What is the best way to "equalise" the image so that it removes the brighter and darker areas?
You could use a Shadow / Highlight filter, normalize filter, etc (filter tab on the right of the map properties).
You could also use the Input Filter (colored numbers above the map properties) to adjust darker or brighter color areas of the map. You can adjust input and output levels here.
Of course you could use an image editor such as Photoshop or GIMP to adjust the lighting before importing the map into ShaderMap.