x y {\rm d} x,$$ where $L$ is the full size of the edge-on galaxy (the diameter at 3$\sigma$ above the sky background). The absolute value of $\omega$ is a measurement of the strength of a warp, while its sign distinguishes between N-like ($\omega > 0$) and S-like ($\omega < 0$) warps. These types are defined from the similarity of the warp shape and the type letters (see Fig. \[dibu\] for definition of types of warps). This definition is nondimensional and, therefore, independent of a galaxy’s distance and size. It is also independent of the units used and does not strongly depend on the angular resolution of the observations (although a higher resolution would enable a more precise evaluation). For numerical purposes, we have $$\omega=\frac{1}{L^3} \sum_{i=-L/2}^{L/2} x_i y_i.$$

We can also define this parameter for both sides of our galaxies: $\omega_{\rm R}$ for the right-hand side $(^1 \! /_{L^3}
\sum_{i=0}^{L/2} x_i y_i)$ and $\omega_{\rm L}$ for the left-hand side $(^1 \! /_{L^3} \sum_{i=-L/2}^{0} x_i y_i)$. Because of the flattening of the radial profile in the inner regions of our sample galaxies, it is not critical to have a precise estimate of the position of the galaxy centre. Warps can appear 