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In this paper a novel intermediate view synthesis algorithm for 3D video rendering is presented. The proposal is based on the representation of the pixels to be warped as intervals of finite length. The warping, hole-filling and merging stages of the view synthesis procedure can be recast according to this notation with significant advantages from the point of view of algorithm complexity, memory requirements and image synthesis quality. A novel interpolation rule based on the definition of a foreground and a background weight associated to each warped pixel is proposed and compared with linear interpolation based on pixels distance. The experimental results show that the designed technique yields a noticeable gain in terms of rendered image quality, while at the same time halving the execution time with respect to the MPEG view synthesis reference software.