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Structure-from-Motion (SfM) and Multi-View Stereo (MVS) are widely used methods in three dimensional (3D) model reconstruction for an infrastructure maintenance purpose. However, if a set of images is not captured from well-placed positions, the final dense model can contain low-quality regions. Since MVS requires a much longer processing time than SfM as larger amounts of images are provided, it is impossible for surveyors to wait for the SfM–MVS process to complete and evaluate the geometric quality of a final dense model on-site. This challenge results in response inefficiency and the deterioration of dense models in 3D model reconstruction. If the quality of the final dense model can be predicted immediately after SfM, it will be possible to revalidate the images much earlier and to obtain the dense model with better quality than the existing SfM–MVS process. Therefore, we propose a method for reconstructing a more plausible 3D mesh model that accurately approximates the geometry of the final dense model only from sparse point clouds generated from SfM. This approximated mesh model can be generated using Delaunay triangulation for the sparse point clouds and triangle as well as tetrahedron filtering. The approximated model can be used to predict the geometric quality of the final dense model and for an optimization-based view planning. Some experimental results showed that our method is effective in predicting the quality of the final dense model and finding the potentially degraded regions. Moreover, it was confirmed that the average reconstruction errors of the dense model generated by the optimization-based view planning went below tens of millimeters and falls within an acceptable range for an infrastructure maintenance purpose.