1) Semantical grouping
 
O(N_{
p
}(N_{
i
} + log N_{
i
})

By type

O(1)
 
By property

O(N_{
i
} + log N_{
i
})
 
2) Geometric comparison
 
\( O\left({N}_p^2{N}^2\right) \)

Topological comparison

O(N log N)
 
Compare underlying point sets

O(N^{2})
 
Removing scale and translation

O(N)
 
Create H = Q*Q’

O(N^{2})
 
Singular value decomposition

O(1)
 
Point comparison p’ = M*p

O(N) or O(N^{2})
 
3) Share identified duplicates
 
O(N_{
p
}N^{2})

Assign representation

O(1)
 
Premultiply transformation

O(N^{2})
 
∑
 
O(N_{
p
}(N_{
i
} log N_{
i
} + N_{
p
}N^{2}))
