As one type of structured points, the layered depth-normal images (LDNIs) is a discrete representation of solid models. It uses sampling points to sparsely encode the shape boundary in three orthogonal directions. Geometric modeling operations on the LDNIs solids can be performed robustly and easily. However, it is generally challenging to faithfully reconstruct the boundary representation (B-Rep) from the LDNIs solid especially for features whose sizes are close to the resolution of sampling points. In this paper, we present a novel contouring method to generate boundary surfaces from a LDNIs solid. In our method, we first consistently classify the inside/outside status of all the nodes and accordingly verify the Hermite data of sampling points. We then individually construct a set of contour edges on each cell face. We illustrate that complex shells can be more easily handled by using the approach of constructing contour edges. In addition, we develop simple and effective approaches to address the topology ambiguity cases that are typical in the contouring process. By forming the contour edges into contour loops, we can construct 2-manifold polygonal mesh surfaces for the LDNIs solid. Compared to other contouring methods, the proposed method can faithfully capture all the features that are 1-dimensionally smaller than the sampling resolution. We report experimental results on a variety of CAD models.