In the design of the fractional order filters, fractional Laplacian operator
[s.sup.[beta]] (0 < [beta] < 1) has been used .
The other possible approach to the design of fractional-order filters supposes an approximation of the given fractional-order Laplacian operator
[s.sup.[alpha]] by a suitable integer-order filter function of higher order .
To solve (16), we use a 5-point finite difference scheme to approximate the Laplacian operator
. This 5-point scheme is based on the following well-known formula:
Sun and Han enhanced images by extracting the edge and texture information from the original images using the Laplacian operator
This fact shows that hermiticity of the Laplacian operator
in step-index fiber waveguides underlies on the boundary conditions, which supports the discussion presented in  about the nonhermiticity of the operator that results from (2a) after multiplying from the left by [[??].sup.-1].
With discrete divergence and gradient defined for both primal and dual cochains, the Laplacian operator
[nabla] * [nabla] can then be well defined for a scalar field [phi](r).
Because of a large number of internal texture details and lots of mixed noise in UAVRSI, many traditional edge detection operators are sensitive to noise, such as Robert operator, Prewitt operator, and Laplacian operator
; these result in low detection accuracy of UAVRSI.
Here, [DELTA] is the Laplacian operator
. From (43) and (44), we can identify the exterior derivative with [s.sub.1] and coexterior derivative [delta] with [s.sub.2].
In more detail, for both the outer surface and inner surface mesh of posterior sclera, we would like to construct a harmonic field f such that [DELTA]f = 0, where A is the Laplacian operator
, subject to the Dirichlet boundary conditions.
where [I.sub.t] is the image at current iteration, [I.sub.t+1] is the image at next iteration, [DELTA][I.sub.t] is the map derived from Laplacian operator
at iteration t, [DELTA][I.sub.t] is the gradient of I at current iteration, and dt is time step.
that detects sudden transitions intensity of image requires fewer calculations, it is defined by second order partial derivatives:
where c is the speed of light, which is equal to 1/ [square root of [[member of].sub.0][[mu].sub.0]] for vacuum, and [[nabla].sup.2] is the Laplacian operator