Digital watermarking technology plays an essential role in the work of anti-counterfeiting and traceability. However, image watermarking algorithms are weak against hybrid attacks, especially geometric attacks, such as cropping attacks, rotation attacks, etc. We propose a robust blind image watermarking algorithm that combines stable interest points and deep learning networks to improve the robustness of the watermarking algorithm further. First, to extract more sparse and stable interest points, we use the Superpoint algorithm for generation and design two steps to perform the screening procedure. We first keep the points with the highest possibility in a given region to ensure the sparsity of the points and then filter the robust interest points by hybrid attacks to ensure high stability. The message is embedded in sub-blocks centered on stable interest points using a deep learning-based framework. Different kinds of attacks and simulated noise are added to the adversarial training to guarantee the robustness of embedded blocks. We use the ConvNext network for watermark extraction and determine the division threshold based on the decoded values of the unembedded sub-blocks. Through extensive experimental results, we demonstrate that our proposed algorithm can improve the accuracy of the network in extracting information while ensuring high invisibility between the embedded image and the original cover image. Comparison with previous SOTA work reveals that our algorithm can achieve better visual and numerical results on hybrid and geometric attacks.