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; wherein the processing module uses the characteristic value to determine the weight value according to a specific curve; and wherein the weight value further comprises a first weight value, a second weight value and a predetermined total weight value, and an abscissa of the specific curve is a numerical value of the characteristic value, and an ordinate of the specific curve is the first weight value of the first sharpening algorithm, and the processing module obtains the first weight value according to a position on the specific curve corresponding to the characteristic value, and further obtains the second weight value of the second sharpening algorithm according to the first weight value and the predetermined total weight value.