In this paper, we deal with the 3D image segmentation where the segmented surface is reconstructed by using 3D point cloud data and 3D digital image information. For this task, we apply a mathematical model and numerical method based on the so-called level set algorithm. This method solves surface reconstruction by the application of advection equation with a curvature term, which gives the evolution of an initial condition to the final state. This is done by defining the advective velocity in the level set equation as the weighted sum of distance function and edge detector function gradients. The distance function to the shape, represented by the point cloud, is computed using the so-called fast sweeping method. The edge detector function is applied to the presmoothed 3D image. A crucial point for efficiency is the construction of an initial condition by a simple tagging algorithm, which allows us also to highly speed up the numerical scheme when solving PDEs. For the numerical discretization, we use a semi-implicit co-volume scheme in the curvature part and implicit upwind scheme in the advective part. The method was tested on representative examples and applied to real data representing 3D biological microscopic images of developing mammalian embryo.