22.09.2021

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Kernel-generating functions

These functions can be used to generate kernels for morphological, smoothingor resampling operations. There are two types of kernels: kernel arrays,which are used with morph, and kernel functions, which areused with resample.

Usage
Arguments
object

Any object.

values

A numeric vector or array, containing the values of the kernelarray.

width

A numeric vector giving the width of the shape in eachdimension, in array elements. Does not need to be integer-valued, or equalfor all dimensions. Will be recycled to length dim if thatparameter is also specified.

dim

An integer value giving the dimensionality of the kernel.Defaults to the length of width or sigma, where available.

type

A string giving the type of shape to produce. In one dimension,these shapes are all equivalent.

binary

If FALSE, the value of the kernel at each pointrepresents the proportion of the array element within the shape. IfTRUE, these values are binarised to be 1 if at least half of theelement is within the shape, and 0 otherwise.

normalised

If TRUE, the sum of non-missing elements of thekernel will be unity. Note that this is the default forgaussianKernel, but not for shapeKernel.

sigma

A numeric vector giving the standard deviation of theunderlying Gaussian distribution in each dimension, in array elements.Does not need to be equal for all dimensions. Will be recycled to lengthdim if that parameter is also specified.

size

A numeric vector giving the width of the kernel in eachdimension, which will be rounded up to the nearest odd integer. Defaultsto four times the corresponding sigma value.

axis

The axis along which the gradient operator will be applied.

name

A string giving the name of the kernel function required.

Parameters for the kernel function.

B, C

Mitchell-Netravali coefficients, each of which must be between 0and 1.

Details

There are two forms of kernel used by this package. Kernel arrays, otherwiseknown in mathematical morphology as structuring elements, are numeric arrayswith class kernelArray. They are defined on a grid of odd width, andare used by morph and related functions. Kernel functions, bycontrast, are represented in R as a list containing a name and, optionally,some parameters. The real implementation is in C++. They are definedeverywhere within the support of the kernel, and are used byresample and friends. The key distinction is in whether thekernel will always be centred exactly on the location of an existing valuein the data (for kernel arrays) or not (for kernel functions).

The kernelArray and kernelFunction functions create objects ofthe corresponding classes, while isKernelArray andisKernelFunction test for them. In addition, isKernel returnsTRUE if its argument is of either kernel class.

The remaining functions generate special-case kernels: shapeKernelgenerates arrays with nonzero elements in a box, disc or diamond shape foruse with morphology functions; gaussianKernel generatesGaussian coefficients and is used by gaussianSmooth;sobelKernel generates the Sobel-Feldman gradient operator, for use bysobelFilter; boxKernel is used for ``nearestneighbour' resampling, and triangleKernel for linear, bilinear, etc.The Mitchell-Netravali kernel, a.k.a. BC-spline, is based on a family ofpiecewise-cubic polynomial functions, with support of four times the pixelseparation in each dimension. The default parameters are the onesrecommended by Mitchell and Netravali as a good trade-off between variousartefacts, but other well-known special cases include B=1, C=0 (the cubicB-spline) and B=0, C=0.5 (the Catmull-Rom spline). mnKernel is ashorter alias for mitchellNetravaliKernel. Finally, the Lanczoskernel is a five-lobe windowed sinc function.

Value

For isKernel, isKernelArray and isKernelFunction, a logical value. For kernelArray, shapeKernel, gaussianKernel and sobelKernel, a kernel array. For kernelFunction, boxKernel, triangleKernel, mitchellNetravaliKernel and mnKernel, a kernel function.

References

The Mitchell-Netravali kernel is described in the following paper.

D.P. Mitchell & A.N. Netravali (1988). Reconstruction filters in computer graphics. Computer Graphics 22(4):221-228.

See Also

morph for general application of kernel arrays to data, morphology for mathematical morphology functions, resample for resampling, and gaussianSmooth for smoothing. Also see sampleKernelFunction for kernel sampling and plotting.

Aliases
  • isKernel
  • kernels
  • isKernelArray
  • isKernelFunction
  • kernelArray
  • shapeKernel
  • gaussianKernel
  • sobelKernel
  • kernelFunction
  • boxKernel
  • triangleKernel
  • mitchellNetravaliKernel
  • mnKernel
  • lanczosKernel
Iskernel
Examples
Documentation reproduced from package mmand, version 1.6.1, License: GPL-2

Community examples

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API documentation
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