Which resize algorithm is the best ?

I'm trying different resize algorithms and I'd like to know which one is the best.
Can you compare the following pics and let me know which one is the best for you and why ?
RESIZE1
RESIZE2
RESIZE3
RESIZE4

The original pic is here : ORIGINAL (28 MB).
All the files are in TIF format to avoid compression bias.
If you think this pic is not good to have an idea about the resize performance, and if you have one which is more pertinent, please send it to me and I'll try the different algorithms on it and I will post the results.
Thanks.

Yves, this might interest you:
http://www.americaswon​derlands.com …l_photo_interpo​lation.htm

One of the first three.
#4 looks very much oversharpened.

(Guessing bicubic, smoother, sharper, nearest neighbor?)

Another link that might be of interest: http://www.4p8.com/eri​c.brasseur/gamma.html

Agree #4 oversharpened, full of sharpening artifacts. In #3 the high frequency edges (around left ear) are too harsh for me. I like #2.

Here is my favorite method for downsizing, Lanczos + Hi-pass sharpening (1 pixel radius, 80% opacity):
http://photos.imageeve​nt.com/elied/misc/lanc​zos-hipass.tif

I use bicubic sharper when downsizing pictures in CS5. I then apply proper output sharpening.

Number Three

Thanks everyone for the contrribution.
Number 1 is DPP resize algorithm.
Others are different algorithms.
Thanks Elie for the link. Interesting.
And thanks René for the link. Quit impressive.

What software are you useing ? It´s hard to see when they are not side by side, but number 4 is really bad. I downsize from 4752 px long side to 1280 px in CS5 useing bicubic (best for smooth gradients) and then use smart sharpen at strenth 75/100 0.3 px. depending on the photo, more fine detale lower the strenth.
I´m happy with the results, but if anyone knows a better method lets hear it.

wfarrell4...can you say what you mean by "proper output sharpening"

wfarrell4 wrote in post #13453466
I use bicubic sharper when downsizing pictures in CS5. I then apply proper output sharpening.

This and interesting video on the subject. The presenter suggests not to use bicubic sharper.

http://www.youtube.com …4mV3NsLmXw&feat​ure=relmfu

I've adopted this method. I have two actions now for the resizing part. PS Image size and Resize Magic.

http://www.earthboundl​ight.com …search=edge+mas​k&bool=and

If I could download the original I'd have a go at it. I just keep getting the spinning wheel telling me it is downloading.

digital paradise wrote in post #13454289
This and interesting video on the subject. The presenter suggests not to use bicubic sharper.

http://www.youtube.com …4mV3NsLmXw&feat​ure=relmfu

He doesn't say not to use it. I received simply stunning 15x10 test prints from AsukaBook after using bicubic sharper down sampling and applying an edge mask/Gaussian blur for sharpening.

At about 12:15 states that bicubic sharper will create more halos but they are pretty small. He does suggest to use bicubic and then use Smart Sharpen. He does say it was not critical but I guess he used it for that example. I used to use bicubic sharper. Maybe I'll revisit it. A very good video - for me anyway.

@René Damkot's link http://www.4p8.com/eri​c.brasseur/gamma.html

Wow!
Quick test in CS5 shows that you need to go to 32bit for scaling to be mathematically correct. Disappointed with Adobe right now.