1. An image sharpness processing apparatus, comprising: an image capturing module, arranged for capturing an image having a plurality of pixels; and a processing module, arranged for analyzing each of the pixels of the image to obtain a characteristic value corresponding to each of the pixels, using a first sharpening algorithm and a second sharpening algorithm to calculate respectively a first sharpening compensation value and a second sharpening compensation value corresponding to each of the pixels, using the characteristic value to determine a weight value of the first sharpening algorithm and the second sharpening algorithm, calculating a third sharpening compensation value according to the first sharpening compensation value, the second sharpening compensation value and the weight value, and using the third sharpening compensation value to adjust the sharpness of the image.