Robust Fitting of Circle Arcs

Guevara, Isidro Ladrón de; Muñoz, José Manuel Rodríguez; Cózar, O. D.; Blazquez, Elidia B.

doi:10.1007/s10851-010-0249-8

Cited by 34 publications

(18 citation statements)

References 29 publications

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“…This means that there may be some missing cross sections because they have few or no TLS points due to occlusion problems during the scanning process. The points included in each cross section i, after their 2D projection onto the horizontal plane, are adjusted to a circle using the robust adjustment method proposed by Ladrón de Guevara et al [44]. This method of adjustment is very suitable when outliers are foreseen due to TLS points not belonging to the tree stem (e.g., those located in epiphytic vegetation, nearby branches, or understory vegetation).…”

Section: Automatic Extraction Of Tree Level Informationmentioning

confidence: 99%

Developing Allometric Equations for Teak Plantations Located in the Coastal Region of Ecuador from Terrestrial Laser Scanning Data

Aguilar

Nemmaoui

Peñalver

et al. 2019

Forests

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Traditional studies aimed at developing allometric models to estimate dry above-ground biomass (AGB) and other tree-level variables, such as tree stem commercial volume (TSCV) or tree stem volume (TSV), usually involves cutting down the trees. Although this method has low uncertainty, it is quite costly and inefficient since it requires a very time-consuming field work. In order to assist in data collection and processing, remote sensing is allowing the application of non-destructive sampling methods such as that based on terrestrial laser scanning (TLS). In this work, TLS-derived point clouds were used to digitally reconstruct the tree stem of a set of teak trees (Tectona grandis Linn. F.) from 58 circular reference plots of 18 m radius belonging to three different plantations located in the Coastal Region of Ecuador. After manually selecting the appropriate trees from the entire sample, semi-automatic data processing was performed to provide measurements of TSCV and TSV, together with estimates of AGB values at tree level. These observed values were used to develop allometric models, based on diameter at breast height (DBH), total tree height (h), or the metric DBH2 × h, by applying a robust regression method to remove likely outliers. Results showed that the developed allometric models performed reasonably well, especially those based on the metric DBH2 × h, providing low bias estimates and relative RMSE values of 21.60% and 16.41% for TSCV and TSV, respectively. Allometric models only based on tree height were derived from replacing DBH by h in the expression DBH2 x h, according to adjusted expressions depending on DBH classes (ranges of DBH). This finding can facilitate the obtaining of variables such as AGB (carbon stock) and commercial volume of wood over teak plantations in the Coastal Region of Ecuador from only knowing the tree height, constituting a promising method to address large-scale teak plantations monitoring from the canopy height models derived from digital aerial stereophotogrammetry.

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Section: Automatic Extraction Of Tree Level Informationmentioning

confidence: 99%

Developing Allometric Equations for Teak Plantations Located in the Coastal Region of Ecuador from Terrestrial Laser Scanning Data

Aguilar

Nemmaoui

Peñalver

et al. 2019

Forests

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“…We note that the derivative of the absolute value function |φ S j | (left-hand side term of (2.8)) is not defined at zero. A more stable alternative to the sign function used here would be based on the left-and right-side partial derivatives as suggested by [38]. The volume preserving term generalizes the commonly used balloon term [12], where the scalar A diff A j − A 0 j determines both the size and the direction (expansion or contraction) of the evolution of φ S j and its respective boundary (zero-level).…”

Section: Level-set-based Shape Morphingmentioning

confidence: 99%

Statistical Shape Analysis of Neuroanatomical Structures via Level-Set--based Shape Morphing

Raviv¹,

Gao²,

Levitt³

et al. 2014

SIAM J. Imaging Sci.

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Groupwise statistical analysis of the morphometry of brain structures plays an important role in neuroimaging studies. Nevertheless, most morphometric measurements are often limited to volume and surface area, as further morphological characterization of anatomical structures poses a significant challenge. In this paper, we present a method that allows the detection, localization, and quantification of statistically significant morphological differences in complex brain structures between populations. This is accomplished by a novel level-set framework for shape morphing and a multishape dissimilarity-measure derived by a modified version of the Hausdorff distance. The proposed method does not require explicit one-to-one point correspondences and is fast, robust, and easy to implement regardless of the topological complexity of the anatomical surface under study. The proposed model has been applied to well-defined regions of interest using both synthetic and real data sets. This includes the corpus callosum, striatum, caudate, amygdala-hippocampal complex, and superior temporal gyrus. These structures were selected for their importance with respect to brain regions implicated in a variety of neurological disorders. The synthetic databases allowed quantitative evaluations of the method. Results obtained with real clinical data of Williams syndrome and schizophrenia patients agree with published findings in the psychiatry literature. A preliminary version of this paper appeared as Statistical shape analysis for population studies via level-set based shape morphing in the proceedings Computer Vision-ECCV 2012.interest, the morphometric measures are often limited to volume and surface area, as well as other quantitative measures such as curvature, smoothness, and thickness. Yet, these features provide only a partial description of the anatomy and are often insufficient to define a clear distinction between populations.Deformation-based morphometry (DBM) methods, e.g., tensor-based morphometry (TBM), and voxel-based morphometry (VBM) are image analysis tools for identifying regional structural differences from the gradients (Jacobian matrices) of deformation fields [1,16]. In its classical form, VBM does not refer explicitly to specific anatomical structures but considers images as continuous scalar measurements and tests for local differences at a predefined spatial scale. The art of setting the smoothness kernel, which determines the scale at which spatial anatomical differences can be expressed, is a major limitation in VBM [77,78]. Nevertheless, VBM methods gain their popularity in morphological studies, since they work directly on the grayscale images without having to extract the boundaries of particular structures of interest.The shape of a structure, however, often provides rich anatomical characteristics, which may allow one to distinguish between groups of subjects, and could be related to differences in cognitive functioning, development, or neurological symptoms, for example, in cortical folding studies [7...

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“…Many fields in science and technology are faced with the problem of fitting a surface to a set of 3D data. This problem is also investigated in a variety of 2D cases in which fitting a quadratic surface to a set of data is desired [1][2][3][4][5]. Quadratic surfaces almost fit every set of 3D data [6] which have a wide range of application such as 3D reconstruction [7], pose estimation [8], restricted stereo correspondence problem [9] and object recognition analysis and sensor calibration [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Robust ellipsoid fitting method based on optimization of a novel nonlinear cost function in navigation systems

Mirzaei

Hosseini

2019

J Braz. Soc. Mech. Sci. Eng.

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Low-cost sensors based on micro-electro-mechanical systems (MEMS) are typically used for attitude determination in navigation systems especially magnetometer which is used for heading determination. The measured value of the MEMS magnetometer is subjected to different kinds of error such as random noise, constant bias, non-orthogonality, scale factor deviation and more importantly hard iron and soft iron effects. Therefore, in order to reach more accurate measurement, highprecision calibration is needed. One of the most common methods for calibrating MEMS magnetic sensors is least squares ellipsoid fitting. But, the common least squares ellipsoid fitting method can be inefficient for real-time applications in the presence of colored noise and outliers. In this paper, a modified ellipsoid fitting method is proposed in which a nonlinear optimization is developed to minimize a novel cost function. In the cost function of the proposed robust method, the effect of outliers and noise is considered and the standard deviation of the data is kept minimum. Finally, the efficiency of the new algorithms is demonstrated through the experimental results.

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Robust Fitting of Circle Arcs

Cited by 34 publications

References 29 publications

Developing Allometric Equations for Teak Plantations Located in the Coastal Region of Ecuador from Terrestrial Laser Scanning Data

Developing Allometric Equations for Teak Plantations Located in the Coastal Region of Ecuador from Terrestrial Laser Scanning Data

Statistical Shape Analysis of Neuroanatomical Structures via Level-Set--based Shape Morphing

Robust ellipsoid fitting method based on optimization of a novel nonlinear cost function in navigation systems

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