Local Spatial Statistics

Local spatial statistics look for specific areas in an image that have clusters of similar or dissimilar values. The statistics output is an image for each index you select to calculate; each image contains a measure of autocorrelation around that pixel. ENVI provides three local spatial statistics: Anselin Local Moran’s I, Getis-Ord Local G_i, and Anselin Local Geary’s C.

The Local Moran’s I index identifies pixel clustering. Positive values indicate a cluster of similar values, while negative values imply no clustering (that is, high variability between neighboring pixels). ENVI uses the Anselin method (Equation 12) for the Moran's I index by computing a row-standardized spatial weights matrix and standardized variables. The factor of proportionality between the sum of the local and global Geary's C statistic is n. The mean value of the local Moran's I image is close to the global Moran's I statistic.
The Getis-Ord G_i index identifies hot spots, such as areas of very high or very low values that occur near one another. This is useful for determining clusters of similar values, where concentrations of high values result in a high G_i value and concentrations of low values result in a low G_i value. The results of this index differ from the results of the Local Moran’s I index because clusters of negative values give high values for I, but low values for G_i.
The Local Geary’s C index identifies areas of high variability between a pixel value and its neighboring pixels. It is useful for detecting edge areas between clusters and other areas with dissimilar neighboring values. ENVI uses the Anselin method (Equation 17) for the Geary's C index by computing a row-standardized spatial weights matrix and standardized variables. The factor of proportionality between the sum of the local and global Geary's C statistic is [2*n*n / (n-1)].

To compute local spatial statistics:

From the Toolbox, select Statistics > Compute Local Spatial Statistics. The Local Spatial Statistics Input File dialog appears.
Select an input file and perform optional spatial and spectral subsetting, and/or masking, then click OK. The Local Spatial Statistics Parameters dialog appears.

If the input file has a bad bands list associated with it, the default spectral subset excludes the bands specified in the list.
From the Neighborhood Rule drop-down list, select which adjacency rule to use in the calculation. This rule defines which adjacent pixels to compare to the central pixel. The choices are:

Rook’s Case (default): Selects the pixels on the top, bottom, left, and right.
Bishop’s Case: Selects four diagonal neighboring pixels.
Queen’s Case: Selects all eight neighboring pixels.
Horizontal: Selects two neighboring pixels in the same row.
Vertical: Selects two neighboring pixels in the same column.
Positive Slope: Selects two neighboring pixels in opposite corners in a positive diagonal.
Negative Slope: Selects two neighboring pixels in opposite corners in a negative diagonal.

Select the Calculate Statistics at Multiple Ranges check box to calculate a multi-range correlogram. Selecting this check box causes the Select Maximum Lag (Pixels) and Include Intermediate Lags options to display.
Use Select Maximum Lag (Pixels) with the Calculate Statistics at Multiple Ranges option to specify the maximum lag distance, in pixels, to use in the correlogram calculation. The autocorrelation statistics are calculated at each lag distance, up to the specified maximum lag. For example, a value of 5 means that autocorrelation will be calculated for lags of 5, 4, 3, 2, and for each pixel’s nearest neighbors. The statistics for each lag are stored as a separate band in the output image. This value must be greater than 1, but less than the lesser value of the number of rows and columns in the source dataset divided by 4. The default is 2 pixels.
Use Include Intermediate Lags with the Select Maximum Lag (Pixels) option to use all pixel values inside the range specified in the Select Maximum Lag field for the local calculation. If this value is not set, ENVI uses only the pixels at the specified range in the calculation.
Select the Output Local Moran’s I (Clustering) check box to calculate the Local Moran’s I correlation image. At least one of the three local output types is required. The default is selected.
Select the Output Local Getis-Ord Gi (Hot Spots) check box to calculate the Local Getis-Ord G_i correlation image. At least one of the three local output types is required. The default is selected.
Select the Output Local Geary’s C (Variability) check box to calculate the Local Geary’s C correlation image. At least one of the three local output types is required. The default is selected.
Select output to File or Memory. Enter the root name for the output file in Output Root Name field. ENVI appends a string to the root name for each output type you select (for example, the output filenames for the root name bighorn would be: bighornmoran_i, bighorngeary_c, bighorngetis_ord_gi).
Click OK. ENVI adds the resulting output to the Layer Manager.

Tip: When calculating statistics for multiple ranges, you can use the Z Profile tool to view the correlogram for an individual pixel.

References

Contact Technical Support to obtain copies of these references:

Anselin, L., 1995. Local Indicators of Spatial Association – LISA. Geographical Analysis 27(2):93-115.
Getis, A. and J.K. Ord, 1992. The Analysis of Spatial Association by Use of Distance Statistics. Geographical Analysis 24(3):189-206.