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Laplacian Filter
Author(s) Module: Andre Ringeler, (c) 2003 and Olaf Conrad, (c) 2008
Author(s) Wiki Documentation: Vern Cimmery, (c) 2011 2011 (kapcimmery at hotmail dot com)
License Wiki Documentation: Creative Commons Attribution-ShareAlike 3.0 Unported License
Description:
The Laplacian Filter is an edge detection or sharpening filter. This filter is commonly used in image processing. The filter highlights regions of rapid intensity change. When used with a digital elevation model (DEM), it can be used to study landforms and detect concave and convex land areas.
The filter functions by weighting the target cell and de-emphasizing the adjacent cell data values.
Figure LF.1. Settings page for the module Laplacian Filter.
Inputs
Grid system
The entry for the ‘Grid system’ parameter must be the grid system the input grid data layer (‘>>Input’) is a part.
>>Grid
The single input parameter is the grid data layer containing grid cells you wish to be filtered using the Laplacian filter approach of this module. This is a mandatory input. The default entry is "[not set]". As noted above, this grid data layer must be a part of the grid system chosen for the 'Grid system' parameter, otherwise, it will not ba available to choose.
Output
<Filtered Grid
The output for the module is identified in the value field to the right of the ‘<Filtered Grid’ parameter. The default is “[create]”. The output layer name will be the name of the grid data layer for the '>>Grid' parameter concatenated with "[Laplace Filter]".
Options
Method The first option in the ‘Options’ section is the ‘Method’ parameter. There are three choices: User defined (the default), Standard Kernel 1, and Standard Kernel 2.
User defined
The “User defined” choice uses three parameters: ‘Standard Deviation (Percent of Radius)’ (default of "50"), ‘Radius’ (default of "3"), and ‘Search Mode’ (default is “Circle”).
The ‘Standard Deviation (Percent of Radius)’ parameter controls the smoothing intensity. This parameter supports a number between 0 and 100. If you do not change the ‘Radius’ parameter value, the higher the percent, the more smoothing is applied.
The ‘Search Mode’ and ‘Radius’ parameters control the number of neighboring values that will be used for calculating a new data value for the central or target cell. The ‘Search Mode’ option supports two choices: “Circle” and “Square”. The default entry for this parameter is “Circle”. This option identifies whether a circular or square shaped grouping of cells will be considered around the central one that is to be defined.
The radius defines the size of the grouping of cells that will be used. The higher the value for the radius, the more smoothing is applied if the value for the ‘Standard Deviation (Percent of Radius)’ parameter does not change.
Standard Kernel 1
The ‘Standard Kernel 1’ option uses the 3 x 3 kernel displayed below.
0 -1 0
-1 4 -1
0 -1 0
The center cell, i.e., the target cell is weighted with a value of 4. Four adjacent values are pulled down or decreased using a –1 multiplier for their cell values. The resulting values are then averaged with the average replacing the original value in the target cell.
Standard Kernel 2
The ‘Standard Kernel 2’ option uses a different 3 x 3 kernel.
-1 -1 -1
-1 8 -1
0 -1 0
The center cell or target cell is weighted with a value of 8. Six of the adjacent cell values are pulled down or decreased using a multiplier of –1 on their cell values. The resulting values are then averaged with the average replacing the original value in the target cell.
Execution Example:
This example uses the digital terrain model (DEM) for Mason County, Washington named 'MCdem'. The "User defined" method will be used with a value of "5" for the 'Standard Deviation (Percent of Radius)' parameter. The value for the ‘Radius’ parameter will be "20" and the ‘Search Mode’ will be "Circle".
1. Execute the Laplacian Filter module.
2. Choose the grid system the input grid data layer is a part for the 'Grid system' paramter.
3. Select the DEM grid data layer from the drop-down list of data layers for the grid system chosen for the '>>Grid' parameter.
4. Choose the "[create]" option for the output parameter '<Filtered Grid'.
5. In the 'Options' section, choose the "User defined" option for the 'Method' parameter. 6. In the 'Options: User defined' parameter section, enter a "5" for the 'Standard Deviation (Percent of Radius' parameter.
7. In the 'Options: User defined' parameter section, enter "20" for the 'Radius' parameter. This value defines the size of the matrix of cells contributing to the calculation of a new value for the central cell.
8. In the 'Options: User defined' parameter section, choose "Circle" for the 'Search MOde' parameter. 9. When changes have been made to the module parameters and options, click on the 'Okay' button to execute the module.
10. When module execution is complete, the output grid data layer name will appear in the 'Tab' area of the Workspace. The layer name will be the name of the grid data layer for the '>>Grid' parameter concatenated with "[Laplace Filter]".
Notes:
1. The input grid data layer (for the '>>Grid' parameter) must be a member of the grid system chosen for the 'Grid system' parameter.
2. The single output parameter ('>Filtered Grid') must be set to the "[create]" option; "[not set]" is the default entry. If you use the default, there will be no output.
References:
Cimmery, Vern (2011): 'Laplacian Filter', SAGA References, unpublished .pdf document. [PENDING]
