1. A method for performing colour space conversion on an image to up-sample the image from a lower quality colour space to a higher quality colour space, the method comprising: receiving image data representing the image, the image data comprising a luminance component at a first spatial resolution and at least one chrominance component at a second, lower, spatial resolution; up-sampling the spatial resolution of the at least one chrominance component to form an up-sampled chrominance component having a higher resolution than the at least one chrominance component; determining a value of a radius parameter for a guided image filter for filtering the image, wherein: the value of the radius parameter is variable for different pixels of the image or for different regions of pixels of the image, and the radius parameter determines an extent of the effect of the guided image filter around each pixel; and filtering the up-sampled chrominance component using the guided image filter to provide a resulting up-sampled image for display.