Robust Fitting Algorithm Research Articles

Microstructural and thermodynamic characterization of wormlike micelles formed by polydisperse ionic surfactant solutions.

For industrial applications of self-assembled wormlike micelles, measurement and characterization of a micellar material's microstructure and rheology are paramount for the development and deployment of new high-performing and cost-effective formulations. Within this workflow, there are significant bottlenecks associated with experimental delays and a lack of transferability of results from one chemistry to another. In this work, we outline a process to predict microscopic and thermodynamic characteristics of wormlike micelles directly from rheological data by combining a more robust and efficient fitting algorithm with a recently published constitutive model called the Toy Shuffling model [J. D. Peterson and M. E. Cates, J. Rheol. 64, 1465-1496 (2020) and J. D. Peterson and M. E. Cates, J. Rheol. 65, 633-662 (2021)]. To support this work, linear rheology measurements were taken for 143 samples comprising a common base formulation of commercial sodium lauryl ether sulfate, cocamidopropyl betaine, and salt (NaCl). The steady state zero shear viscosity evident in linear rheology was measured in duplicate via direct steady and oscillatory shear experiments. Fitting the collected data to the model, we found trends in the microstructural and thermodynamic characteristics that agree with molecular dynamics simulations. These trends validate our new perspective on the parameters that inform the study of the relationship between chemical formulation and rheology. This work, when implemented at scale, can potentially be used to inform and test strategies for predicting self-assembled micellar structures based on chemical formulation.

Measuring food volume from RGB-Depth image with point cloud conversion method using geometrical approach and robust ellipsoid fitting algorithm

Volume measurement is an essential feature for food analysis and recognition systems to estimate nutritional intake from patients. Understanding the volume of consumed food is one approach for calculating how much food is consumed. This research provides a novel method for estimating food volume from RGB-Depth images using a combined point cloud conversion method and fitting points into ellipsoids using a geometrical approach. Point cloud segmentation is also utilized to separate the main object from the background. After the point cloud is downsampled, it is converted into real-world coordinates using the conversion method. The volume prediction is generated via numerical approaches, that is fitting to an ellipsoid using the least square approach. The objects in this study were tomatoes, oranges, kiwis, lemons, and potatoes, which were examined through multiple experiments. The evaluation results show that the predicted volume with the proposed method produces an Absolute Relative Error (ARE) of 2.6% for objects with a spherical shape, ARE of 3.1% for objects with an ellipsoid shape, and ARE of 3.0% for objects with an irregular surface, such as potatoes. When items are put on a white or blue background, volume predictions reach the ARE of 3.0% and 4.1%, respectively. As a result, white backgrounds were used more frequently in this study. Furthermore, experiments were carried out with various object orientations, camera distance locations, and object centers to evaluate the point cloud conversion method, yielding ARE of 3.4% and 4.4%, respectively. The obtained ARE indicates that the proposed approach makes reliable volume estimation.

Low cost inertial sensor attitude fixation algorithm and accuracy analysis

Aiming at the problems of angle oscillation, slow convergence speed, and low accuracy of traditional algorithms in low cost inertial element attitude determination, this study proposes an improved attitude algorithm based on geomagnetic correction robust model assisted adaptive step gradient descent. Firstly, a robust ellipsoid fitting algorithm is proposed to correct the geomagnetic anomaly data. Then, an adaptive step size model is established based on the momentum gradient descent method, and the iterative optimization parameters are automatically adjusted according to the error function. At the same time, the dynamic limiting mean filter is used to constrain the attitude angle, to calculate the optimal attitude information of the sensor. Finally, the algorithm is verified by static and dynamic experimental data. The results show that the improved algorithm can effectively suppress the angle oscillation, optimize the attitude convergence effect, and improve the accuracy of low cost inertial sensor attitude calculation.

USING MACHINE LEARNING ON DEPTH MAPS AND IMAGES FOR TUNNEL EQUIPMENT SURVEYING

Abstract. In this contribution, we illustrate how to use high-resolution 3D data and images to model the global shape of a tunnel and to survey its equipment, in a semi-automatic way using pattern recognition and machine learning techniques. We first implement a robust B-spline fitting algorithm, based on a parametric family of M-estimators that allows an efficient deterministic optimization strategy, to accurately model the tunnel lining using range data, despite the presence of acquisition artifacts and significant perturbations related to the equipment and some surface defects. The residual maps from the robust fit can be exploited to segment the equipment in an unsupervised manner using clustering algorithms, but at the cost of post-processing which makes the method rather ineffective for routine use. However, we deploy it to annotate data for the supervised learning of a deep learning model, namely Mask R-CNN.We comment on the first results, obtained on a still limited number of examples, and from image data only, and discuss the possibilities of improving the method, in the immediate or longer term.

Technical note: Do different projections matter for the Budyko framework?

Abstract. The widely used Budyko framework defines the water and energy limits of catchments. Generally, catchments plot close to these physical limits, and Budyko (1974) developed a curve that predicted the positions of catchments in this framework. Often, the independent variable is defined as an aridity index, which is used to predict the ratio of actual evaporation over precipitation (Ea/P). However, the framework can be formulated with the potential evaporation as the common denominator for the dependent and independent variables, i.e., P/Ep and Ea/Ep. It is possible to mathematically convert between these formulations, but if the parameterized Budyko curves are fit to data, the different formulations could lead to differences in the resulting parameter values. Here, we tested this for 357 catchments across the contiguous United States. In this way, we found that differences in n values due to the projection used could be ± 0.2. If robust fitting algorithms were used, the differences in n values reduced but were nonetheless still present. The distances to the curve, often used as a metric in Budyko-type analyses, systematically depended on the projection, with larger differences for the non-contracted sides of the framework (i.e., Ep/P>1 or P/Ep>1). When using the two projections for predicting Ea, we found that uncertainties due to the projections used could exceed 1.5 %. An important reason for the differences in n values, curves and resulting estimates of Ea could be found in data points that clearly appear as outliers in one projection but less so in the other projection. We argue here that the non-contracted side of the framework in the two projections should always be assessed, especially for data points that appear as outliers. At least, one should consider the additional uncertainty of the projection and assess the robustness of the results in both projections.

Robust estimation of charge carrier diffusivity using transient photoluminescence microscopy.

Transient microscopy has emerged as a powerful tool for imaging the diffusion of excitons and free charge carriers in optoelectronic materials. In many excitonic materials, extraction of diffusion coefficients can be simplified because of the linear relationship between signal intensity and local excited state population. However, in materials where transport is dominated by free charge carriers, extracting diffusivities accurately from multidimensional data is complicated by the nonlinear dependence of the measured signal on the local charge carrier density. To obtain accurate estimates of charge carrier diffusivity from transient microscopy data, statistically robust fitting algorithms coupled to efficient 3D numerical solvers that faithfully relate local carrier dynamics to raw experimental measurables are sometimes needed. Here, we provide a detailed numerical framework for modeling the spatiotemporal dynamics of free charge carriers in bulk semiconductors with significant solving speed reduction and for simulating the corresponding transient photoluminescence microscopy data. To demonstrate the utility of this approach, we apply a fitting algorithm using a Markov chain Monte Carlo sampler to experimental data on bulk CdS and methylammonium lead bromide (MAPbBr3) crystals. Parameter analyses reveal that transient photoluminescence microscopy can be used to obtain robust estimates of charge carrier diffusivities in optoelectronic materials of interest, but that other experimental approaches should be used for obtaining carrier recombination constants. Additionally, simplifications can be made to the fitting model depending on the experimental conditions and material systems studied. Our open-source simulation code and fitting algorithm are made freely available to the scientific community.

Quantitative Bioreactor Monitoring of Intracellular Bacterial Metabolites in Clostridium autoethanogenum Using Liquid Chromatography-Isotope Dilution Mass Spectrometry.

We report a liquid chromatography–isotope dilution mass spectrometry method for the simultaneous quantification of 131 intracellular bacterial metabolites of Clostridium autoethanogenum. A comprehensive mixture of uniformly 13C-labeled internal standards (U-13C IS) was biosynthesized from the closely related bacterium Clostridium pasteurianum using 4% 13C–glucose as a carbon source. The U-13C IS mixture combined with 12C authentic standards was used to validate the linearity, precision, accuracy, repeatability, limits of detection, and quantification for each metabolite. A robust-fitting algorithm was employed to reduce the weight of the outliers on the quantification data. The metabolite calibration curves were linear with R2 ≥ 0.99, limits of detection were ≤1.0 μM, limits of quantification were ≤10 μM, and precision/accuracy was within RSDs of 15% for all metabolites. The method was subsequently applied for the daily monitoring of the intracellular metabolites of C. autoethanogenum during a CO gas fermentation over 40 days as part of a study to optimize biofuel production. The concentrations of the metabolites were estimated at steady states of different pH levels using the robust-fitting mathematical approach, and we demonstrate improved accuracy of results compared to conventional regression. Metabolic pathway analysis showed that reactions of the incomplete (branched) tricarboxylic acid “cycle” were the most affected pathways associated with the pH shift in the bioreactor fermentation of C. autoethanogenum and the concomitant changes in ethanol production.

Inversion probability enhancement of all-fiber CDWL by noise modeling and robust fitting.

Accurate power spectrum analysis of weak backscattered signals are the primary constraint in long-distance coherent Doppler wind lidar (CDWL) applications. To study the atmospheric boundary layer, an all-fiber CDWL with 300µJ pulse energy is developed. In principle, the coherent detection method can approach the quantum limit sensitivity if the noise in the photodetector output is dominated by the shot noise of the local oscillator. In practice, however, abnormal power spectra occur randomly, resulting in error estimation and low inversion probability. This phenomenon is theoretically analyzed and shown to be due to the leakage of a time-varying DC noise of the balanced detector. Thus, a correction algorithm with accurate noise modeling is proposed and demonstrated. The accuracy of radial velocity, carrier-to-noise ratio (CNR), and spectral width are improved. In wind profiling process, a robust sine-wave fitting algorithm with data quality control is adopted in the velocity-azimuth display (VAD) scanning detection. Finally, in 5-day continuous wind detection, the inversion probability is tremendously enhanced. As an example, it is increased from 8.6% to 52.1% at the height of 4 km.

Calibration of Spectral Imaging Devices With Oxygenation-Controlled Phantoms: Introducing a Simple Gel-Based Hemoglobin Model

An optical phantom model with stable oxygen saturation (StO2) and optical properties (OPs) is the key for quick and accurate calibration of spectral imaging devices. Toward this goal, we have developed gel-based phantoms using Agarose, polystyrene microsphere, purified hemoglobin and yeast. Theoretical values of OPs were calculated by applying Beer Lambert law and Mie theory whereas a robust fitting algorithm was used to extract StO2. Stability of OPs and StO2 in the phantoms was validated experimentally over a period of two weeks and the effect of pre-heating at 65o C degrees on StO2 was observed. Multi-spectral imaging (750, 780, 850 and 945 nm) of the phantoms were also performed on the FDA-approved commercial system to demonstrate the utility of the phantoms.

Semantic mapping for orchard environments by merging two‐sides reconstructions of tree rows

AbstractMeasuring semantic traits for phenotyping is an essential but labor‐intensive activity in horticulture. Researchers often rely on manual measurements which may not be accurate for tasks, such as measuring tree volume. To improve the accuracy of such measurements and to automate the process, we consider the problem of building coherent three‐dimensional (3D) reconstructions of orchard rows. Even though 3D reconstructions of side views can be obtained using standard mapping techniques, merging the two side‐views is difficult due to the lack of overlap between the two partial reconstructions. Our first main contribution in this paper is a novel method that utilizes global features and semantic information to obtain an initial solution aligning the two sides. Our mapping approach then refines the 3D model of the entire tree row by integrating semantic information common to both sides, and extracted using our novel robust detection and fitting algorithms. Next, we present a vision system to measure semantic traits from the optimized 3D model that is built from the RGB or RGB‐D data captured by only a camera. Specifically, we show how canopy volume, trunk diameter, tree height, and fruit count (FC) can be automatically obtained in real orchard environments. The experiment results from multiple data sets quantitatively demonstrate the high accuracy and robustness of our method.

Accurate extraction of brick shapes in masonry walls from dense terrestrial laser scanning point cloud

Masonry structures commonly composed of a large amount of bricks or stones. Making an inventory of bricks in masonry walls is of great importance in the fields of building documentation, change detection and pattern recognition. This paper explores the problem of brick shape extraction for point cloud data with outliers as gathered by a laser scanner. For this purpose, we establish the basic brick shape model. Next, dimension reduction from 3D to 2D is done using principal component analysis (PCA). Traditionally, the bounding rectangle, as well as four vertices of the brick, are estimated by computing the maximum and minimum values of the coordinates of the brick points in 2D space. However, the existence of outliers in brick point cloud is common that may occur as random or systematic errors. If so, the brick shape extraction results are unreliable. To address this problem, we present a robust rectangle fitting algorithm for dense point cloud that uses PCA. Theoretically, the rectangle fitting model is established based on the geometry of the brick itself. We introduce the slack variable and critical rectangle to improve the anti-noise capability. The accuracy and consistency of the proposed robust rectangle fitting is evaluated by analysing single brick. Afterward, the method implemented on two patches of a masonry wall and the performance is demonstrated.

Robust cylinder fitting in laser scanning point cloud data

Cylinders play a vital role in representing geometry of environmental and man-made structures. Most existing cylinder fitting methods perform well for outlier free data sampling a full cylinder, but are not reliable in the presence of outliers or incomplete data. Point Cloud Data (PCD) are typically outlier contaminated and incomplete. This paper presents two robust cylinder fitting algorithms for PCD that use robust Principal Component Analysis (PCA) and robust regression. Experiments with simulated and real data show that the new methods are efficient (i) in the presence of outliers, (ii) for partially and fully sampled cylinders, (iii) for small and large numbers of points, (iv) for various sizes: radii and lengths, and (v) for cylinders with unequal radii at their ends. A simulation study consisting of 1000 cylinders of 1 m radius with 20% clustered outliers, reveals that a PCA based method fits cylinders with an average radius of 2.84 m and with a principal axis biased by outliers of 9.65° on average, whereas the proposed robust method correctly estimates the average radius of 1 m with only 0.27° bias angle in the principal axis.

A Robust Feature Extraction and Parameterized Fitting Algorithm for Bottom‐Side Oblique and Vertical Incidence Ionograms

AbstractAutomatic processing of ionograms to extract ionospheric propagation characteristics and electron density profile parameters is an important enabling step toward constructing real time data‐assimilative models of the ionosphere. A robust and reliable feature extraction and fitting algorithm that supports both oblique and vertical incidence ionograms has recently been developed to enhance the regional ionospheric model for Australia's Jindalee Operational Radar Network. The so‐called DST‐IIP algorithm is an autoscaling technique based on a constrained quasi‐parabolic segment profile, which is modified from its climatological estimate to fit a set of key peak, edge, and line features in the ionogram image, representing the E, sporadic‐E (Es), and F2 layers. The F2 fitting, in particular, is performed in the ionogram domain, using analytic ray‐tracing and homing to produce a synthetic trace that reproduces the image features. Following thorough testing on a large database of midlatitude Australian ionograms, the DST‐IIP algorithm now runs routinely on‐board DST Group's Digital Oblique Receiving System. This paper provides an overview of the technique, along with sample results and performance statistics.

A Spatiotemporal Contextual Model for Forest Fire Detection Using Himawari-8 Satellite Data

Two of the main remote sensing data resources for forest fire detection have significant drawbacks: geostationary Earth Observation (EO) satellites have high temporal resolution but low spatial resolution, whereas Polar-orbiting systems have high spatial resolution but low temporal resolution. Therefore, the existing forest fire detection algorithms that are based on a single one of these two systems have only exploited temporal or spatial information independently. There are no approaches yet that have effectively merged spatial and temporal characteristics to detect forest fires. This paper fills this gap by presenting a spatiotemporal contextual model (STCM) that fully exploits geostationary data’s spatial and temporal dimensions based on the data from Himawari-8 Satellite. We used an improved robust fitting algorithm to model each pixel’s diurnal temperature cycles (DTC) in the middle and long infrared bands. For each pixel, a Kalman filter was used to blend the DTC to estimate the true background brightness temperature. Subsequently, we utilized the Otsu method to identify the fire after using an MVC (maximum value month composite of NDVI) threshold to test which areas have enough fuel to support such events. Finally, we used a continuous timeslot test to correct the fire detection results. The proposed algorithm was applied to four fire cases in East Asia and Australia in 2016. A comparison of detection results between MODIS Terra and Aqua active fire products (MOD14 and MYD14) demonstrated that the proposed algorithm from this paper effectively analyzed the spatiotemporal information contained in multi-temporal remotely sensed data. In addition, this new forest fire detection method can lead to higher detection accuracy than the traditional contextual and temporal algorithms. By developing algorithms that are based on AHI measurements to meet the requirement to detect forest fires promptly and accurately, this paper assists both emergency responders and the general public to mitigate the damage of forest fires.

Estimating option-implied distributions in illiquid markets and implementing the Ross recovery theorem

In this research we describe how forward-looking information on the statistical properties of an asset can be extracted directly from options market data and demonstrate how this can be practically applied to portfolio management. Although the extraction of a forward-looking risk-neutral distribution is well-established in the literature, the issue of estimating distributions in an illiquid market is not. We use the deterministic SVI volatility model to estimate weekly risk-neutral distribution surfaces. The issue of calibration with sparse and noisy data is considered at length and a simple but robust fitting algorithm is proposed. We further attempt to extract real-world implied information by implementing the recovery theorem introduced by Ross (2015). Recovery is an ill-posed problem that requires careful consideration. We describe a regularisation methodology for extracting real-world implied distributions and implement this method on a history of SVI volatility surfaces. We analyse the first four moments from the implied risk-neutral and real-world implied distributions and use them as signals within a simple tactical asset allocation framework, finding promising results.Keywords: Option-implied distributions; SVI volatility model; Ross recovery theorem; Tikhonov regularisation; illiquid derivative markets

FPGA-based architecture of a real-time SIFT matcher and RANSAC algorithm for robotic vision applications

A fundamental problem in computer vision is finding correspondences between features in pairs of similar images. By comparing feature descriptors instead of pixel intensities, the matching capability is significantly increased. Keypoints extracted by Scale-Invariant Feature Transform (SIFT) provide superior matching ability, however, a small proportion of false corresponcences is always inevitable. The exemption of false matches is achieved using robust fitting algorithms, with RANSAC (random sample consensus) being a popular one. SIFT and RANSAC are computationally demanding and time consuming algorithms. When the target application operates in real-time, conventional approaches based on personal computers usually fail to meet the requirements. In this paper, an FPGA-based architecture for real-time SIFT matching and RANSAC algorithm is presented. The proposed scheme is applied to identify the correspondences between point features across consecutive video frames and reject the false matches. The architecture is verified using the DE2i-150 development board. Using Cyclone IV technology, the system supports a processing rate of 40fps for VGA resolution and therefore meets real-time requirements.

ROBUST CYLINDER FITTING IN THREE-DIMENSIONAL POINT CLOUD DATA

Abstract. This paper investigates the problems of cylinder fitting in laser scanning three-dimensional Point Cloud Data (PCD). Most existing methods require full cylinder data, do not study the presence of outliers, and are not statistically robust. But especially mobile laser scanning often has incomplete data, as street poles for example are only scanned from the road. Moreover, existence of outliers is common. Outliers may occur as random or systematic errors, and may be scattered and/or clustered. In this paper, we present a statistically robust cylinder fitting algorithm for PCD that combines Robust Principal Component Analysis (RPCA) with robust regression. Robust principal components as obtained by RPCA allow estimating cylinder directions more accurately, and an existing efficient circle fitting algorithm following robust regression principles, properly fit cylinder. We demonstrate the performance of the proposed method on artificial and real PCD. Results show that the proposed method provides more accurate and robust results: (i) in the presence of noise and high percentage of outliers, (ii) for incomplete as well as complete data, (iii) for small and large number of points, and (iv) for different sizes of radius. On 1000 simulated quarter cylinders of 1m radius with 10% outliers a PCA based method fit cylinders with a radius of on average 3.63 meter (m); the proposed method on the other hand fit cylinders of on average 1.02 m radius. The algorithm has potential in applications such as fitting cylindrical (e.g., light and traffic) poles, diameter at breast height estimation for trees, and building and bridge information modelling.

Modeling Dormant Fruit Trees for Agricultural Automation

Dormant pruning of fruit trees is one of the most costly and labor‐intensive activities in specialty crop production. We present a system that solves the first step in the process of automated pruning: accurately measuring and modeling the fruit trees. Our system employs a laser sensor to collect observations of fruit trees from multiple perspectives, and it uses these observations to measure parameters needed for pruning. A split‐and‐merge clustering algorithm divides the collected data into three sets of points: trunk candidates, junction point candidates, and branches. The trunk candidates and junction point candidates are then further refined by a robust fitting algorithm that models as cylinders each segment of the trunk and primary branches. In this work, we focus on measuring the diameters of the primary branches and the trunk, which are important factors in dormant pruning and can be obtained directly from the cylindrical models. We show that the results are qualitatively satisfactory using synthetic and real data. Our experiments with three synthetic and three real apple trees of two different varieties showed that the system is able to identify the primary branches with an average accuracy of 98% and estimate their diameters with an average error of 0.6 cm. Although the current implementation of the system is too slow for large‐scale practical applications (it can measure approximately two trees per hour), our study shows that the proposed approach may serve as a fundamental building block of robotic pruners in the near future.

Estimating Option-Implied Distributions in Illiquid Markets and Implementing the Ross Recovery Theorem

We describe how forward-looking information on the statistical properties of an asset can be extracted directly from options market data and how this can be used practically in portfolio management. Although the extraction of a forward-looking risk-neutral distribution is well-established in the literature, the issue of estimation in an illiquid market is not. We use the deterministic SVI volatility model to estimate weekly risk-neutral distribution surfaces. The issue of calibration with sparse and noisy data is considered at length and a simple but robust fitting algorithm is proposed. Furthermore, we attempt to extract real-world implied information by implementing the recovery theorem introduced by Ross (2015). Recovery is an ill-posed problem that requires careful consideration. We describe a regularization methodology for extracting real-world implied distributions and implement this method on a history of SVI volatility surfaces. We analyse the first four moments from the implied risk-neutral and real-world implied distributions and use them as signals within a simple tactical asset allocation framework, finding promising results.

Algebraic method to speed up robust algorithms: example of laser-scanned point clouds

Surface reconstruction from point clouds generated by laser scanning technology has become a fundamental task in many fields of geosciences, such as robotics, computer vision, digital photogrammetry, computational geometry, digital building modelling, forest planning and operational activities. Point clouds produced by laser scanning, however, are limited due to the occurrence of occlusions, multiple reflectance and noise, and off-surface points (outliers), thus necessitating the need for robust fitting techniques. In this contribution, a fast, non-iterative and data invariant algebraic algorithm with constant O(1) complexity that fits planes to point clouds in the total least squares sense using Gaussian-type error distribution is proposed. The maximum likelihood estimator method is used, resulting in a multivariate polynomial system that is solved in an algebraic way. It is shown that for plane fitting when datasets are affected heavily by outliers, the proposed algebraic method can be embedded into the framework of robust methods like the Danish or the RANdom SAmple Consensus methods and computed in parallel to provide rigorous algebraic fitting with significantly reduced running times. Compared to the embedded traditional singular value decomposition and principal component analysis approaches, the performance of the proposed algebraic algorithm demonstrated its efficiency on both synthetic data and real laser-scanned measurements. The evaluation of a symbolic algebraic formula is practically independent of the values of its coefficients; however, the computation of the coefficients depends on the complexity of the data. Since the main advantage of the symbolic solution is its non-requirement of numerical iteration, the data complexity will have weak influence on the speed-up. The novelty of the proposed method is the use of algebraic technique in a robust plane fitting algorithm that could be applied to remote sensing data analysis/delineation/classification. In general, the method could be applied to most plane fitting problems in the geoscience field.