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Commonly used are: zero-order hold (for film/video frames), cubic (for image processing) and windowed sinc function (for audio). The two methods are mathematically identical: picking an interpolation function in the second scheme is equivalent to picking the impulse response of the filter in the first scheme.
In computer vision, the Lucas–Kanade method is a widely used differential method for optical flow estimation developed by Bruce D. Lucas and Takeo Kanade.It assumes that the flow is essentially constant in a local neighbourhood of the pixel under consideration, and solves the basic optical flow equations for all the pixels in that neighbourhood, by the least squares criterion.
In computational fluid dynamics QUICK, which stands for Quadratic Upstream Interpolation for Convective Kinematics, is a higher-order differencing scheme that considers a three-point upstream weighted by quadratic interpolation for the cell face values.
Spurious oscillation may occur as particles cross the boundaries of the mesh in MPM, although this effect can be minimized by using generalized interpolation methods (GIMP). In MPM as in FEM, the size and orientation of the mesh can impact the results of a calculation: for example, in MPM, strain localisation is known to be particularly ...
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [ 4 ] The function depends on three parameters, the input x , the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." [1] [2] They were introduced to geometric design by Duchon. [3] They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and ...
This process yields p 0,4 (x), the value of the polynomial going through the n + 1 data points (x i, y i) at the point x. This algorithm needs O(n 2) floating point operations to interpolate a single point, and O(n 3) floating point operations to interpolate a polynomial of degree n.
The simulation was carried out on a mesh of 200 cells using Matlab code (Wesseling, 2001), adapted to use the KT algorithm with Parabolic Extrapolation and van Albada limiter. The alternative form of van Albada limiter, ϕ v a ( r ) = 2 r 1 + r 2 {\displaystyle \phi _{va}(r)={\frac {2r}{1+r^{2}}}\ } , was used to avoid spurious oscillations.