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The identification of gully-type debris flow remains a challenging task due to the irregularity of terrain, which causes significant fluctuations in local curvature and hinders accurate feature extraction using traditional methods. To address this issue, this study proposes a novel identification approach based on point cloud local curvature extrema. The methodology involves collecting image data of debris flow and landslide areas using DJI Matrice 300 RTK (M300RTK), planning control points and flight routes, and generating three-dimensional point cloud data through image matching and point cloud reconstruction techniques. A quadratic surface fitting method was employed to calculate the curvature of each point in the point cloud, while a topological k-neighborhood algorithm was introduced to establish spatial relationships and extract extreme curvature features. These features were subsequently used as inputs to a convolutional neural network (CNN) for landslide identification. Experimental results demonstrated that the CNN architecture used in this method achieved rapid convergence, with the loss value decreasing to 0.0032 (cross-entropy loss) during training, verifying the model’s effectiveness. The introduction of early stopping and learning rate decay strategies effectively prevented overfitting. Receiver-operating characteristic (ROC) curve analysis revealed that the proposed method achieved an area under the ROC curve (AUC) of 0.92, significantly outperforming comparative methods (0.78–0.85). Full article