Direct use of denoising and mesh reconstruction algorithms on point clouds originating from multi-view images is often oblivious to the reprojection error. This can be a severe limitation in applications which require accurate point tracking, e.g., metrology. In this paper, we propose a method for improving the quality of such data without forfeiting the original matches. We formulate the problem as a robust smoothness cost function constrained by a bounded reprojection error. The arising optimization problem is addressed as a sequence of unconstrained optimization problems by virtue of the barrier method. Substantiated experiments on synthetic and acquired data compare our approach to alternative techniques.

**Figure 1:** Starting from a converged bundle adjustment, our approach (left) searches for new
spatial position of the 3d point while guaranteeing that the reprojection error is bounded i.e. the
matches are maintained within a disk around the input matches. On the other hand, constraining the
smoothing within a ball around the initial spatial position (right) can lead to larger reprojection
errors as the shape of the corresponding projection (planar ellipses) is not taken into account.

**Figure 3:** A noisy point cloud (left-top) is processed using BA with Laplacian regularization
(middle-top) smoothing and BA constrained smoothing (right-top), all views are shown in
splating mode. The middle row shows the reprojection error for the same view. The bottom row shows a
zoom on the corresponding point cloud data.

**Figure 4:** Illustration of our method on a large data set (200K points). Image correspondences
across 56 views were perturbed by a gaussian noise with a unit variance and a peak of 3 which
yields the noisy reconstruction (left). The result of our approach is shown to the right. Middle
image show a zoom on the elephant head. All views are shown in splatting mode.