A fast robust geometric fitting method for parabolic curves

López‐Rubio, Ezequiel; Thurnhofer‐Hemsi, Karl; Blázquez-Parra, Elidia Beatriz; Cózar-Macías, Óscar David de; Ladrón-de-Guevara-Muñoz, M. Carmen

doi:10.1016/j.patcog.2018.07.019

Cited by 12 publications

(2 citation statements)

References 40 publications

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“…Song et al introduced the Levenberg Marquardt algorithm to manage the fitting of horizontal and vertical curve transitions [12]. Lopez-Rubio et al fit a parabola based on the minimum absolute error [13]. Sa et al fitted a buried-hole conic model based on a circular curve [14].…”

Section: Introductionmentioning

confidence: 99%

Automatic Identification and Intelligent Optimization of Tunnel-Free Curve Reconfiguration

Wang

Shi

et al. 2022

Symmetry

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Extracting complete cross-sectional geometric features from the large amount of point cloud data acquired by laser scanners plays an important part in the detection of deformations in tunnel inspection projects. Tunnel cross-sections have symmetrical geometric features, and information is traditionally collected manually. The traditional manual extraction of point clouds is inefficient and limited by the subjectivity of the operators when addressing the problems. This paper proposes a new algorithm for the automatic identification of tunnel lining section curves, the rapid separation of common interference targets, and the optimization of curve geometry features. The innovation of this approach lies in the combination of B-spline and Euclidean clustering methods and the comprehensive evaluation of the denoising results in terms of precision, recall, F-score, and rand index (RI). In this way, the automatically extracted health point cloud data are refitted to optimize the tunnel profile model.

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Section: Introductionmentioning

confidence: 99%

Automatic Identification and Intelligent Optimization of Tunnel-Free Curve Reconfiguration

Wang

Shi

et al. 2022

Symmetry

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“…To single out the related waveform, we transform the filtered signal into a quadratic form. A quadratic linear-parabolic model is then fitted to the transformed signal, using the curve fitting technique [2,3]. The fitting is assessed using four statistical parameters (weighted sum of squared residuals, R-square, adjusted R-square, and root mean squared error).…”

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confidence: 99%

A quadratic linear-parabolic model-based classification to detect epileptic EEG seizures

Quintero-Rincon,

D'Giano,

Batatia

2019

Preprint

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The two-point central difference is a common algorithm in biological signal processing and is particularly useful in analyzing physiological signals. In this paper, we develop a model-based classification method to detect epileptic seizures that relies on this algorithm to filter EEG signals.The underlying idea is to design an EEG filter that enhances the waveform of epileptic signals. The filtered signal is fitted to a quadratic linear-parabolic model using the curve fitting technique. The model fitting is assessed using four statistical parameters, which are used as classification features with a random forest algorithm to discriminate seizure and non-seizure events. The proposed method was applied to 66 epochs from the Children Hospital Boston database. Results show that the method achieves fast and accurate detection of epileptic seizures, with a 92% sensitivity, 96% specificity, and 94.1% accuracy.Epilepsy is a neurological disease that affects people of all ages. It is characterized by unpredictable seizures resulting from the hyperexcitability of neurons. The electroencephalogram (EEG) is the predominant modality to study cerebral activity. The analysis of EEG signals is nearly completely dependent on visual inspection by the physician to quantify or qualify the morphology of waves, their goal being the identification and classification of abnormal patterns in order to provide aid for an epilepsy diagnosis.This study proposes a simple, fast and adaptable method, implementable in real-time, to help physicians visually inspect EEG signals for epileptic seizure detection. The proposed method fits within the framework of model-based classification. It is based on the statistical parameters obtained from fitting a quadratic parabolic model to specifically filtered and transformed EEG signals. Precisely, the two-point central difference algorithm is used to build a filter for the EEG signals. The filtered signal is subsequently represented using a quadratic linear-parabolic model, using the curve fitting approach. Four statistical parameters are then calculated to characterize the model fitting. These parameters are considered as a feature-vector in the classification stage.The literature abounds with research work dealing with the detection of epileptic seizure onset. Various methods and techniques have been proposed for this purpose. Many existing methods fit within the large framework of the feature-based machine learning approach.The two-point central difference algorithm has proven useful in analyzing physiological signals, with various medical applications reported in the literature. A typical work has been reported by Frei et al. to detect epileptiform discharges

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