Directed Energy Deposition (DED) is a crucial additive manufacturing process used in aerospace and health-care applications, among others. However, ensuring defect-free production remains a challenge due to the difficulty in detecting defect-related anomalies in real-time. In this study, we address the problem of defect detection in DED processes through thermal images of melt pools. As an anomaly detection problem, we adopt a semi-supervised approach based on One-Class Support Vector Machine (OCSVM) and Isolation Forest (iForest). We analyze the performance of these models across different feature sets. Additionally, this semi-supervised approach is compared against an unsupervised approach utilizing the same learning algorithms. The results indicate the superiority of the semi-supervised approach for both algorithms. Yet, iForest outperforms OCSVM with an accuracy of 95% and an F1-score of 0.88, demonstrating its robustness in distinguishing defective from non-defective instances. This work provides valuable insights into the applicability of semi-supervised machine learning techniques for real-time defect detection in DED processes. By leveraging thermal imaging data and feature-based anomaly detection models, our findings contribute to the development of efficient, non-destructive quality control mechanisms for additive manufacturing processes.

This study investigates the application of Online Dynamic Mode Decomposition (Online DMD) for real-time system identification and control in an autonomous vehicle lane-keeping system. The Online DMD algorithm dynamically updates a linear state-space model of lateral vehicle dynamics, enabling continuous adaptation to changing road conditions. To test the robustness and predictive capabilities of these models, Model Predictive Control (MPC) and Linear Quadratic Regulator (LQR) strategies are designed and implemented in MATLAB/Simulink. The system is evaluated under constant longitudinal velocity across diverse road sections in simulation environment. The results demonstrate that combining data-driven system identification with optimal control frameworks achieves robust lane tracking and adaptability, while also revealing that the short-term prediction capability of Online DMD may pose limitations in certain dynamic scenarios.

Accurate camera pose estimation is crucial for autonomous driving and vehicle networking. Traditional pipelines based on geometric models and feature matching struggle in dynamic, featureless environments which are common in many environments. Inspired by the success of vision transformers (ViT), our approach uses a ViT backbone with an attention-based mask to extract a global image descriptor, which is then passed through fully connected layers for pose regression. The multi-headed self-attention in ViT helps the model learn scene layouts and focus on relevant features. We introduce an attention mask to improve performance in challenging scenes, especially dynamic or featureless ones. We compare three backbones: ViT (multi-headed self-attention throughout), ConViT (self-attention in the last two layers, gated positional self-attention elsewhere), and ResNet (pure convolution). We evaluate our model on two commonly used benchmarks for outdoor and indoor localization and we show that our model which uses ViT backbone achieves the state of the art results for both indoor and outdoor multi-scene absolute localization benchmarks.

Obstacle avoidance and path planning are essential for guiding unmanned ground vehicles (UGVs) through environments that are densely populated with dynamic obstacles. This paper develops a novel approach that combines tangent-based path planning and extrapolation methods to create a new decision-making algorithm for local path planning. In the assumed scenario, a UGV has a prior knowledge of its initial and target points within the dynamic environment. A global path has already been computed, and the robot is provided with waypoints along this path. As the UGV travels between these waypoints, the algorithm aims to avoid collisions with dynamic obstacles. These obstacles follow polynomial trajectories, with their initial positions randomized in the local map and velocities randomized between 0 and the allowable physical velocity limit of the robot, along with some random accelerations. The developed algorithm is tested in several scenarios where many dynamic obstacles move randomly in the environment. Simulation results show the effectiveness of the proposed local path planning strategy by gradually generating a collision free path which allows the robot to navigate safely between initial and the target locations.

Relative camera pose regressors estimate the relative pose between two cameras from two input images. A convolutional network with a multi layer perceptron head is usually trained per scene with ground truth relative poses. However, such methods are still suffering from limited accuracy and generalization. Inspired by the success of vision transformers on computer vision tasks, we propose to learn relative pose between two cameras using only vision transformer backbone with fully connected layers. The multiheaded self attention mechanism of the vision transformer allows our model to attend to the full image even from the lowest layers which further enables our model to learn the layout of the scene and focuses only the features that are relevant to our task. We evaluate our model on one outdoor and two indoor datasets. We show that our model achieves new competitive accuracies for both outdoor and indoor multi-scene relative localization benchmarks. We further compare our pose estimation results to those obtained using recent local keypoints based approaches and we show that our model outperforms these methods particularly for frames with small translation, where such methods mostly fail.

Automated fiber placement (AFP) technology, while highly beneficial, is susceptible to defects that compromise the final product’s mechanical integrity. Traditional manual inspection methods are labor-intensive, error-prone, and result in significant downtime. This study introduces an innovative framework for AFP process inspection and quality assessment using thermal imaging, machine learning algorithms, and computer vision techniques. The system comprises defect detection, defect segmentation, and quality assessment components. By providing real-time feedback, it offers qualitative defect attributes (shape, size, and location) and a novel quantitative defect impact metric. An active knowledge-driven decision support system (AFP-DSS) aids operator maintenance and repair decisions. Experimental validation shows the defect detection component achieving 96.4% accuracy with a 2.8% false negative rate, and the defect segmentation component attaining 93.2% mean pixel accuracy and a mean Intersection over Union (IoU) score of 0.72. Operating in real-time, the system effectively reduces machine downtime, enhances production quality, and improves the economic viability of AFP technology.

The air pressure system (APS) plays a prime role in pressurizing various subsystems of heavy-duty vehicles (HVDs). However, its reliability is crucial to ensure uninterrupted operation where failures in APS lead to HVDs being stranded on the road with the manufacturers and operators incurring associated high costs. This paper addresses the problem of predicting failures in APS using a semi-supervised transformer-based framework. The proposed framework commences with important preprocessing steps including data segmentation followed by sliding windows to handle the big raw data, and subsequent extraction of distinctive features. Using these features, the transformer model was trained to reconstruct data from healthy vehicles (i.e., vehicles without any APS failures) to capture the normal behavior of the healthy vehicles. At inference, the trained model distinguished the faulty vehicles with detected APS failure from the healthy ones based on their reconstruction errors. This semi-supervised formulation of APS failure detection overcomes limitations such as the imbalanced data issue and anomaly heterogeneity that are associated with the conventional supervised formulation. The model demonstrated robust performance with an F1 score of approximately 0.76, an accuracy of about 85%, and a high recall of 0.833, indicating successful detection of most faulty vehicles. Such advancements promise significant improvements in vehicle diagnostics and predictive maintenance.

Directed energy deposition (DED) stands as a pivotal additive manufacturing technique, revolutionizing the landscape of modern manufacturing. However, process-related defects hin-der its broad application across different sectors. In this paper, we propose a novel methodology for the in-situ prediction of defects in DED processes based on the thermal images of the melt pools. Initially, multiple features, summarizing the thermal and geometric characteristics of the melt pool, were extracted. Based on these features, an ensemble of unsupervised clustering models was constructed to distinguish anomalies - images with defects - from the defect-free images. Roughly 3% of the acquired images were predicted to include defects. Upon visual inspection, these images exhibited distinctive thermal distributions and geometric configurations compared to the remaining dataset. Furthermore, a 2D approximate visualization of the feature space revealed the clustering structure of the thermal images in their feature space. This visualization showed that the anomalies could be distinguished from the majority of normal images, which further validates the prediction model's effectiveness.

In this paper, a machine learning (ML) system is introduced to detect high fuel consumption in heavy-duty vehicles (HDVs) using operational data. The system addresses environmental and efficiency challenges in the transportation industry by precisely monitoring fuel consumption to curb CO2 emissions. An ensemble learning method that integrates unsupervised anomaly detection techniques, including Isolation Forest, Autoencoder, and k-NN Regressor models, is proposed. The anomaly detection results from these models are combined using a weighted majority voting (WMV) approach. This method was tested on a dataset comprising 459 driving records and 14 signals collected from 187 HDVs. Additionally, the Local Outlier Factor (LOF) model was employed to validate the ensemble learning method and investigate the factors contributing to the anomalies. This work enhances transportation efficiency by offering a novel approach for analyzing fuel consumption in HDVs, thereby paving the way for future advancements in sustainable transportation practices.

This paper presents a novel learning-based approach for automatic detection and classification of production defects in the automated fiber placement (AFP) process using thermography as a solution to the error-prone and time consuming manual inspection problem. We introduce a hierarchical framework designed to achieve reliable performance, optimize computational resources, and address challenges such as inherent data imbalance. First, a high-level lay-up status classifier, that utilize traditional vision and classical machine learning algorithms, is fetched to decide whether a lay-up region is healthy or defective. Then, a low-level model based on a proposed deep learning architecture classifies the defective instance into specific defect classes. A comprehensive thermal image database, including both natural and synthetically induced defect experiments, is built and used to train, test, and evaluate the models. The performance of each classification level is analyzed individually, yielding promising results with accuracy rates exceeding 95%. Moreover, the proposed approach demonstrates real-time operation capability.

This paper presents a novel image-based path planning algorithm that was developed using computer vision techniques, as well as its comparative analysis with well-known deterministic and probabilistic algorithms, namely A* and Probabilistic Road Map algorithm (PRM). The terrain depth has a significant impact on the calculated path safety. The craters and hills on the surface cannot be distinguished in a two-dimensional image. The proposed method uses a disparity map of the terrain that is generated by using a UAV. Several computer vision techniques, including edge, line and corner detection methods, as well as the stereo depth reconstruction technique, are applied to the captured images and the found disparity map is used to define candidate way-points of the trajectory. The initial and desired points are detected automatically using ArUco marker pose estimation and circle detection techniques. After presenting the mathematical model and vision techniques, the developed algorithm is compared with well-known algorithms on different virtual scenes created in the V-REP simulation program and a physical setup created in a laboratory environment. Results are promising and demonstrate effectiveness of the proposed algorithm.

In this paper, an in-situ defect detection system is proposed for automated fiber placement (AFP) process monitoring. To acquire meaningful data about the laid-up tows, the design, manufacturing and integration of a flexible three degrees of freedom vision system to the AFP machine is proposed. An image segmentation algorithm is developed to locate and isolate defects in input images. The proposed algorithm utilizes Gabor filters to extract the desired texture features which is followed by an adaptive thresholding. Successful results with four of the main defect classes namely, foreign bodies, wrinkles, gaps and bridging, were obtained. This monitoring system can reduce time-consuming and expensive efforts of manual quality inspection and will significantly increase AFP process reliability.

In this paper, we propose a hybrid visual-LiDAR odometry (H-VLO) framework that fuses predicted visual depth map and completed LiDAR map. Compared to the previous visual-LiDAR odometry methods, our approach leverages 2D feature matching and 3D association by utilizing deep depth map, deep flow map and deep LiDAR depth completion networks. Rather than extraction of the depth values from LiDAR measurements for each visual feature, our method first densifies a LiDAR scan with a deep depth completion network and then fuses it with visual deep depth map estimation in a Bayesian framework. This method reduces pose estimation drift by improving feature-to-feature and point-to-feature matching, as well as scale recovery. The evaluations on the public KITTI odometry benchmark show that our technique achieves better or at least comparable estimates than the state-of-the-art visual-LiDAR and monocular visual odometry approaches.

This paper proposes a robust and safe perception system for an odometry framework based on the fusion of LiDAR data with an RGB image. These multi-modal sensor measurements are fused using their depth proposals and confidence measures in a Bayesian inference module. The resulting fused depth map enhances unsupervised odometry estimates. Experimental results show that the LiDAR-camera fused depth map is an accurate 3D structure representation of the environment. This method can be used in an online adaption of the learning-based odometry algorithms to increase their generalizability to different scenes. We perform experiments on the benchmark odometry datasets and obtain promising results compared to the previous approaches. Compared to the state-of-the-art methods, the average translation error shows a 44% reduction, and the average rotation error is better or comparable.

In this paper, a fault tolerant control system for a quadrotor helicopter is developed. Fault tolerant controllers have many advantages over regular controllers for keeping midair flight safety and increasing mission reliability. A high-fidelity nonlinear model of a quadrotor is constructed using Newton-Euler formulation where Dryden wind effects and sensor noise are included to simulate real-world fight conditions. For managing accurate full state estimations, an Extended Kalman Filter is utilized. To increase robustness to external disturbances and uncertainties in the plant dynamics, a Velocity-based Disturbance Observer (VbDOB) is constructed and combined with the control law. Simulations carried out with the high fidelity model have shown that the proposed method has successfully compensated for actuator faults in a trajectory tracking task, and hence provides good tracking performance with a feasible control effort.

This paper deals with the development of a machine vision based pose estimation system for industrial robots and improving accuracy of the estimated pose using Long Short Term Memory (LSTM) neural networks. To this end, an LSTM network is proposed in order to improve the accuracy obtained from the Levenberg-Marquardt (LM) based pose estimation algorithm during trajectory tracking of the robot's end effector. The proposed method utilizes an LSTM network to extract dynamic features from the pose estimated by the LM algorithm and then feeding it to a regression layer to estimate the correct pose. Moreover, a target object trackable with a monocular camera with ± 90° in all directions was designed and fitted with fiducial markers. The designed placement of these fiducial markers guarantees the detection of at least two non-planar markers thus preventing ambiguities in pose estimation. The effectiveness of the proposed method is validated by an experimental study performed using a KUKA KR240 R2900 ultra robot while following sixteen distinct trajectories based on ISO 9238. The obtained results show that the proposed method significantly improves the pose estimation accuracy and precision of the vision based system during trajectory tracking of industrial robots' end effector.

In this paper a neural network based modeling approach is proposed for localization and estimation of loads acting on aircraft wings from full field depth measurements. These measurements can be provided by a multitude of sensors such as depth cameras. Depth cameras have many advantages over other intensity sensors in that they can work in low light conditions and they are invariant to texture and color changes. First, an autoencoder is proposed to extract maximum informative data from the depth images and encode them at a much smaller dimension. Next, to develop the models for localization and estimation of loads, supervised multinomial classification and logistic regression networks are proposed, where the encoded depth features are utilized as input in both networks. The performance of the proposed method is validated on a composite wing subject to concentrated and distributed loads, during which the proposed methods for localization and estimation of loads achieved high accuracies of 90.6% and 90.5%, respectively.

In this paper, we present a real-time driver evaluation system for heavy-duty vehicles by focusing on the classification of risky acceleration and braking behaviors. We utilize an improved version of our previous Long Short Memory (LSTM) based acceleration behavior model [10] to evaluate varying acceleration behaviors of a truck driver in small time periods. This model continuously classifies a driver as one of six driver classes with specified longitudinal-lateral aggression levels, using driving signals as time-series inputs. The driver gets acceleration score updates based on assigned classes and the geometry of driven road sections. To evaluate the braking behaviors of a truck driver, we propose a braking behavior model, which uses a novel approach to analyze deceleration patterns formed during brake operations. The braking score of a driver is updated for each brake event based on the pattern, magnitude, and frequency evaluations. The proposed driver evaluation system has achieved significant results in both the classification and evaluation of acceleration and braking behaviors.

Feedforward control is widely used in electronic control units of internal combustion engines besides feedback controls. However, almost all feedforward control values are used in table form, also called maps, having engine speed and engine torque in their axes. Table approach limits all interactions in two input dimensions. This paper focuses on application of Gaussian process modelling of errors of inverse parametric model of the valve position. Validation results based on real engine data are presented for steady and dynamic conditions.

Linear parameter varying (LPV) models are widely used in control applications of the nonlinear MIMO dynamic systems. LPV models depend on the time varying parameters. This paper develops a polytopic quasi-LPV model for a nonlinear pan-tilt robotic system. A Linear Quadratic Regulator (LQR) that utilizes Linear Matrix Inequalities (LMIs) with well tuned weighting matrices is synthesized based on the developed LPV model. The number of time varying parameters in the developed polytopic LPV model is 4 so the number of vertices becomes 16. The desired controller is generated by the interpolation of LMIs at each vertex. The performance of the optimal LQR controller is evaluated by using the designed feedback gain matrix to stabilize the nonlinear pan-tilt system. Simulations performed on the nonlinear model of the pan-tilt system demonstrate success of the proposed LPV control approach.

Self-balancing mobile platforms with single spherical wheel, generally called ballbots, are suitable example of underactuated systems. Balancing control of a ballbot platform, which aims to maintain the upright orientation by rejecting external disturbances, is important during station keeping or trajectory tracking. In this paper, acceleration based balancing and position control of a single spherical wheeled mobile platform that has three single-row omniwheel drive mechanism is examined. Robustness of the balancing controller is achieved by employing cascaded position, velocity and current control loops enhanced with acceleration feedback (AFB) to provide higher stiffness to the platform. The effectiveness of the proposed balancing controller is compared with commonly used optimal state feedback method. Additionally, the position controller is designed by utilizing the dynamic conversion of desired torques on the ball that are calculated from virtual control inputs generated in the inertial coordinates. Dynamical model of a ballbot platform is investigated by considering highly nonlinear couplings. Performance of the controllers are presented via simulation results where the external torques were applied on the body in order to test disturbance rejection capabilities.

Hydrodynamic cavitation is an effective and alternative treatment method in various biomedical applications such as kidney stone erosion, ablation of benign prostatic hyperplasia tissues and annihilation of detrimental cells. In order to effectively position the orifice of bubbly cavitating flow generator towards the target and control the destructive cavitation effect, cone angle of multi-phase bubbly flow and distributions of scattered bubble swarms around main flow must be determined. This paper presents two vision based solutions to determine these quantities. 3D Gaussian modeling of multi-phase flow and edge slopes of cross-section are used to estimate the cone angle in a Kalman filter framework. Scattered bubble swarm distributions around main flow were assumed as a normal distribution and analyzed with the help of covariance matrix of the bubble position data. Hydrodynamical cavitating bubbles were generated from 0.45 cm long micro probe with 152μm inner diameter under 10 to 120 bars pressures and monitored via Particle Shadow Sizing technique. Proposed methods enabled to quantize the increasing inlet pressure effect on bubbly cavitating multi-phase flow.

Stringent international regulations in terms of emissions necessitate more efficient transient calibration procedures for diesel engines which in turn implies utilization of dynamic models of the combustion process. In this paper, a novel input design framework in terms of multi-sweep chirp signals is developed and airpath input channels are excited by designed chirp signals. Linear and nonlinear system identification methods are utilized to model NOx emissions with airpath input channels. Experimental results show that while linear identification techniques provide poor performance in terms of training and validation fits, nonlinear models achieve remarkable performance in training and validation fits.

There have been several attempts to create scalable and hardware independent software architectures for Unmanned Aerial Vehicles (UAV). In this work, we propose an onboard architecture for UAVs where hardware abstraction, data storage and communication between modules are efficiently maintained. All processing and software development is done on the UAV while state and mission status of the UAV is monitored from a ground station. The architecture also allows rapid development of mission-specific third party applications on the vehicle with the help of the core module.

In recent years, under vehicle surveillance and the classification of the vehicles become an indispensable task that must be achieved for security measures in certain areas such as shopping centers, government buildings, army camps etc. The main challenge to achieve this task is to monitor the under frames of the means of transportations. In this paper, we present a novel solution to achieve this aim. Our solution consists of three main parts: monitoring, detection and classification. In the first part we design a new catadioptric camera system in which the perspective camera points downwards to the catadioptric mirror mounted to the body of a mobile robot. Thanks to the catadioptric mirror the scenes against the camera optical axis direction can be viewed. In the second part we use speeded up robust features (SURF) in an object recognition algorithm. Fast appearance based mapping algorithm (FAB-MAP) is exploited for the classification of the means of transportations in the third part. Proposed technique is implemented in a laboratory environment.

Coordination of autonomous mobile robots has received significant attention during the last two decades. Coordinated motion of heterogenous robot groups are more appealing due to the fact that unique advantages of different robots might be combined to increase the overall efficiency of the system. In this paper, a heterogeneous robot group composed of multiple Unmanned Ground Vehicles (UGVs) and an Unmanned Aerial Vehicle (UAV) collaborate in order to accomplish a predefined goal. UGVs follow a virtual leader which is defined as the projection of UAV's position onto the horizontal plane. The UAV broadcasts its position at certain frequency. The position of the virtual leader and distances from the two closest neighbors are used to create linear and angular velocity references for each UGV. Several coordinated tasks have been presented and the results are verified by simulations where certain amount of communication delay between the vehicles is also considered. Results are quite promising.

Coordinated motion of Unmanned Aerial Vehicles (UAVs) has been a growing research interest in the last decade. In this paper we propose a coordination model that makes use of virtual springs and dampers to generate reference trajectories for a group of quad rotors. Virtual forces exerted on each vehicle are produced by using projected distances between the quadrotors. Several coordinated task scenarios are presented and the performance of the proposed method is verified by simulations.

This paper develops a recursive method for computing moments of 2D objects described by elliptic Fourier descriptors (EFD). Green's theorem is utilized to transform 2D surface integrals into 1D line integrals and EFD description is employed to derive recursions for moments computations. Experiments are performed to quantify the accuracy of our proposed method. Comparison with Bernstein-Bézier representations is also provided.

This paper presents two novel estimation methods that are designed to enhance our ability of observing, positioning, and physically transforming the objects and/or biological structures in micromanipulation tasks. In order to effectively monitor and position the microobjects, an online calibration method with submicron precision via a recursive least square solution is presented. To provide the adequate information to manipulate the biological structures without damaging the cell or tissue during an injection, a nonlinear spring-mass-damper model is introduced and mechanical properties of a zebrafish embryo are obtained. These two methods are validated on a microassembly workstation and the results are evaluated quantitatively.

SURALP is a new walking humanoid robot platform designed at Sabanci University - Turkey. The kinematic arrangement of the robot consists of 29 independently driven axes, including legs, arms, waist and a neck. This paper presents the highlights of the design of this robot and experimental walking results. Mechanical design, actuation mechanisms, sensors, the control hardware and algorithms are introduced. The actuation is based on DC motors, belt and pulley systems and Harmonic Drive reduction gears. The sensory equipment consists of joint encoders, force/torque sensors, inertial measurement systems and cameras. The control hardware is based on a dSpace digital signal processor. A smooth walking trajectory is generated. A variety of controllers for landing impact reduction, body inclination and Zero Moment Point (ZMP) regulation, early landing trajectory modification, and foot-ground orientation compliance and independent joint position controllers are employed. A posture zeroing procedure is followed after manual zeroing of the robot joints. The experimental results indicate that the control algorithms presented are successful in improving the stability of the walk.

Visual servoing schemes generally employ various image features (points, lines, moments etc.) in their control formulation. This paper presents a novel method for using boundary information in visual servoing. Object boundaries are modeled by algebraic equations and decomposed as a unique sum of product of lines. We propose that these lines can be used to extract useful features for visual servoing purposes. In this paper, intersection of these lines are used as point features in visual servoing. Simulations are performed with a 6 DOF Puma 560 robot using Matlab Robotics Toolbox for the alignment of a free-form object. Also, experiments are realized with a 2 DOF SCARA direct drive robot. Both simulation and experimental results are quite promising and show potential of our new method.

Although algebraic or so-called “implicit polynomial ” curves have been studied rather extensively for several decades, to the best of our knowledge, a dynamic formulation of them, similar to active contours, has not been done yet. This paper develops a dynamic formulation for implicit polynomial curves based on level set formalism. In particular, it is shown that utilization of an implicit polynomial distance function in the level set equation yields an ordinary differential equation (ODE) for the temporal behavior of the polynomial coefficients. Using a control theoretic approach, several problems such as curve morphing, dynamic conic fitting without and with constraint, i.e. dynamic ellipse fit, and dynamic curve fitting can be tackled within this new framework. Results are verified by several examples on real images. 1

This paper presents an experimental comparison of conventional (calibrated and uncalibrated) image based visual servoing methods in various microsystem applications. Both visual servoing techniques were tested on a microassembly workstation, and their regulation and tracking performances are evaluated. Calibrated visual servoing demands the optical system calibration for the image Jacobian estimation and if a precise optical system calibration is done, it ensures a better accuracy, precision and settling time compared with the uncalibrated approach. On the other hand, in the uncalibrated approach, optical system calibration is not required and since the Jacobian is estimated dynamically, it is more flexible.

Linear fitting of implicit algebraic models to data usually suffers from global stability problems. Complicated object structures can accurately be modeled by closed-bounded surfaces of higher degrees using ridge regression. This paper derives an explicit formula for computing a Euclidean invariant 3D ridge regression matrix and applies it for the global stabilization of a particular linear fitting method. Experiments show that the proposed approach improves global stability of resulting surfaces significantly

Both parametric and implicit representations can be used to model 2D curves and 3D surfaces. Each has certain advantages compared to the other. Implicit polynomial (IP) methods are not as popular as parametric procedures because the lack of general procedures for obtaining IP models of higher degree has prevented their general use in many practical applications. In most cases today, parametric equations are used to model curves and surfaces. One such parametric representation, elliptic Fourier descriptors (EFD) has been widely used to represent 2D and 3D curves, as well as 3D surfaces. Although EFDs can represent nearly all curves, it is often convenient to have an implicit algebraic description, F(x,y)=0, especially for determining whether given points lie on the curve. Algebraic curves and surfaces have proven very useful also in many model-based applications. Various algebraic and geometric invariants obtained from these implicit models have been studied rather extensively. We present a new non-symbolic implicitization technique called the matrix annihilation method, for converting parametric Fourier representations to implicit polynomial form.

Presents novel techniques to modify free-form shapes defined by implicit algebraic models. These models are first simplified by introducing a decomposition in terms of conic-line primitives, and then the desired local/global shape changes are produced by varying the parameters of these primitives. A decomposed model provides efficient control of each primitive using its canonical frame. To make the analysis simpler, we restrict our attention to free-form curves modeled by a 4th-degree (quartic) equation. However, all of the analysis can be directly extended to higher-degree models. We also provide some 3D interpolation procedures based on the resulting primitives to illustrate the potential of our methods in 3D.

Many free-form object boundaries can be modeled by quartics with bounded zero sets. The fact that any nondegenerate closed-bounded algebraic curve of even degree n=2p can be expressed as the product of p conics, which are real ellipses, plus a remaining polynomial of degree n-2,12 can be utilized to express a nondegenerate quartic as the product of two leading ellipses plus a third conic which might be either a closed curve (an ellipse) or an open curve (a hyperbola). However, it can be shown that the leading ellipses can be modified with appropriate constants by constraining the third conic to be a circle, thus implying a 2-ellipse and 1-circle; i.e. an elliptical-circular(E2C)representation of the quartic. The use of such representations is to simplify the analysis of quartics by exploiting the well-known properties of conics and to develop a set of functionally independent geometric invariants for recognition purposes. Also, it is shown that the underlying Euclidean transformation between two configurations of the same quartic can be determined using the centers of the three conics.

We employ a complex representation for an algebraic curve, and illustrate how the algebraic transformation which relates two Euclidean equivalent curves can be determined using this representation. The idea is based on a complex representation of 2D points expressed in terms of the orthogonal x and y variables, with rotations of the complex numbers described using Euler's identity. We develop a simple formula for integer multiples of the rotation angle of the Euclidean transformation in terms of the real coefficients of implicit polynomial equations that are used to model various 2D free-form objects. When there is a translation, it can be determined in a straightforward manner using an estimation of the rotation angle and some new results on conic-line decompositions.

A new method is presented for identifying and comparing closed, bounded, free-form curves that are defined by even implicit polynomial (IP) equations in the X-Y Cartesian coordinates. The method provides a new expression for an IP involving a product of conic factors with unique conic factor centers. The critical points for an IP curve are also defined. The conic factor centers and the critical points are shown to be useful related points that directly map to one another under affine transformations. In particular, the explicit determination of such points implies both a canonical form for the curves and the transformation matrix which relates affine equivalent curves.