In scenarios with only single-view or sparse images, precise distance perception between objects remains a challenging problem. Traditional single-view distance perception methods either consider only the visible-side point cloud of objects or employ simple symmetry for point cloud completion. Meanwhile, deep learning approaches still face limitations in data requirements and computational efficiency for real-time point cloud completion in highly diverse scenes. Building upon traditional symmetry-based methods, this paper proposes an unsupervised Gaussian Mixture Model (GMM)-based point cloud completion algorithm for distance estimation. The algorithm utilizes a GMM to fit the visible-side point cloud of objects and completes the occluded-side point cloud through symmetry constraints. Subsequently, the closest point distance between point clouds is calculated to achieve accurate 3D distance perception from single images. Experimental results demonstrate that the application of Gaussian Mixture Models in point cloud completion effectively reduces distance estimation errors, making it applicable to scenarios such as safety space monitoring of critical facilities, robot navigation, and obstacle avoidance.