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Semi-supervised object detection (SSOD) aims to boost detection performance by leveraging extra unlabeled data. The teacher-student framework has been shown to be promising for SSOD, in which a teacher network generates pseudo-labels for unlabeled data to assist the training of a student network. Since the pseudo-labels are noisy, filtering the pseudo-labels is crucial to exploit the potential of such framework. Unlike existing suboptimal methods, we propose a two-step pseudo-label filtering for the classification and regression heads in a teacher-student framework. For the classification head, OCL (Object-wise Contrastive Learning) regularizes the object representation learning that utilizes unlabeled data to improve pseudo-label filtering by enhancing the discriminativeness of the classification score. This is designed to pull together objects in the same class and push away objects from different classes. For the regression head, we further propose RUPL (Regression-Uncertainty-guided Pseudo-Labeling) to learn the aleatoric uncertainty of object localization for label filtering. By jointly filtering the pseudo-labels for the classification and regression heads, the student network receives better guidance from the teacher network for object detection task. Experimental results on Pascal VOC and MS-COCO datasets demonstrate the superiority of our proposed method with competitive performance compared to existing methods.