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Texture reconstruction techniques generally suffer from the errors in keyframe poses. We present a non-iterative method for seamless texture reconstruction of a given 3D scene. Our method finds the best texture alignment in a single shot using a global optimisation framework. First, we automatically select the best keyframe to texture each face of the mesh. This leads to a decomposition of the mesh into small groups of connected faces associated to a same keyframe. We call such groups fragments. Then, we propose a geometry-aware matching technique between the 3D keypoints extracted around the fragment borders, where the matching zone is controlled by the margin size. These constraints lead to a least squares (LS) model for finding the optimal alignment. Finally, visual seams are further reduced by applying a fast colour correction. In contrast to pixel-wise methods, we find the optimal alignment by solving a sparse system of linear equations, which is very fast and non-iterative. Experimental results demonstrate low computational complexity and outperformance compared to other alignment methods.