In the design of the fractional order filters, fractional

Laplacian operator [s.sup.[beta]] (0 < [beta] < 1) has been used [13].

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 [4].

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 [16].

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 [5] 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.

Laplacian operator 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. Eqs.