Hi Ken,
Technically, the Maximum filter applies a choke spreading out white ares and choking black ones. Within a specified radius the Maximum replaces the current pixel brightness value with the highest value of the surrounding pixels.
This filter is typically used on masks to contract or expand the active area. For example if you have made a layer mask of a subject and pasted in a new background and you have a fine white or black fringe / halo around the subject which is being caused by the mask, you can just click on the mask and do a Maximum to expand or contract the masks active area by 1 or 2 pixels. There is no need to select anything.
A practical use of the Filter>Other>Maximum in
PS is equivalent to Select>Modify>Expand but here is the difference. Say you make selection with the lasso tool and you want to expand it a bit because it looks too small. You go Select>Modify>Expand. The question is how many pixels is correct? You don't have a preview window so you need to proceed on trial and error. Now try the following. Make the same selection. Next click on the Quick Mask button which you will find in your tool bar, 3rd from the bottom - it is just below the Foreground/Background color swatches, and it is the circle on your right. You will see the image masked in red except for your selection. Now go Filter>Other >Maximum and enter a pixel value. Voila, you can actually preview the result accurately. When you are done, just click the circle to the left of the Quick Mask button and you are back to Normal mode with your selection still active and modified. This method takes an extra couple of steps but can save you time in the end.
While we are on the Max filter it is worth noting that Filter>Other >Minimum ihas the opposite effect of Maximum it chokes white and expands black. An use of it is equivalent to Select>Modify>Contract. The technique is exactly the same using Quick Mask, but this time you will be shrinking the selection by some number of pixels.
Regards, Murray
Regards, Murray