Smart Size - Smart Size allows Paint Shop Pro will choose the best algorithm based on the image characteristics.
Bicubic Resample - Bicubic Resample uses a process called interpolation to reduce the "jaggies" associated with expanding an image. Therefore, choosing this resize algorithm is always best when you are enlarging a graphic, especially photographs.
Bilinear Resample - Bilinear Resample works the opposite of Bicubic in that it applies the opposite algorithm. Use Bilinear Resample when you are reducing the size of a photograph.
Pixel Resize - Pixel Resize removes or adds pixels as necessary to achieve the new height and width specified for the graphic. This resize algorithm works best with graphics with clear sharp hard edges. To see how this works, create a new graphic 150x150. Draw a black rectangle with Antialias unchecked. You will have a black rectangle with clear sharp straight edges. Now, duplicate the graphic (Shift+D). Resize both to 70%, one with Pixel Resize and with Smart Size. Zoom in on both graphics. You will see that with Pixel Resize, the edges are still clear and sharp, whereas the Smart Size edges are now slightly blurry due to the antialiasing that went on during the resize.
TLDR: use "Smart Size".
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