laplaceLaplaceLaplacelaplacelaplace🔗

Short description🔗

laplaceLaplaceLaplacelaplacelaplace — Calculate the Laplace operator by using finite differences.

Signature🔗

laplace( image Image, out image ImageLaplace, string ResultType, integer MaskSize, string FilterMask )

Description🔗

laplaceLaplace filters the input images Imageimageimage using a Laplace operator. Depending on the parameter FilterMaskfilterMaskfilter_mask the following approximations of the Laplace operator are used:

'n_4'"n_4"

                             1
                    1       -4      1
                             1

'n_8'"n_8"

                    1       1       1
                    1       -8      1
                    1       1       1

'n_8_isotropic'"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" normalization by 1, 'n_8'"n_8", normalization by 2 and for '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_imageGaussImage) or a binomial filter (see binomial_filterBinomialFilter) of size MaskSizemaskSizemask_size-2. The Gaussian filter is selected for the above values of ResultTyperesultTyperesult_type. Here, MaskSizemaskSizemask_size = 5, 7, 9, 11, or 13 must be used. The binomial filter is selected by appending '_binomial'"_binomial" to the above values of ResultTyperesultTyperesult_type. Here, MaskSizemaskSizemask_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 MaskSizemaskSizemask_size. Here, the first value of MaskSizemaskSizemask_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 MaskSizemaskSizemask_size \(>\) 33 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:)`.

laplaceLaplace either returns the absolute value of the Laplace filtered image (ResultTyperesultTyperesult_type \(=\) 'absolute'"absolute") in a byte or uint2 image or the signed result (ResultTyperesultTyperesult_type \(=\) 'signed'"signed" or '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", while the output image has the next larger number of pixels (i.e., int2 or int4) for '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🔗

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🔗

Imageimageimage (input_object) (multichannel-)image(-array) → object (byte / uint2)HObject (byte / uint2)HImage (byte / uint2)HObject (byte / uint2)Hobject (byte / uint2)

Input image.

ImageLaplaceimageLaplaceimage_laplace (output_object) (multichannel-)image(-array) → object (byte / uint2 / int2 / int2 / int4)

Laplace-filtered result image.

ResultTyperesultTyperesult_type (input_control) string → (string)HTuple (HString)HTuple (string)strHtuple (char*)

Type of the result image, whereas for byte and uint2 the absolute value is used.

Default: 'absolute'"absolute"
List of values: 'absolute', 'absolute_binomial', 'signed', 'signed_binomial', 'signed_clipped', 'signed_clipped_binomial'

MaskSizemaskSizemask_size (input_control) integer(-array) → (integer)HTuple (Hlong)HTuple (int / long)MaybeSequence[int]Htuple (Hlong)

Size of filter mask.

Default: 33
List of values: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39

FilterMaskfilterMaskfilter_mask (input_control) string → (string)HTuple (HString)HTuple (string)strHtuple (char*)

Filter mask used in the Laplace operator

Default: 'n_4'"n_4"
List of values: 'n_4', 'n_8', 'n_8_isotropic'"n_4", "n_8", "n_8_isotropic"

Example🔗

(C)

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

Result🔗

laplaceLaplace returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty the behavior can be set via set_system('no_object_result',<Result>). If necessary, an exception is raised.

Combinations with other operators🔗

Combinations

Possible successors

zero_crossingZeroCrossing, dual_thresholdDualThreshold, thresholdThreshold

Alternatives

diff_of_gaussDiffOfGauss, laplace_of_gaussLaplaceOfGauss, derivate_gaussDerivateGauss

Module🔗

Foundation