Structure from Motion (SfM) algorithms take as input multiview stereo images (along with internal calibration information) and yield a 3D point cloud and camera orientations/poses in a common 3D coordinate system. In the case of an incremental SfM pipeline, the process requires repeated model estimations based on detected feature points: homography, fundamental and essential matrices, as well as camera poses. These estimations have a crucial impact on the quality of 3D reconstruction. We propose to improve these estimations using the a contrario methodology. While SfM pipelines usually have globallyxed thresholds for model estimation, the a contrario principle adapts thresholds to the input data and for each model estimation. Our experiments show that adaptive thresholds reach a signi cantly better precision. Additionally, the user is free from having to guess thresholds or to optimistically rely on default values. There are also cases where a globallyxed threshold policy, whatever the threshold value is, cannot provide the best accuracy, contrary to an adaptive threshold policy.