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Robust motion estimation and segmentation are two important interrelated tasks with a variety of applications. Traditional motion estimation and segmentation methods focus on normal scenarios. However, they may fail to robustly estimate and segment the moving objects because of the ill-defined edges and boundaries in these scenarios. In this paper, a robust framework for motion estimation and segmentation in adverse outdoor conditions is presented. In the proposed framework, a non-local total variation motion estimation method (NLTV- L 1 ) with a support weight function is proposed. It is efficient to preserve the edges and handle the smoothness near the edges using a coarse-to-fine strategy for adverse outdoor scenarios. To deal with the segmentation problem, we take advantage of the motion pattern based background-foreground layer extraction to segment the moving objects. Such a way effectively groups the pixels that move in a similar direction and thus these pixels can be extracted from the noisy background. In addition, our framework does not require any post-processing step to remove noise. We demonstrate that the proposed framework outperforms other state-of-the-art methods on two commonly used datasets (i.e., Middlebury and MPI Sintel) for motion estimation and segmentation. Moreover, the experiments on real outdoor benchmarks (i.e., Foggy Zurich, Traffic and CDnet2014) show the robustness and efficiency of our framework in adverse outdoor conditions. [ABSTRACT FROM AUTHOR]

Nonparametric univariate regression via wavelets is usually implemented under the assumptions of dyadic sample size, equally spaced fixed sample points, and i.i.d. normal errors. In this work, we propose, study and compare some wavelet based nonparametric estimation methods designed to recover a one-dimensional regression function for data that not necessary possess the above requirements. These methods use appropriate regularizations by penalizing the decomposition of the unknown regression function on a wavelet basis of functions evaluated on the sampling design. Exploiting the sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, we use some efficient proximal gradient descent algorithms, available in recent literature, for computing the estimates with fast computation times. Our wavelet based procedures, in both the standard and the robust regression case have favorable theoretical properties, thanks in large part to the separability nature of the (non convex) regularization they are based on. We establish asymptotic global optimal rates of convergence under weak conditions. It is known that such rates are, in general, unattainable by smoothing splines or other linear nonparametric smoothers. Lastly, we present several experiments to examine the empirical performance of our procedures and their comparisons with other proposals available in the literature. An interesting regression analysis of some real data applications using these procedures unambiguously demonstrate their effectiveness. [ABSTRACT FROM AUTHOR]

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Robustly fitting a linear model from outlier-contaminated data is an important and basic task in many scientific fields, and it is often tackled by consensus set maximization. There have been several studies on globally optimal methods for consensus set maximization, but most of them are currently confined to problems with small number of input observations and low outlier ratios. In this paper, we develop a globally optimal algorithm aiming at consensus set maximization to solve the robust linear model fitting problems with the unit-norm constraint, which is based on the branch-and-bound optimization framework. The unit-norm constraint is utilized to fix the unknown scale of linear model parameters, and we propose a compact representation of the unit-bounded searching domain to avoid introducing the additional non-linearity in the unit-norm constraint. The compact representation leads to a geometrically derived bound, which accelerates the calculation and enables the method to handle the problems with large number of observations. Experiments on both synthetic and real data show that the proposed algorithm outperforms existing globally optimal methods, especially in low dimensional problems with large number of input observations and high outlier ratios. The implementation of the source code is publicly available https://github.com/YiruWangYuri/Demo-for-GoCR. [ABSTRACT FROM AUTHOR]

Robust fitting is a basic technique and has been widely applied in photogrammetry and remote sensing, such as geometric correction. As known, typical robust estimators (include M-estimators, S-estimators, MM-estimators, etc.) often fail when outlier rate is higher than 50%, even if the outliers are uniformly distributed. In this article, we propose simple yet effective estimators, called adaptive M-estimators (AM-estimators). They are still robust under 80% of outliers. The proposed AM-estimators are very important supplements of M-estimators. Different from M-estimators, we use a varying parameter (shape-control parameter) instead of the original constant parameter in the weight function. The shape-control parameter decreases along with iterations in iteratively reweighted least squares, namely, AM-estimators are optimized in a coarse-to-fine manner. We adapt the proposed estimators into classical remote sensing and photogrammetry tasks, including mismatch removal, camera orientation (or called perspective-n-point), and point set registration to demonstrate their powers. Extensive synthetic and real experiments show that AM-estimators are superior to M-estimators, S-estimators, MM-estimators, and RANSAC-type methods. The source code of AM-estimators will be publicly available at https://ljy-rs.github.io/web.

Acoustic tomography methods belong to the class of nondestructive inspection techniques and are used in engineering applications. One of the main issues for these methods is the direct arrival, which can be noisy or can be affected by scattering or other propagation effects. In this paper, we present the mathematical deduction and analysis of the so-called robust mean traveltime curves—the median, p-percentiles, inter-quartile range and minimum absolute deviation—for homogeneous isotropic or elliptical anisotropic media. Robust mean traveltime curves are a simple model used to describe the variation of the traveltime statistical descriptors for the different gathering subsets as a function of a gather index, and generalize the mean traveltime curves introduced in the past to the case of robust statistics. These curves admit analytical expression for zonal isotropic and elliptical anisotropic media explored via rectangular or irregular acquisition geometries, and thus, apply to 2D acoustic transmission tomography experiments conducted in relatively homogeneous blocks. The robust mean traveltime curves are more resistant to the presence of outliers, and thus they are preferred to infer background velocity models which can be taken into account in the resolution of the tomographic inverse problem. The property of robust descriptors to find blocky solutions in presence of velocity heterogeneities is also illustrated. Finally, we show the application of this methodology to a granitic medium (Febex Project, Nagra, Switzerland).

Robust model fitting plays a vital role in computer vision, and research into algorithms for robust fitting continues to be active. Arguably the most popular paradigm for robust fitting in computer vision is consensus maximisation, which strives to find the model parameters that maximise the number of inliers. Despite the significant developments in algorithms for consensus maximisation, there has been a lack of fundamental analysis of the problem in the computer vision literature. In particular, whether consensus maximisation is "tractable" remains a question that has not been rigorously dealt with, thus making it difficult to assess and compare the performance of proposed algorithms, relative to what is theoretically achievable. To shed light on these issues, we present several computational hardness results for consensus maximisation. Our results underline the fundamental intractability of the problem, and resolve several ambiguities existing in the literature. [ABSTRACT FROM AUTHOR]

Maximum consensus robust fitting is a fundamental problem in many computer vision applications, such as vision-based robotic navigation and mapping. While exact search algorithms are computationally demanding, randomized algorithms are cheap but the solution quality is not guaranteed. Deterministic algorithms fill the gap between these two kinds of algorithms, which have better solution quality than randomized algorithms while being much faster than exact algorithms. In this article, we develop two highly efficient deterministic algorithms based on the alternating direction method of multipliers (ADMM) and proximal block coordinate descent (BCD) frameworks. Particularly, the proposed BCD algorithm is guaranteed convergent. Furthermore, on the slack variable in the BCD algorithm, which indicates the inliers and outliers, we establish some meaningful properties, such as support convergence within finite iterations and convergence to restricted strictly local minimizer. Compared with state-of-the-art algorithms, the new algorithms with initialization from a randomized or convex relaxed algorithm can achieve improved solution quality while being much more efficient (e.g., more than an order of magnitude faster). An application of the new ADMM algorithm in simultaneous localization and mapping (SLAM) has also been provided to demonstrate its effectiveness. Code for reproducing the results is available online.1 [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Usual fitting methods for the nested error linear regression model are known to be very sensitive to the effect of even a single outlier. Robust approaches for the unbalanced nested error model with proved robustness and efficiency properties, such as M-estimators, are typically obtained through iterative algorithms. These algorithms are often computationally intensive and require robust estimates of the same parameters to start the algorithms, but so far no robust starting values have been proposed for this model. This paper proposes computationally fast robust estimators for the variance components under an unbalanced nested error model, based on a simple robustification of the fitting-of-constants method or Henderson method III. These estimators can be used as starting values for other iterative methods. Our simulations show that they are highly robust to various types of contamination of different magnitude. [ABSTRACT FROM AUTHOR]

Data pits commonly appear in lidar-derived canopy height models (CHMs) owing to the penetration ability of airborne light detection and ranging (lidar) into tree crowns. They have a seriously negative effect on the quality of tree detection and subsequent biophysical measurements. In this study, we propose an algorithm based on robust locally weighted regression and robust z-scores for the construction of a pit-free CHM. A significant advantage of the new algorithm is that it is parameter free, which makes it efficient and robust for practical applications. Simulated and airborne lidar-derived data sets are employed to assess the performance of the new method for CHM construction, and its results are compared to those of three classical methods, namely the natural neighbor (NN) interpolation of the highest point method (HPM), mean filter, and median filter. The results from the simulated data set demonstrate that our algorithm is more accurate compared to the three classical methods for generating pit-free CHMs in the presence of data pits. CHM construction using the lidar-derived data set shows that, compared to the classical methods, the new method has a better ability to remove data pits as well as preserving the edges, shapes, and structures of canopy gaps and crowns. Moreover, the proposed method performs better compared to the classical methods in deriving plot-level maximum tree heights from CHMs. Thus, the new method shows high potential for pit-free CHM construction. [ABSTRACT FROM AUTHOR]

When sampling minimal subsets for robust parameter estimation, it is commonly known that obtaining an all-inlier minimal subset is not sufficient; the points therein should also have a large spatial extent. This paper investigates a theoretical basis behind this principle, based on a little known result which expresses the least squares regression as a weighted linear combination of all possible minimal subset estimates. It turns out that the weight of a minimal subset estimate is directly related to the span of the associated points. We then derive an analogous result for total least squares which, unlike ordinary least squares, corrects for errors in both dependent and independent variables. We establish the relevance of our result to computer vision by relating total least squares to geometric estimation techniques. As practical contributions, we elaborate why naive distance-based sampling fails as a strategy to maximise the span of all-inlier minimal subsets produced. In addition we propose a novel method which, unlike previous methods, can consciously target all-inlier minimal subsets with large spans. [ABSTRACT FROM AUTHOR]

Precise laser welding plays a fundamental role in the production of high-tech goods, particularly in precision engineering. In this working field, precise adjustment and compensation of positioning tolerances of the parts to be welded with respect to the laser beam is of paramount importance. This procedure mostly requires tedious and error-prone manual adjustment, which additionally results in a sharp increase in production costs. We therefore developed a system which automates and thus accelerates this procedure significantly. To this end, the welding machine is equipped with a camera to acquire high resolution images of the parts to be welded. In addition, a software framework is developed which enables precise automatic position detection of these parts and adjusts the position of the welding contour correspondingly. As a result, the machine is rapidly prepared for welding, and it is much more flexible in adapting to unknown parts.This paper describes the entire concept of extending a conventional welding machine with means for image acquisition and position estimation. In addition to this description, the algorithms, the results of an evaluation of position estimation, and a final welding result are presented.

Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. Magn Reson Med 70:358-369, 2013. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Abstract: Diffusion tensor imaging (DTI) provides information about the microstructure in the brain and spinal cord. While new neuroimaging techniques have significantly advanced the accuracy and sensitivity of DTI of the brain, the quality of spinal cord DTI data has improved less. This is in part due to the small size of the spinal cord (ca. 1cm diameter) and more severe instrumental (e.g. eddy current) and physiological (e.g. cardiac pulsation) artefacts present in spinal cord DTI. So far, the improvements in image quality and resolution have resulted from cardiac gating and new acquisition approaches (e.g. reduced field-of-view techniques). The use of retrospective correction methods is not well established for spinal cord DTI. The aim of this paper is to develop an improved post-processing pipeline tailored for DTI data of the spinal cord with increased quality. For this purpose, we compared two eddy current and motion correction approaches using three-dimensional affine (3D-affine) and slice-wise registrations. We also introduced a new robust-tensor-fitting method that controls for whole-volume outliers. Although in general 3D-affine registration improves data quality, occasionally it can lead to misregistrations and biassed tensor estimates. The proposed robust tensor fitting reduced misregistration-related bias and yielded more reliable tensor estimates. Overall, the combination of slice-wise motion correction, eddy current correction, and robust tensor fitting yielded the best results. It increased the contrast-to-noise ratio (CNR) in FA maps by about 30% and reduced intra-subject variation in fractional anisotropy (FA) maps by 18%. The higher quality of FA maps allows for a better distinction between grey and white matter without increasing scan time and is compatible with any multi-directional DTI acquisition scheme. [Copyright &y& Elsevier]

Abstract: This work addresses the matching of a 3D deformable face model to 2D images through a 2.5D Active Appearance Models (AAM). We propose a 2.5D AAM that combines a 3D metric Point Distribution Model (PDM) and a 2D appearance model whose control points are defined by a full perspective projection of the PDM. The advantage is that, assuming a calibrated camera, 3D metric shapes can be retrieved from single view images. Two model fitting algorithms and their computational efficient approximations are proposed: the Simultaneous Forwards Additive (SFA) and the Normalization Forwards Additive (NFA), both based on the Lucas–Kanade framework. The SFA algorithm searches for shape and appearance parameters simultaneously whereas the NFA projects out the appearance from the error image and searches only for the shape parameters. SFA is therefore more accurate. Robust solutions for the SFA and NFA are also proposed in order to take into account the self-occlusion or partial occlusion of the face. Several performance evaluations for the SFA, NFA and theirs efficient approximations were performed. The experiments include evaluating the frequency of converge, the fitting performance in unseen data and the tracking performance in the FGNET Talking Face sequence. All results show that the 2.5D AAM can outperform both the 2D+3D combined models and the 2D standard methods. The robust extensions to occlusion were tested on a synthetic sequence showing that the model can deal efficiently with large head rotation. [Copyright &y& Elsevier]

Abstract: An analytical equation of state is commonly fitted to the energy versus volume theoretical data to determine the equilibrium properties and obtain derivatives. A weighted average of polynomials is shown to extract optimally the information contained in the data set and provide conservative and meaningful error bars. The fitting becomes problematic when the data contains noise and small jumps. We examine some techniques that can detect and deal with those problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes an active model with a robust texture model built on-line. The model uses one camera and it is able to operate without active illumination. The texture model is defined by a series of clusters, which are built in a video sequence using previously encountered samples. This model is used to search for the corresponding element in the following frames. An on-line clustering method, named leaderP is described and evaluated on an application of face tracking. A 20-point shape model is used. This model is built offline, and a robust fitting function is used to restrict the position of the points. Our proposal is to serve as one of the stages in a driver monitoring system. To test it, a new set of sequences of drivers recorded outdoors and in a realistic simulator has been compiled. Experimental results for typical outdoor driving scenarios, with frequent head movement, turns and occlusions are presented. Our approach is tested and compared with the Simultaneous Modeling and Tracking (SMAT) [1], and the recently presented Stacked Trimmed Active Shape Model (STASM) [2], and shows better results than SMAT and similar fitting error levels to STASM, with much faster execution times and improved robustness. [ABSTRACT FROM AUTHOR]

Abstract: Range sensors, in particular time-of-flight and stereo cameras, are being increasingly used for applications such as robotics, automotive, human-machine interface and virtual reality. The ability to recover the geometrical structure of visible surfaces is critical for scene understanding. Typical structured indoor or urban scenes are often represented via compositional models comprising multiple planar surface patches. The RANSAC robust regression algorithm is the most popular technique to date for extracting individual planar patches from noisy data sets containing multiple surfaces. Unfortunately, RANSAC fails to produce reliable results in situations with two nearby patches of limited extent, where a single plane crossing through the two patches may contain more inliers than the “correct” models. This is the case of steps, curbs, or ramps, which represent the focus of our research for the impact they can have on cars’ safe parking systems or robot navigation. In an effort to improve the quality of regression in these cases, we propose a modification of the RANSAC algorithm, dubbed CC-RANSAC, that only considers the largest connected components of inliers to evaluate the fitness of a candidate plane. We provide experimental evidence that CC-RANSAC may recover the planar patches composing a typical step or ramp with substantially higher accuracy than the traditional RANSAC algorithm. [ABSTRACT FROM AUTHOR]

Two theorems for robust density fitting are proved: A. For a given electron density, the best robust density fitting approximation to the Coulomb electron repulsion energy results from the unconstrained Coulomb metric fit, B. For infinite periodic systems, the necessary condition for correct long-range behavior of any robust density fitting approximation of the Coulomb electron repulsion energy is the exact reproduction of the number of electrons. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a robust on-line appearance modeling and tracking method, based on simultaneous modeling and tracking (SMAT). The appearance model is defined by a series of clusters, built in a video sequence using previously encountered samples. This model is used to search for the corresponding element in the following frames. Three alternative incremental clustering methods are proposed to increase the robustness and description capabilities of the model. The proposal is evaluated on an application of face tracking for driver monitoring. The test set comprises sequences of drivers recorded outdoors and in a truck simulator, which contain examples of occlusions and self-occlusions, as well as illumination changes. The performance is evaluated and compared with that of the original SMAT proposal and the recently presented stacked trimmed active shape model (STASM). Our proposal shows better results than the original SMAT and similar fitting error levels to STASM, with much faster execution times and better robustness to self-occlusions. [ABSTRACT FROM AUTHOR]

Detection of lane markings based on a camera sensor can be a low-cost solution to lane departure and curve-over-speed warnings. A number of methods and implementations have been reported in the literature. However, reliable detection is still an issue because of cast shadows, worn and occluded markings, variable ambient lighting conditions, for example. We focus on increasing detection reliability in two ways. First, we employed an image feature other than the commonly used edges: ridges, which we claim addresses this problem better. Second, we adapted RANSAC, a generic robust estimation method, to fit a parametric model of a pair of lane lines to the image features, based on both ridgeness and ridge orientation. In addition, the model was fitted for the left and right lane lines simultaneously to enforce a consistent result. Four measures of interest for driver assistance applications were directly computed from the fitted parametric model at each frame: lane width, lane curvature, and vehicle yaw angle and lateral offset with regard the lane medial axis. We qualitatively assessed our method in video sequences captured on several road types and under very different lighting conditions. We also quantitatively assessed it on synthetic but realistic video sequences for which road geometry and vehicle trajectory ground truth are known. [ABSTRACT FROM AUTHOR]

A single-camera iris-tracking and remapping approach based on passive computer vision is presented. Tracking is aimed at obtaining accurate and robust measurements of the iris/pupil position. To this purpose, a robust method for ellipse fitting is used, employing search constraints so as to achieve better performance with respect to the standard RANSAC algorithm. Tracking also embeds an iris localization algorithm (working as a bootstrap multiple-hypotheses generation step), and a blink detector that can detect voluntary eye blinks in human-computer interaction applications. On-screen remapping incorporates a headtracking method capable of compensating for small user-head movements. The approach operates in real time under different light conditions and in the presence of distractors. An extensive set of experiments is presented and discussed. In particular, an evaluation method for the choice of layout of both hardware components and calibration points is described. Experiments also investigate the importance of providing a visual feedback to the user, and the benefits gained from performing head compensation, especially during image-to-screen map calibration. [ABSTRACT FROM AUTHOR]

Abstract: An algorithm is proposed, based principally on an earlier proposition of Flaud and co-workers [Mol. Phys. 32 (1976) 499], that inverts the information contained in uniquely assigned experimental rotational–vibrational transitions in order to obtain measured active rotational–vibrational energy levels (MARVEL). The procedure starts with collecting, critically evaluating, selecting, and compiling all available measured transitions, including assignments and uncertainties, into a single database. Then, spectroscopic networks (SN) are determined which contain all interconnecting rotational–vibrational energy levels supported by the grand database of the selected transitions. Adjustment of the uncertainties of the lines is performed next, with the help of a robust weighting strategy, until a self-consistent set of lines and uncertainties is achieved. Inversion of the transitions through a weighted least-squares-type procedure results in MARVEL energy levels and associated uncertainties. Local sensitivity coefficients could be computed for each energy level. The resulting set of MARVEL levels is called active as when new experimental measurements become available the same evaluation, adjustment, and inversion procedure should be repeated in order to obtain more dependable energy levels and uncertainties. MARVEL is tested on the example of the H2 17O isotopologue of water and a list of 2736 dependable energy levels, based on 8369 transitions, has been obtained. [Copyright &y& Elsevier]

Abstract: This paper presents a new method for robust recognition and separation of outliers in image data of microstructures with subsequent precise fitting of geometrical primitives to the measurement points. The known iterative approaches for robust fitting often yield unsatisfactory results if the start conditions are influenced by outliers. Thus, in a first step the outlier detection and filtering in the coordinate space is done by the Hough transform. The geometrical primitive is calculated by least squares fitting of orthogonal distances to the outlier free coordinates with high and certified accuracy. The performance of this approach is exemplified on the geometrical primitive circle with different outlier populations which are typical for industrial applications. The originality consists in the combination of a recognition approach for robust feature detection with a least squares fitting for highly precise results. This approach has an enormous relevance for applications of non-contact dimensional metrology, where the existence of dirt and burr leads to a high measurement uncertainty. [Copyright &y& Elsevier]

Modelling mixtures of multivariate t-distributions are usually used instead of Gaussian mixture models as a robust approach, when one fits a set of continuous multivariate data which have wider tail than Gaussian''s or atypical observations. Further, the multivariate data set often involves missing values, which cannot be circumvented and then the missing values must be handled properly. In this paper, we present a framework for fitting mixtures of multivariate t-distributions when data are missing at random on the basis of maximum likelihood estimation. We resort to EM algorithm both for the estimation of mixture components and for coping with missing values. The iterative algorithm obtained can be applied to an extensive range of unsupervised clustering as well as supervised discrimination. [Copyright &y& Elsevier]

The registration of two event characteristics, for example, e (energy) and t (time), gives us a two-dimensional experimental distribution A( e, t), where the extraction of the information of interest stumbles upon the absence of the appropriate parametrical model. A significant advantage of using the autocorrelation spectrometer of delayed coincidences is the possibility to determine the scintillator decay time τ from an energy dependence E = g( t, τ), which, unlike the classical decay time model N( t) = f( t, τ), allows us to establish its parametrical correspondence to some elements of the 2-dimensional data and so to estimate τ by a procedure of the robust fitting which automatically suppresses the impact of parts of data not adequate to the model. [ABSTRACT FROM AUTHOR]

Three-dimensional light detection and ranging (LiDAR) point clouds acquired from unmanned aerial vehicles (UAVs) represent a relatively new type of remotely sensed data. Point cloud density of thousands of points per square meter with survey-grade accuracy makes the UAV laser scanning (ULS) a very suitable tool for detailed mapping of forest environment. We used RIEGL VUX-SYS to scan forest stands of Norway spruce and Scots pine, the two most important economic species of central European forests, and evaluated the suitability of point clouds for individual tree stem detection and stem diameter estimation in a fully automated workflow. We segmented tree stems based on point densities in voxels in subcanopy space and applied three methods of robust circle fitting to fit cross-sections along the stems: (1) Hough transform; (2) random sample consensus (RANSAC); and (3) robust least trimmed squares (RLTS). We detected correctly 99% and 100% of all trees in research plots for spruce and pine, respectively, and were able to estimate diameters for 99% of spruces and 98% of pines with mean bias error of −0.1 cm (−1%) and RMSE of 6.0 cm (19%), using the best performing method, RTLS. Hough transform was not able to fit perimeters in unfiltered and often incomplete point representations of cross-sections. In general, RLTS performed slightly better than RANSAC, having both higher stem detection success rate and lower error in diameter estimation. Better performance of RLTS was more pronounced in complicated situations, such as incomplete and noisy point structures, while for high-quality point representations, RANSAC provided slightly better results. [ABSTRACT FROM AUTHOR]

Spectroscopic data sets often contain a significant number of outliers due to effects such as misassignments, trial assignments, or local perturbations. Standard fitting routines can be made robust to such outliers by the method of iteratively reweighted least squares. It is proposed here that the weight of datum i in a give iteration is given by wi=1/(σi2+αri2), where σi is the standard deviation for the idealized distribution without outliers, and ri is the residual from the previous iteration. The value of α should depend on the fractional number of outliers and the size of their residuals, but a standard value of α=1/3 is suggested for spectroscopic applications. [Copyright &y& Elsevier]