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Infrared (IR) small target detection in sky scenes is crucial for aerospace, border security, and atmospheric monitoring. Most current works are typically designed for generalized IR scenes, which may not be optimal for the specific scenario of sky backgrounds, particularly for detecting small and dim targets at long ranges. In these scenarios, the presence of heavy clouds usually causes significant false alarms due to factors such as strong edges, streaks, large undulations, and isolated floating clouds. To address these challenges, we propose an infrared dim and small target detection algorithm based on morphological filtering with dual-structure elements. First, we design directional dual-structure element morphological filters, which enhance the grayscale difference between the target and the background in various directions, thus highlighting the region of interest. The grayscale difference is then normalized in each direction to mitigate the interference of false alarms in complex cloud backgrounds. Second, we employ a dynamic scale awareness strategy, effectively preventing the loss of small targets near cloud edges. We enhance the target features by multiplying and fusing the local response values in all directions, which is followed by threshold segmentation to achieve target detection results. Experimental results demonstrate that our method achieves strong detection performance across various complex cloud backgrounds. Notably, it outperforms other state-of-the-art methods in detecting targets with a low signal-to-clutter ratio (MSCR ≤ 2). Furthermore, the algorithm does not rely on specific parameter settings and is suitable for parallel processing in real-time systems. [ABSTRACT FROM AUTHOR]