  We apply the morphological descriptions of two-dimensional contour map, the
so-called Minkowski functionals (the area fraction, circumference, and Euler
characteristics), to the convergence field $\kappa(\bm{\theta})$ of the
large-scale structure reconstructed from the shear map produced by the
ray-tracing simulations. The perturbation theory of structure formation has
suggested that the non-Gaussian features on the Minkowski functionals with
respect to the threshold in the weakly nonlinear regime are induced by the
three skewness parameters of $\kappa$ that are sensitive to the density
parameter of matter, $\Omega_{\rm m}$. We show that, in the absence of noise
due to the intrinsic ellipticities of source galaxies with which the
perturbation theory results can be recovered, the accuracy of $\Omega_{\rm m}$
determination is improved by $\sim 20%$ using the Minkowski functionals
compared to the conventional method of using the direct measure of skewness.
