Bicubic Smoother versus Bicubic Sharper, and Which You Should Really Use
Tastes great. Less filling. Back when Photoshop CS added Bicubic Smoother and Bicubic Sharper to the list of resizing options, most photographers took Adobe's advice and used the former when enlarging and the latter for reducing image size. But that may not give you the best results.
Before I get into the details of this, there are actually five choices for interpolation method in Photoshop although at least two are rarely used. Nearest Neighbor takes the easy way out and simply fills in new pixels with the same value as one of the adjacent ones. Bilinear does a little bit better by averaging all the surrounding pixels. Both of these yield results that make evident how little CPU power they take to execute. At least when working on photographic images, forget that these methods even exist. Bicubic employs a detailed examination of surrounding pixels and creates new pixels based on a statistically weighted average of what it finds. It can be slower than Nearest Neighbor and Bilinear but on modern computers you are not apt to notice much difference. What you will notice is that your results look much better. Bicubic was long the standard interpolation method for resizing images in Photoshop.
Once the first version of Adobe's Creative Suite shipped, photographers had two new interpolation choices in Photoshop CS: Bicubic Smoother and Bicubic Sharper. Since then, it has generally been explained that the difference is that the Smoother version should be used for enlargements and that the Sharper version was best for reducing image size. The original Bicubic method is still there and Adobe says that it is best for when you want smooth gradients. If you've ever stopped and thought about this, these descriptions don't make much sense. Wouldn't you expect that if Bicubic produced smooth gradients that Bicubic Smoother would produce even smoother gradients? Of course it does, but Adobe hasn't updated the descriptions for the original three interpolation methods. The truth is all three Bicubic methods produce smoother gradients when comparing against Nearest Neighbor and Bilinear, but the question remains as to what really is the difference between the Bicubic variants?
Adobe doesn't really document the precise differences, but what appears to be the case is that the weightings used in the basic Bicubic algorithm are slightly biased to make the Sharper version pay attention only to pixels very close to each one it examines while the Smoother version takes into account pixels further away. You can think of this as being somewhat similar to the radius slider when blurring or sharpening. The original Bicubic would therefore fall somewhere in between these two.
Adobe says to use Bicubic Sharper when decreasing image size. I believe the premise is that since making an image smaller naturally loses detail, the added sharpness of the modified interpolation method would help accentuate what detail remains. In my experience though, this generally yields images with too much sharpening and I prefer to use regular Bicubic when downsizing, reserving the right to apply my own sharpening afterwards as warranted.
The standard line when increasing image size is to use Bicubic Smoother as it yields smoother gradients and the other Bicubic methods might produce undesirable artifacts. But upsizing an image naturally softens an image since the details you started with now occupy greater areas (they got bigger) with no additional details available to fill things in. Remember that if you never captured the finest details they won't be there to start showing up as you make an image bigger. So in most cases I find that Bicubic Smoother really doesn't do me any favors. I have to sharpen anyway to minimize the inherent softness of the upsizing process. And since, like resizing, sharpening directly modifies image pixels, both contribute to image degradation. As such, I find it often preferable to do as much as I can of both in a single step by means of Bicubic Sharper when upsizing. Perhaps this goes against Adobe's learned advice, but I know other photographers who feel likewise.
Of course all this is somewhat irrelevant unless you are changing the size of an image by a not insignificant degree. If double the size of an image the three Bicubic variants will give slightly different results. If you only need to increase the size of an image by ten percent, you may as well stick with the default regular Bicubic.
Speaking of defaults, if you find you generally prefer something other than standard Bicubic, you can specify your default in the Photoshop Preferences dialog on the General tab. Note that the default you specify here is also used for resizing operations such as Edit >> Transform that don't give you a choice of interpolation method.