Table 1: 𝑥 t m p and 𝑦 t m p values for histogram calculation in  (11).


Direction 𝑥 t m p 𝑦 t m p Condition

1 Up 𝑥 𝑖 𝑢 𝑦 𝑖 𝑢 = { 1 to 𝑥 1 𝑥 1 > 0 }
2 Up-right 𝑥 𝑖 𝑢 𝑟 𝑦 + 𝑖 𝑢 𝑟 𝑖 𝑢 𝑟 = { 1 to m i n ( 𝑥 1 , 𝐶 𝑦 ) m i n ( 𝑥 1 , 𝐶 𝑦 ) > 0 }
3 Right 𝑥 𝑦 + 𝑖 𝑟 𝑖 𝑟 = { 1 to 𝐶 𝑦 𝐶 𝑦 > 0 }
4 Down-right 𝑥 + 𝑖 𝑑 𝑟 𝑦 + 𝑖 𝑑 𝑟 𝑖 𝑑 𝑟 = { 1 to m i n ( 𝑅 𝑥 , 𝐶 𝑦 ) m i n ( 𝑅 𝑥 , 𝐶 𝑦 ) > 0 }
5 Down 𝑥 + 𝑖 𝑑 𝑦 𝑖 𝑑 = { 1 to 𝑅 𝑥 𝑅 𝑥 > 0 }
6 Down-left 𝑥 + 𝑖 𝑑 𝑙 𝑦 𝑖 𝑑 𝑙 𝑖 𝑑 𝑙 = { 1 to m i n ( 𝑅 𝑥 , 𝑦 1 ) m i n ( 𝑅 𝑥 , 𝑦 1 ) > 0 }
7 Left 𝑥 𝑦 𝑖 𝑙 𝑖 𝑙 = { 1 to 𝑦 1 𝑦 1 > 0 }
8 Up-left 𝑥 𝑖 𝑢 𝑙 𝑦 𝑖 𝑢 𝑙 𝑖 𝑢 𝑙 = { 1 to m i n ( 𝑥 1 , 𝑦 1 ) m i n ( 𝑥 1 , 𝑦 1 ) > 0 }