  We propose a multi-scale edge-detection algorithm to search for the
Gott-Kaiser-Stebbins imprints of a cosmic string (CS) network on the Cosmic
Microwave Background (CMB) anisotropies. Curvelet decomposition and extended
Canny algorithm are used to enhance the string detectability. Various
statistical tools are then applied to quantify the deviation of CMB maps having
a cosmic string contribution with respect to pure Gaussian anisotropies of
inflationary origin. These statistical measures include the one-point
probability density function, the weighted two-point correlation function
(TPCF) of the anisotropies, the unweighted TPCF of the peaks and of the
up-crossing map, as well as their cross-correlation. We use this algorithm on a
hundred of simulated Nambu-Goto CMB flat sky maps, covering approximately
$10\%$ of the sky, and for different string tensions $G\mu$. On noiseless sky
maps with an angular resolution of $0.9'$, we show that our pipeline detects
CSs with $G\mu$ as low as $G\mu\gtrsim 4.3\times 10^{-10}$. At the same
resolution, but with a noise level typical to a CMB-S4 phase II experiment, the
detection threshold would be to $G\mu\gtrsim 1.2 \times 10^{-7}$.
