A priority-based method for pixel reconstruction and incrementalhole filling in incomplete images and 3D surface data is presented.The method is primarily intended for reconstruction of occluded areasin 3D surfaces and makes use of a novel prioritizing scheme, based on apixelwise defined confidence measure, that determines the order in whichpixels are iteratively reconstructed. The actual reconstruction of individualpixels is performed by interpolation using normalized convolution.The presented approach has been applied to the problem of reconstructing3D surface data of a rock pile as well as randomly sampled imagedata. It is concluded that the method is not optimal in the latter case,but the results show an improvement to ordinary normalized convolutionwhen applied to the rock data and are in this case comparable to thoseobtained from normalized convolution using adaptive neighborhood sizes.