The idea behind the geometric filter is that all pixels in a very small region should be roughly the same. Therefore, the filter iteratively either increases or decreases every pixel to make it better resemble its neighbors.
Below: CP ultrasound of a 12 mm target at +6 dB from the background. Bottom is the geometric filter with 5 iterations applied to an eREC-FC ultrasound image of the same target. Bottom shows the filter's effects on the CP image in an overlaid manner.
Geometric Filter Results