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In this paper we define two bi-adaptive mesh filtering algorithms for efficient features preserving restoration of noisy models acquired from 3D scanners. The new filters are based on 2D image processing adaptive algorithms extended to 3D mesh processing. We combine two adaptive algorithms to design more efficient bi-adaptive algorithms. The first filter is applied on the mesh triangles normal vector orientation and the second filter is applied on the vertices normal vector orientation. Both filters are applied on adaptively selected local neighborhood based on a threshold angle between normal vectors. Then the algorithm to update the vertices position is also adaptive according to a local variance evaluation compared to a noise variance threshold. We compare our two bi-adaptive algorithms results to other filtering algorithms according to reliable error metrics and show the new filters outperform previous features preserving and adaptive mesh denoising methods.