How many towers can you see?
APL 19

≢¨∪/⌈\(⍉⍪⌽⍪⊖∘⌽∘⍉⍪⊖)


(golfed a bit more after ngn's suggestion, thanks)

Explanation:

(⍉⍪⌽⍪⊖∘⌽∘⍉⍪⊖)  rotates matrix 4 times appending results
⌈\ gets maximums for each row up to current column (example: 4 2 3 5 1 gives 4 4 4 5 5)
≢¨∪/ counts unique elements for each row


Try it on tryapl.org