约束下的鱼眼相机单像高精度标定

多几何约束下的鱼眼相机单像高精度标定

Geometric design optimization of an under-actuated tendon-driven robotic gripper

We build the mathematical model between the actuated force and the contact force for an under-actuated tendon-driven robotic gripper based on the geometric analysis.A mathematical model is constructed to obtain the transmission efficiency of the tension force when a tendon wraps a joint mandrel by the geometric relations.The geometric model of transmission characteristics determined by the tendon routes for reducing the resistance is generated.Genetic Algorithm is applied to optimizing the dimensions of the gripper and the tendon routes.The geometrically optimal approach provided by us has the characteristics of the versatility and can also be referred to optimizing most of the under-actuated robotic gripper with tendon-driven mechanisms. The design optimization of a robotic gripper is of utmost importance for achieving a stable grasp behaviour. This work focuses on analysing the optimal design of an under-actuated tendon-driven robotic gripper with two 3-phalange fingers and a geometric design optimization method is proposed to achieve a stable grasp performance. The problem has twenty-two design variables, including three phalange lengths, three phalange widths, three radii of joint mandrels, a palm width and twelve route variables for allocation of six pulleys. First, the mathematical model between the active and contact forces is expressed in relation to the geometric dimensions of the robotic gripper. Second, the geometric model of transmission characteristics determined by the tendon routes for reducing the resistance is generated. Next, three objective functions and multiple geometric constraints are derived and integrated into two fitness models. Finally, the genetic algorithm is applied to addressing the optimization problem. Practical experiments are performed as well to validate the proposed approach. The approach is universal for optimizing any conventional under-actuated tendon-driven gripper.

A model for phonon thermal conductivity of multi-constrained nanostructures

The rapid development of nanotechnology makes it possible to further understand nanoscale heat conduction. Theoretical analysis and experimental measurement have demonstrated the size-dependence of thermal conductivity on a nanoscale. As dielectric material (such as silicon), phonons are the predominant carriers of heat transport. Phonon ballistic transport and boundary scattering lead to the significant reduction of thermal conductivity. Various models, in which only one geometrical constraint of phonon transport is considered, have been proposed. In engineering situations the phonon transport can be influenced by multiple geometrical constraints, especially for material with long intrinsic phonon mean free path. However, at present a phonon thermal conductivity model in which the multiple geometrical constraints of phonon transport are taken into account, is still lacking. In the present paper, a multi-constrained phonon thermal conductivity model is obtained by using the phonon Boltzmann transport equation and modifying the phonon mean free path. The geometrical constraints are dealt with separately, and the effects of these constraints on thermal conductivity are then combined by the Matthiessen's rules. Different boundary conditions can lead to different influences on the phonon transport, so different methods should be used for different boundary constraints. The differential approximation method is utilized for the constraint in the direction of heat flux, while phonon scatterings on side surfaces are characterized by modifying the phonon mean free path. The model which characterizes various nanostructures including nanofilms(in-plane and cross-plane) and finite length rectangular nanowires, can well agree with the Monte Carlo simulations of different Knudsen numbers. The model with the Knudsen number Knx equal to 0 can well predict the experimental data for the in-plane thermal conductivity of nanofilm. When the Knudsen numbers Kny and Knz vanish, the model corresponds to the cross-plane thermal conductivity of nanofilm. Moreover, with Knx=0 and Kny=Knz, the model corresponds to the square nanowires of infinite length, and the similar slopes between the model and the experimental data of nanowires can be achieved.

Automatic Construction of 3-D Building Model From Airborne LIDAR Data Through 2-D Snake Algorithm

The snake algorithm has been proposed to solve many remote sensing and computer vision problems such as object segmentation, surface reconstruction, and object tracking. This paper introduces a framework for 3-D building model construction from LIDAR data based on the snake algorithm. It consists of nonterrain object identification, building and tree separation, building topology extraction, and adjustment by the snake algorithm. The challenging task in applying the snake algorithm to building topology adjustment is to find the global minima of energy functions derived for 2-D building topology. The traditional snake algorithm uses dynamic programming for computing the global minima of energy functions which is limited to snake problems with 1-D topology (i.e., a contour) and cannot handle problems with 2-D topology. In this paper, we have extended the dynamic programming method to address the snake problems with a 2-D planar topology using a novel graph reduction technique. Given a planar snake, a set of reduction operations is defined and used to simplify the graph of the planar snake into a set of isolated vertices while retaining the minimal energy of the graph. Another challenging task for 3-D building model reconstruction is how to enforce different kinds of geometric constraints during building topology refinement. This framework proposed two energy functions, deviation and direction energy functions, to enforce multiple geometric constraints on 2-D topology refinement naturally and efficiently. To examine the effectiveness of the framework, the framework has been applied on different data sets to construct 3-D building models from airborne LIDAR data. The results demonstrate that the proposed snake algorithm successfully found the global optima in polynomial time for all of the building topologies and generated satisfactory 3-D models for most of the buildings in the study areas.

Camera Self-calibration Using Multiple Geometric Constraints in a Single Image

Camera self-calibration is a key step to acquisition 3D space information from 2D image,and it is always one of the important issues in photogrammetry.However,present methods for camera self-calibration need two or more images and/or their corresponding points.With the development of digital devices for image taken and(wireless) network,a method not depending on digital device,images taken process,or multiple images,is badly needed.Consequently this paper presented a novel method that makes full use of various geometric constraints to realize reliable camera calibration for a single image.Firstly,this paper summarized various geometric constraints and invariants for the existing camera self-calibration method.Secondly,in order to build the relationships among geometric constraints for calibration,we coded for different planes and geometric features in an image.Because variance represents the error distribution,it can be considered as the determinant.In this paper,we obtained the variance of different combination of geometric features for camera calibration by means of fitting each groups of geometric features for thirty times,and then depended on the variance above to determine the weight of each camera's internal parameters.Finally,based on each camera's internal parameters,here we only focus on foci length,and their corresponding weights,the ultimate results are computed.Two images which depict inside and outside scene respectively were chosen to test the usability of our methods.In order to avoid the influence of image distortion,we corrected it using amethod we proposed in another paper before tests.The test results show that: 1) the weighted method gave a more stable result,relative to the result of each group geometric constraints,that is one group's relative error is two high and in other may be lower;2) the weighted method obtained a higher accuracy result than the mean of all groups.The results of verification testing for the two images of the indicated that our weighted method can comprehensive employs variety of geometric constraints in single image,in the other side,it also takes their corresponding variance into account.It makes full use of the variety,usability and stability of geometric constraints.It can be employed to images depict indoor and outdoor which contains more geometric constraints.

New General Tools for Constrained Geometry Optimizations.

A modification of the constrained geometry optimization method by Anglada and Bofill (Anglada, J. M.; Bofill, J. M. J. Comput. Chem. 1997, 18, 992-1003) is designed and implemented. The changes include the choice of projection, quasi-line-search, and the use of a Rational Function optimization approach rather than a reduced-restricted-quasi-Newton-Raphson method in the optimization step. Furthermore, we show how geometrical constrains can be implemented in an approach based on nonredundant curvilinear coordinates avoiding the inclusion of the constraints in the set of redundant coordinates used to define the internal coordinates. The behavior of the new implementation is demonstrated in geometry optimizations featuring single or multiple geometrical constraints (bond lengths, angles, etc.), optimizations on hyperspherical cross sections (as in the computation of steepest descent paths), and location of energy minima on the intersection subspace of two potential energy surfaces (i.e. minimum energy crossing points). In addition, a novel scheme to determine the crossing point geometrically nearest to a given molecular structure is proposed.

Interactive optimization of 3D shape and 2D correspondence using multiple geometric constraints via POCS

The traditional approach of handling motion tracking and structure from motion (SFM) independently in successive steps exhibits inherent limitations in terms of achievable precision and incorporation of prior geometric constraints about the scene. This paper proposes a projections onto convex sets (POCS) framework for iterative refinement of the measurement matrix in the well-known factorization method to incorporate multiple geometric constraints about the scene, thereby improving the accuracy of both 2D feature point tracking and 3D structure estimates. Regularities in the scene, such as points on line and plane and parallel lines and planes, that can be interactively identified and marked at each POCS iteration, enforce rank and parallelism constraints on appropriately defined local measurement matrices, one for each constraint. The POCS framework allows for the integration of the information in each of these local measurement matrices into a single measurement matrix that is "closest" to the initial observed measurement matrix in Frobenius norm, which is then factored in the usual manner. Experimental results demonstrate that the proposed interactive POCS framework consistently improves both 2D correspondences and 3D shape/motion estimates and similar results cannot be achieved by enforcing these constraints as either post or preprocessing.

Model-based adaptive hybrid control for manipulators under multiple geometric constraints

This paper proposes an adaptive hybrid controller for manipulators constrained on multiple smooth geometric surfaces and reports the experimental results on a six-degree-of-freedom direct-drive manipulator. This controller produces simultaneous position and force tracking of the constrained manipulators even when their physical parameters are unknown since it is incorporated with the model-based adaptive algorithm. The asymptotic stability is guaranteed by a passivity-based Lyapunov function. Further, we present a parallel implementation of this controller using transputers on the six-DOF manipulator. We examine the control performance by experiments of the manipulator in a point-point contact, two point-point contacts, and a face-face contact with the environment, respectively.