Find the center of positive plateaus of rectangular function
Assume $x(t)$ is your original continuous function. The rectangular function $\pi(t)$ is generated by thresholding, something similar to

$$\pi(t)=1_{x(t)&gt;\gamma}$$

where $\gamma$ is the threshold. Consider one of the rectangular segments of $\pi(t)$ which is between $t=t_a$ and $t=t_b$, where there is an upward edge at $t_a$ and a downward edge at $t_b$. The center point is at $$t_m=t_a+\frac{1}{2}(t_b-t_a)$$
So the problem reduces to finding the upward and downward edges of each rectangular segment. This can be done by looking at the first derivative (or if the functions are discrete, the first difference) of $\pi(t)$. The derivative has positive and negative impulses that correspond to upward and downward edges. In vector notation:

$$\mathbf{t}_a=\{t:\pi'(t)&gt;0\}$$

$$\mathbf{t}_b=\{t:\pi'(t)&lt;0\}$$
$$\mathbf{t}_m=\mathbf{t}_a+\frac{1}{2}(\mathbf{t}_b-\mathbf{t}_a)$$