When applying the Laplacian of Gaussian filter (9x9 Symmetric Convolution) to a grid, the result contains anomalies with reversed polarity.

Symptoms:

I have an anomalous grid with negative and positive central logarithmic values. When applying the Laplacian filter the high and low regions are reversed. 

To position the edges of the anomalies at the vicinity of 0, the filter should be applied to a grid with a mean of 0. Since the central values of the LoG filter are large negative values, compared to the input grid, the high/low regions will be flipped on output:

The first grid it’s the original one, the second grid it’s filtered with vertical derivative convolution (twice), and the third it’s the one using Laplacian. We can notice that the big anomaly in the NE region is inverted.  

Resolution 

If you would like to maintain the sign correlation between the input and output grids you could either multiply the output grid by -1, or save and use a custom filter in which all the LoG coefficients are multiplied by -1 .

 

Multiply the output grid by (-1):

1. Grid and Image > Grid Math:

2. Use the following expression: G0=G1*(-1)

G0= The grid with 9x9 Symmeric Convolition filter (The grid using Laplacian of Gaussian filter)

G1= The new grid with 9x9 Symmeric Convolition inverted

Save a custom filter in which all the LoG coefficients are multiplied by -1 or Type the Filter String directly in OPTION 3:

1. Grid and Image > Filters > 9x9 Symmetric Convolution

2. In "OPTION 1 - Select a Predefined Filter" select "User Definition"

3. In "OPTION 3 - Type Coef. Filter String", type: 40,24,12,0,-3,-5,-5,-5,-4,-2,-2,-2,-1,-1,1

Notes:

The Laplacian of Gaussian (LoG) filter helps highlight regions of rapid intensity change. Therefore, it is often used for edge detection. The Laplacian filter would generally produce a noisy outcome, so it is convolved with a Gaussian smoothing filter to yield the Laplacian of Gaussian .

For further details see Spatial Filters - Laplacian/Laplacian of Gaussian (dmu.ac.uk)