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Hyperspectral image analysis for subcutaneous veins localization
Published in Ahmad Fadzil Mohamad Hani, Dileep Kumar, Optical Imaging for Biomedical and Clinical Applications, 2017
Aamir Shahzad, Mohamad Naufal Mohamad Saad, Fabrice Meriaudeau, Aamir Saeed Malik
Figure 7.16 depicts the classification of skin tones into four different classes using FCM classifier. The membership function is constructed by applying Gaussian curve fitting to the dataset. The process of curve fitting is used to construct a mathematical function or curve to infer the value of function where data points are not available [29]. It is also used to visualize the data clustering results [30]. Curve fitting can be best fit or exact fit, based on the number of data points and parameters. In exact fitting (often called interpolation) curve passes through every point, but it is suitable only for small number of parameters. The best-fit curves do not pass through every possible point but the value of data point is estimated on curve keeping it close enough to exact value of data point. The residual error is made as small as possible in best-fit curves [31–33].
Curve Fitting and Interpolation
Published in Ramin S. Esfandiari, Numerical Methods for Engineers and Scientists Using MATLAB®, 2017
An available set of data can be used for different purposes. In some cases, the data is represented by a function, which in turn can be used for numerical differentiation or integration (Chapter 6). Such function may be obtained through curve fitting, or approximation, of the data. Curve fitting is a procedure where a function is used to fit a given set of data in the “best” possible manner without having to match the data exactly. As a result, while the function does not necessarily yield the exact value at the data points, overall it fits the set of data well. Several types of functions and polynomials of different degrees can be used for curve fitting purposes. Curve fitting is normally used when the data has substantial inherent error, such as data gathered from experimental measurements. The aforementioned function or polynomial can then be used for interpolation purposes; that is, to find estimates of values at intermediate points (points between the given data points) where the data is not directly available.
Polylines and splines
Published in Bob McFarlane, Beginning AutoCAD 2002, 2012
A spline is a smooth curve which passes through a given set of points. These points can be picked, entered as coordinates or referenced to existing objects. The spline is drawn as a non-uniform rational B-spline or NURBS. Splines have uses in many CAD areas, e.g. car body design, contour mapping, etc. At our level we will only investigate the 2D spline curve. Open your standard sheet or clear all objects from the screen.Refer to Fig. 27.4 and with layer CL current, draw two circles: centre: 80,150 with radius: 50centre: 280,150 with radius: 25.Layer OUT current and select the SPLINE icon from the Draw toolbar and: Menu bar with Draw-Spline and: At this stage save drawing as C:\BEGIN\SPLINEX.The spline options have not been considered in this example.
The Cooper–Eromanga petroleum province, Australia
Published in Australian Journal of Earth Sciences, 2022
D. Kulikowski, K. Amrouch, K. Pokalai, S. I. Mackie, M. E. Gray, H. B. Burgin
Curvature analysis is a seismic attribute that has been shown to correlate well with wellbore-derived fracture and fault data (e.g. Abul Khair et al., 2012; Al-Dossary & Marfurt, 2006; Chopra & Marfurt, 2007; Hakami et al., 2004; King et al., 2011; Kulikowski, Amrouch, & Burgin, 2018; Lisle, 1994; Murray, 1968; Stewart & Podolski, 1998). The calculated value for curvature is defined as the rate of change of the direction of a curve, such that for any point (P) the curvature (K) is defined as the rate of change of the dip angle (dω) with respect to the arc length (dS) (Roberts, 2001). The arc length, dS, is obtained from the osculating circle that has a common tangent to P and makes the greatest possible contact with the curve. The radius of the osculating circle forms the radius of curvature (R); such that in two dimensions, the value for K can be represented by Equation 8 (Roberts, 2001).
A Novel Method of Curve Fitting Based on Optimized Extreme Learning Machine
Published in Applied Artificial Intelligence, 2020
Curve fitting is the process of finding a parameterized function that best matches a given set of data points. It can be viewed as a function approximation problem in such a way that a certain error measure must be addressed explicitly. Representing the data in a parameterized function or equation has actual significances in data analysis, visualization and computer graphics. Curve fitting can be served as aided tools for many techniques involved modeling and prediction. Particularly, scientists and engineers often notice that the best practice gaining some insight and guide to understand the related scientific phenomenon is to fit a set measured or observed data to an empirical relationship. From the resultant empirical formula, interpolation, extrapolation, differentiation, and finding the maximum or minimum location of the curve can be readily carried out without utilizing a full mathematical treatment based on the underlying theory. In addition, curve fitting is also frequently used to estimate the parameters in a variety of modeling studies. For example, the notch-delay solar model in the climate science has a number of independent parameters, which can be estimated by using a curve fitting method.
The role of socio-economic and property variables in the establishment of flood depth-damage curve for the data-scarce area in Malaysia
Published in Urban Water Journal, 2022
Sumiliana Sulong, Noor Suraya Romali
Curve fitting: Curve fitting is the process of constructing a mathematical function that best fits a series of data points (Pistrika, Tsakiris, and Nalbantis 2014). In the curve-plotting procedure uses empirical and synthetic damage data from the multivariate regression analysis model to perform the best-fitted curve. For the curve-fitting procedure, the value of the correlation coefficient, R-squared (R2), was used as a benchmark to best fit models (Amadio et al. 2019; Romali and Yusop 2021; Win et al. 2018). The damage factor equation from the best-fitted curve functions is established to facilitate flexibility in transferability to new areas and occurrences.