Effective object extraction plays an important role in many point cloud-based applications. This letter proposes a 3-D feature matching framework for point cloud object extraction. To determine the optimal affine transformation parameters for each template feature point, a convex dissimilarity function and the locally affine-invariant geometric constraints are designed to construct the overall objective function. The 3-D feature matching framework is integrated into a point cloud object extraction workflow. Extraction results on six test data sets show that average completeness, correctness, quality, and $F_{1}$ -measure of 0.96, 0.97, 0.93, and 0.96, respectively, are obtained in extracting light poles, vehicles, and palm trees. Comparative studies also confirm that the proposed method performs effectively and robustly, and exhibits superior or compatible performance over the other compared methods.