1st attempt I would get a rubber strap wrench
Dead Link Removed and place it at the rear of the hood and give it a go. If the lens barrel wants to unscrew a second strap wrench on the lens barrel turning the opposite direction will help. Uneven pressure makes filters and hoods hard to remove.
2nd attempt I would get some Penetrating Oil
https://www.amazon.com/LIQUID-WRENC...d=1497039423&sr=8-12&keywords=penetrating+oil and put a light amount around the filter to lens mating area as shown in your picture # 2 and let it sit for several hours to a day.
Other possibilities are heat the oven to 250°F (or its lowest setting) then turn it off when it reaches temperature, put the lens in the center of the oven, close the door, and leave it for 15 to 30 minutes, remove and allow to cool to touch (it will be hot to the touch) and try to unscrew while warm.
Put it in a saleable plastic bag, put it in the freezer for an hour or two, remove and allow to warm to touch then try to unscrew it.
Even pressure while trying to unscrew it is essential.