For each of the sliced SMCE output maps that are currently selected, calculate:
- the Shape Index, or
- the Connectivity Index.
When you have for instance three alternative sliced SMCE output maps, and when you selected for instance Shape Index, you will obtain three Shape Index values, i.e. a Shape Index value for each sliced SMCE output map.
This dialog box appears, after you selected the main goal or a sub goal in the criteria tree viewer, and:
- clicked the Aggregate Values Sliced button in the toolbar,
- chose the Aggregate Values Sliced command from the Generate menu, or
- chose the Aggregate Values Sliced command from the context-sensitive menu.
Notes:
- Aggregate Values Sliced is not available when the SMCE output maps have not yet been sliced.
- Aggregate Values Sliced will force the calculation of sliced SMCE output maps when 'Define' was used during slicing.
Dialog box options:
Operation:
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Choose to calculate for each sliced SMCE output map within the current selection:
the Shape Index or the Connectivity Index.
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Calculation results:
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After the Calculate button has been pressed, calculation results will appear in this pane for all maps within the current selection.
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Power:
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In case of calculating the Connectivity Index: type a value for a user-defined power value that is used in the formula for the Connectivity Index.
The minimum Power value that can be used is 1.0001; the maximum Power value is 1000.
Note: Using a rather large Power value may result in a ? in the Calculation results. This means that the result is an infinitely large value.
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Calculate:
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Click the Calculate button (or press the Spacebar on the keyboard) to start the calculations. Results will appear in the Calculation Results pane.
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Additional information
Shape Index:
- Undefined pixels are ignored; only pixels that are not undefined are considered.
- For each 'polygon', i.e. contiguous 8-connected area of pixels with the same value, a shape index value is calculated as:
Perimeteri / Ö Areai
where Perimeteri is the perimeter of polygon i, and Areai is the area of that polygon.
- Then, these shape indexes of the individual 'polygons' are summed. The complete formula for the Shape Index of a map thus reads:
S (Perimeteri / Ö Areai)
- The Shape Index is a measure for non-compactness of areas in the map:
the less compact the areas are, the larger the Shape Index will be.
- When all pixels in a square map have the same value, the Shape Index is 4.
- When all pixels in a rectangular map (relative size of 4 x 1) have the same value, the Shape Index is 5.
- When a map consists of 4 equally sized square areas, the Shape Index is 16.
- When a map consists of 4 equally sized rectangles (relative size of 4 x 1), the Shape Index is 20.
- When a map consists of 16 equally sized square areas, the Shape Index is 64.
- When a map consists of 16 equally sized rectangles (relative size of 4 x 1), the Shape Index is 80.
Connectivity Index:
- Undefined pixels are ignored; only pixels that are not undefined are considered.
- For each contiguous 8-connected area of pixels with the same value,
the area is raised to power p,
this is summed for all areas, and the pth root is taken of this summed value.
This value is then multiplied by 100 and divided by the sum of all areas, and divided by the number of areas:
where Areai is the area of an 8-connected area in the map, p is the user-defined power value, Areatotal is the sum of all areas, and n is the total number of 8-connected areas in the map.
- The Connectivity Index is a measure for the connectedness of areas with different values in the map;
the less individual areas there are in a map, the larger the Connectivity Index will be.
In the example below, a Power value of 2 is used:
- When a map consists of 100 equally sized areas, the Connectivity Index is 0.1.
- When a map consists of 4 equally sized areas, the Connectivity Index is 12.5.
- When a map consists of 2 equally sized areas, the Connectivity Index is 35.36.
- When all pixels in a map have the same value, the Connectivity Index is 100.
See also:
SMCE window : functionality
SMCE window : toolbar
SMCE window : criteria tree viewer
SMCE window : Aggregate Values