The ability to estimate 3D object shape from a single image is vital to robotics and manufacturing. For instance, it enables iterative trial-and-error in simulated environments. In single-view reconstruction, implicit functions have demonstrated superior results over traditional methods. However, implicit functions suffer from the heavy computation of mesh extraction. This is due to the indirect mesh extraction, where the number of evaluation points grows cubically with resolution. On the other hand, reducing the resolution results in the discretization error of marching cubes (MC). In this work, we aim to perform efficient and accurate mesh extraction from implicit functions. The idea is to directly reconstruct the decision boundary of implicit functions as a mesh by reverse tracing from the output. It eliminates the need for evaluating massive points and error-prone MC. Consequently, we propose implementing an implicit function via a composite function of a flow and Binary-coded Input Neural Network (BCINN). The boundary of BCINN is easily identifiable, and the flow is invertible. Owing to these properties, the decision boundary of the composite function can be directly and efficiently reconstructed. In our experiments, we demonstrate that the proposed method significantly improves runtime/memory efficiency, with results comparable to those of existing methods. Specifically, our method enables real-time high-quality mesh inference from a single image.