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In this paper we introduce a novel self-organizing method of moving surface reconstruction from the data obtained from measuring real-world objects. The core of the approach is using Kohonen's Self Organizing Maps model. As that model is not traditionally applied to mesh deformation or surface reconstruction, in the paper we propose its modification enforcing input data approximation and time-space smoothing. The main idea is to generate the moving surface via deformation. Since the mesh is to be adapted only around areas of surface changes, we deform the existing mesh where it is necessary in order to fit the new point cloud corresponding to the surface. In place of processing all the sample points of unknown surface, we choose the points randomly and therefore it is possible to avoid the issues of oversampling and control the mesh quality in the case of undersampling. We can vary the mesh nodes density by picking the sampled points in the specified areas more often. Due to stochastic nature of the proposed method, in many cases it is not necessary to employ additional denoising or data filtering. Moreover, while deforming a mesh, no user assistance is needed. Underlying self-organizing principles make the technique human-free, efficient and easy to parallelize.