Fig. 3

An illustration of an integral array \(\mathbf{v }\), using cell size \(c=4\). Columns represent data positions, and contain all positions i which are added up and stored at \(\mathbf{v }[t]\); for instance, \(\mathbf{v }[9] = \sum _{i=9}^{11} \mathbf{T }(\mathbf{y }[i])\). The statistics of a block [s, e) are obtained by adding v[s], \(\mathbf{v }[m]\) for all \(s<m<e\), \(m\equiv 0\mod c\), and subtracting \(\mathbf{v }[e]\) iff \(e\not \equiv 0\mod c\). For instance, block [3, 10) is obtained as \(\mathbf{v }[3]+\mathbf{v }[4]+ \mathbf{v }[8]-\mathbf{v }[10]\), yielding \(\sum _{t=3}^9 \mathbf{T }(y[t])\)