In this paper, we present an orientation inference framework for reconstructing implicit surfaces from unoriented point clouds. The proposed method starts from building a surface approximation hierarchy comprising of a set of unoriented local surfaces, which are represented as a weighted combination of radial basis functions. We formulate the determination of the globally consistent orientation as a graph optimization problem by treating the local implicit patches as nodes. An energy function is defined to penalize inconsistent orientation changes by checking the sign consistency between neighboring local surfaces. An optimal labeling of the graph nodes indicating the orientation of each local surface can, thus, be obtained by minimizing the total energy defined on the graph. The local inference results are propagated over the model in a front-propagation fashion to obtain the global solution. The reconstructed surfaces are consolidated by a simple and effective inspection procedure to locate the erroneously fitted local surfaces. A progressive reconstruction algorithm that iteratively includes more oriented points to improve the fitting accuracy and efficiently updates the RBF coefficients is proposed. We demonstrate the performance of the proposed method by showing the surface reconstruction results on some real-world 3-D data sets with comparison to those by using the previous methods.