Point-based object localization (POL), which pursues high-performance object sensing under low-cost data annotation, has attracted increased attention. However, the point annotation mode inevitably introduces semantic variance due to the inconsistency of annotated points. Existing POL heavily rely on strict annotation rules, which are difficult to define and apply, to handle the problem. In this study, we propose coarse point refinement (CPR), which to our best knowledge is the first attempt to alleviate semantic variance from an algorithmic perspective. CPR reduces the semantic variance by selecting a semantic centre point in a neighbourhood region to replace the initial annotated point. Furthermore, We design a sampling region estimation module to dynamically compute a sampling region for each object and use a cascaded structure to achieve end-to-end optimization. We further integrate a variance regularization into the structure to concentrate the predicted scores, yielding CPR++. We observe that CPR++ can obtain scale information and further reduce the semantic variance in a global region, thus guaranteeing high-performance object localization. Extensive experiments on four challenging datasets validate the effectiveness of both CPR and CPR++. We hope our work can inspire more research on designing algorithms rather than annotation rules to address the semantic variance problem in POL.