. Author manuscript; available in PMC: 2010 Jun 1.

Published in final edited form as: IEEE Trans Nucl Sci. 2009 Jun 1;56(3):549–556. doi: 10.1109/TNS.2009.2018841

TABLE I.

Table of flood histogram formulae

Anger’s equations:

\begin{array}{l} X_{a} = \frac{(A + B) - (C + D)}{A + B + C + D}, \\ Y_{a} = \frac{(A + D) - (B + C)}{A + B + C + D} . \end{array}

Zhang’s method:

\begin{array}{l} X_{b} = \frac{A - C}{A + C} cos (π / 4) + \frac{B - D}{B + D} sin (π / 4), \\ Y_{b} = \frac{A - C}{A + C} sin (π / 4) - \frac{B - D}{B + D} cos (π / 4) . \end{array}

Adaptive method:

X_c = αX_a + (1 − α)X_b, where α ∈ [0, 1],
Y_c = αY_a + (1 − α)Y_b.

In magnetic field:

X_d = X_c cos (θ) + Y_c sin (θ),
Y_d = −X_c sin (θ) + Y_c cos (θ).