The following video shows how to use the spike removal tool. You can fine-tune the assigned processing power in the preferences of the program (see the option Allowed CPU Usage in Multiprocessor Systems). The increase in speed corresponds roughly to the number of CPU cores in your system (a four core system will be faster by a factor of 4). The spike detection algorithm is prepared to be executed in parallel on multi-core processors. If more than one pixel mask is available you will be asked which mask to use. This will add all pixels exceeding the current threshold value to the pixel mask. In order to mask the pixels exhibiting spikes (without removing the spikes) right-click the image and select "Add Red Pixels to a Pixel Mask". If any of the spectra exhibits two or more spike which are close together you should repeat the spike detection and removal several times (using a half width of 1). The best threshold varies from case to case, thus you should check the found spikes by clicking the top score entries in the list. Set a threshold for the removal of spikes with a score higher than the threshold.This will analyze the spectra and create a list of spikes ordered by their relative intensity ("Score"). Please note that the parabolic fit is more sensitive but tends to detect spurious spikes at the beginning and at the end of a spectrum. Tick off "Use Linear Fit" for a linear fit, otherwise a parabolic fit is used. The lower the level the more spikes are recognized. Define the half width of the expected spikes (don't set the half width too high, this will probably remove parts of valid peaks - usually a half width of 1 or 2 is sufficient).Subsequently you have to define a threshold for the removal of the spikes. The tool first detects the number of spikes and their intensity. Epina ImageLab provides an efficient spike removal tool which is able to remove spikes automatically. This includes the point F, which is not mentioned above.Spikes are quite common - especially in Raman spectroscopy - and have to be removed before the data is subjected to multivariate statistics. They are in the plane of symmetry of the whole figure. These two chords and the parabola's axis of symmetry PM all intersect at the point M.Īll the labelled points, except D and E, are coplanar. Another chord BC is the perpendicular bisector of DE and is consequently a diameter of the circle. It has a chord DE, which joins the points where the parabola intersects the circle. We will call its radius r.Īnother perpendicular to the axis, circular cross-section of the cone is farther from the apex A than the one just described. This cross-section is circular, but appears elliptical when viewed obliquely, as is shown in the diagram. According to the definition of a parabola as a conic section, the boundary of this pink cross-section EPD is a parabola.Ī cross-section perpendicular to the axis of the cone passes through the vertex P of the parabola. An inclined cross-section of the cone, shown in pink, is inclined from the axis by the same angle θ, as the side of the cone. The diagram represents a cone with its axis AV. The graph of a quadratic function y = a x 2 + b x + c is the eccentricity).Ĭonic section and quadratic form Diagram, description, and definitions Cone with cross-sections Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. One description of a parabola involves a point (the focus) and a line (the directrix). It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. The parabola is a member of the family of conic sections. In this orientation, it extends infinitely to the left, right, and upward. Part of a parabola (blue), with various features (other colours). For other uses, see Parabola (disambiguation).
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