laplacelaplaceLaplaceLaplacelaplace (Operator)

Name

laplacelaplaceLaplaceLaplacelaplace — Calculate the Laplace operator by using finite differences.

Signature

Description

laplacelaplaceLaplaceLaplaceLaplacelaplace filters the input images ImageImageImageImageimageimage using a Laplace operator. Depending on the parameter FilterMaskFilterMaskFilterMaskFilterMaskfilterMaskfilter_mask the following approximations of the Laplace operator are used:

'n_4'

1 1 -4 1 1

'n_8'

1 1 1 1 -8 1 1 1 1

'n_8_isotropic'

10 22 10 22 -128 22 10 22 10

For the three filter masks the following normalizations of the resulting gray values is applied, (i.e., by dividing the result by the given divisor): 'n_4'"n_4""n_4""n_4""n_4""n_4" normalization by 1, 'n_8'"n_8""n_8""n_8""n_8""n_8", normalization by 2 and for 'n_8_isotropic'"n_8_isotropic""n_8_isotropic""n_8_isotropic""n_8_isotropic""n_8_isotropic" normalization by 32.

For a Laplace operator with size 3x3, the corresponding filter is applied directly, while for larger filter sizes the input image is first smoothed using a Gaussian filter (see gauss_imagegauss_imageGaussImageGaussImageGaussImagegauss_image) or a binomial filter (see binomial_filterbinomial_filterBinomialFilterBinomialFilterBinomialFilterbinomial_filter) of size MaskSizeMaskSizeMaskSizeMaskSizemaskSizemask_size-2. The Gaussian filter is selected for the above values of ResultTypeResultTypeResultTypeResultTyperesultTyperesult_type. Here, MaskSizeMaskSizeMaskSizeMaskSizemaskSizemask_size = 5, 7, 9, 11, or 13 must be used. The binomial filter is selected by appending '_binomial'"_binomial""_binomial""_binomial""_binomial""_binomial" to the above values of ResultTypeResultTypeResultTypeResultTyperesultTyperesult_type. Here, MaskSizeMaskSizeMaskSizeMaskSizemaskSizemask_size can be selected between 5 and 39. Furthermore, it is possible to select different amounts of smoothing for the column and row direction by passing two values in MaskSizeMaskSizeMaskSizeMaskSizemaskSizemask_size. Here, the first value of MaskSizeMaskSizeMaskSizeMaskSizemaskSizemask_size corresponds to the mask width (smoothing in the column direction), while the second value corresponds to the mask height (smoothing in the row direction) of the binomial filter. Therefore, laplace(O:R:'absolute',MaskSize,N:) for MaskSize > 3 is equivalent to gauss_image(O:G:MaskSize-2:) > laplace(G:R:'absolute',3,N:). and laplace(O:R:'absolute_binomial',MaskSize,N:) is equivalent to binomial_filter(O:B:MaskSize-2,MaskSize-2:) > laplace(B:R:'absolute',3,N:).

laplacelaplaceLaplaceLaplaceLaplacelaplace either returns the absolute value of the Laplace filtered image (ResultTypeResultTypeResultTypeResultTyperesultTyperesult_type = 'absolute'"absolute""absolute""absolute""absolute""absolute") in a byte or uint2 image or the signed result (ResultTypeResultTypeResultTypeResultTyperesultTyperesult_type = 'signed'"signed""signed""signed""signed""signed" or 'signed_clipped'"signed_clipped""signed_clipped""signed_clipped""signed_clipped""signed_clipped"). Here, the output image type has the same number of bytes per pixel as the input image (i.e., int1 or int2) for 'signed_clipped'"signed_clipped""signed_clipped""signed_clipped""signed_clipped""signed_clipped", while the output image has the next larger number of pixels (i.e., int2 or int4) for 'signed'"signed""signed""signed""signed""signed".

Attention

Note that filter operators may return unexpected results if an image with a reduced domain is used as input. Please refer to the chapter Filters.

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Automatically parallelized on tuple level.
• Automatically parallelized on channel level.
• Automatically parallelized on domain level.

Parameters

Example (C)

read_image(&Image,"mreut");
laplace(Image,&Laplace,"signed",3,"n_8_isotropic");
zero_crossing(Laplace,&ZeroCrossings);

Result

laplacelaplaceLaplaceLaplaceLaplacelaplace returns TRUE if all parameters are correct. If the input is empty the behavior can be set via set_system('no_object_result',<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)set_system("no_object_result",<Result>). If necessary, an exception is raised.

Possible Successors

zero_crossingzero_crossingZeroCrossingZeroCrossingZeroCrossingzero_crossing, dual_thresholddual_thresholdDualThresholdDualThresholdDualThresholddual_threshold, thresholdthresholdThresholdThresholdThresholdthreshold

Alternatives

diff_of_gaussdiff_of_gaussDiffOfGaussDiffOfGaussDiffOfGaussdiff_of_gauss, laplace_of_gausslaplace_of_gaussLaplaceOfGaussLaplaceOfGaussLaplaceOfGausslaplace_of_gauss, derivate_gaussderivate_gaussDerivateGaussDerivateGaussDerivateGaussderivate_gauss

See also

highpass_imagehighpass_imageHighpassImageHighpassImageHighpassImagehighpass_image, edges_imageedges_imageEdgesImageEdgesImageEdgesImageedges_image

Module

Foundation