BBTools

bbkernel

This function is not yet fully documented. This is a transcript of the text-formatted help.

bbkernel   Create a kernel for convolution.
   K=bbkernel(dim,'name',par) creates a hypercube with a standard kernel.
   This is an auxilliary function, mainly intended to create kernels
   to use with bbconvn.

   All kernels are created from a continuous function on a hyper-cube
   ranging from -1 to 1 in all dimensions. By default, this is normalized
   to a unit volume. However, if you give the option 'aver', the
   average of each cell of the unnormalized function is used.

   The function is discretized on a regular grid, with cells covering
   equal volumes. Each element in K is the integral of the kernel over
   a cell.

   Many kernels of interest are separable, i.e. the underlying function
   satisfies f(x,y,z,...)=f(x)*f(y)*f(z)*... The list specifies the
   underlying unnormalized function in one dimension.
      'gauss'  - Gaussian kernel
                 Parameter: sigma (default: 1)
                 Function: f(x)=exp(-x^2/(2*sigma^2))
                 AKA: 'gaussian'
      'linear' - Piecewise linear with with maximum at the origin
                 Function: f(x)=abs(x)
      'box'    - A constant
                 Function: f(x)=1
                 AKA: 'const', 'cube'
      'cossqr' - Squared cosine
                 Function: f(x)=cos(x*pi/2)^2

   The following kernel is non-separable. The argument d is the
   euclidean distance from the origin.
      'ball'   - Solid line (1D), circle (2D), or sphere (3D and up)
                 Parameter: ra (default: 1)
                 Function: f(d)=1 for d<=ra, 0 otherwise.
                 AKA: 'disk', 'circle', 'pillbox', 'sphere'
      'ellip' -  Same as 'ball', except each semi-axis is given.
                 Parameter: len, vector with length of semi-axis
                 Function: f(p)=1 for sum((p./len).^2)<=1
                 AKA: 'ellipse', 'ellipsoid'

   NOTE: 'ball' is only accurate for 1D and 2D. For 3D and higher, an
   approximation is used for cells partly containing the ball.

   See also bbconvn,  (image processing toolbox)

bbinvbbkron