Flexible control of contributions from sources

In practice, the user will often want to control how closely the synthesized volume resembles the low-frequency volume rather than the high-frequency volume, or vice versa. The interface for Velocity View provides a slider bar to control the level of contribution to the result $m(\vec{x})$ from the source volumes $h(\vec{x})$ and $l(\vec{x})$. As the slider moves from left to right, a linear scale from 0 to 1 is traversed. Denoting the current slider value $\gamma$, $m(\vec{x})$ is generated by

$$\begin{eqnarray} m(\vec{x}) = \left\{ \begin{array} {ccc} (2-2\gamma) \cdot m_i(... ...ma) \cdot h(\vec{x}) & & if \: \gamma \le 0.5\end{array}\right\} ,\end{eqnarray}$$ (5)

where $i = \{1, 2\}$ indicates which one of the two data-fusion algorithms previously discussed is used. The construction in Eq. 5 has the following desirable behavior that 1) as $\gamma \rightarrow 0$, $m(\vec{x}) \rightarrow h(\vec{x})$; 2) as $\gamma \rightarrow 1$, $m(\vec{x}) \rightarrow l(\vec{x})$; and 3) as $\gamma \rightarrow 0.5$, $m(\vec{x}) \rightarrow m_i(\vec{x})$. For any value of $\gamma$, $m(\vec{x})$ is defined to be a convex combination of $m_i(\vec{x})$ and either $h(\vec{x})$ or $l(\vec{x})$, depending on whether or not $\gamma \gt 0.5$.