A multi-threaded graphics processor is configured to use to extrapolate low resolution mipmaps stored in physical memory to produce extrapolated texture values while high resolution nonresident mipmaps are retrieved from a high latency storage resource and converted into resident mipmaps. The extrapolated texture values provide an improved image that appears sharper compared with using the low resolution mipmap level texture data in place of the temporarily unavailable high resolution mipmap level texture data. An extrapolation threshold LOD is used to determine when extrapolated magnification or minification texture filtering is used. The extrapolation threshold LOD may be used to smoothly transition from using extrapolated filtering to using interpolated filtering when a nonresident mipmap is converted to a resident mipmap.