Example embodiments may allow for the efficient, edge-preserving filtering, upsampling, or other processing of image data with respect to a reference image. A cost-minimization problem to generate an output image from the input array is mapped onto regularly-spaced vertices in a multidimensional vertex space. This mapping is based on an association between pixels of the reference image and the vertices, and between elements of the input array and the pixels of the reference image. The problem is them solved to determine vertex disparity values for each of the vertices. Pixels of the output image can be determined based on determined vertex disparity values for respective one or more vertices associated with each of the pixels. This fast, efficient image processing method can be used to enable edge-preserving image upsampling, image colorization, semantic segmentation of image contents, image filtering or de-noising, or other applications.