There is described image-processing methods and image processing apparatus, which enable sharpness, scaling coefficients, and image quality to be adjusted with minimum image noise and minimum image quality deterioration and at high processing speed. One of the image-processing methods for creating processed image data by applying a spatial-filtering processing to source image data, comprises the steps of: setting a predetermined upper-limit value for a variation amount of the source image data, before performing an image-conversion processing through which the source image data are converted to the processed image data by applying the spatial-filtering processing; and performing the image-conversion processing for the source image data within a range of the variation amount limited by the predetermined upper-limit value. In the above, a plurality of spatial-filtering processing(s), characteristics of which are different each other, are performed either simultaneously in parallel or sequentially one by one in the image-conversion processing.