I am start porting my Matlab image processing project to C and is
looking for a library that:

* Has basic matrix operation support ( like matrix product,
eigenvalue, etc )
* Basic image processing functions ( canny edge detector,
dilation/erotion, etc)
* Basic GUI so that I can display something easily and interactively
give some input
* Cross platform, namely Win32, Linux, and IRIX
* Used by many people
* Open source or at least free for educational/research usage
* Faster than Matlab C Lib (it's not free anyway)

I found Intel OpenCV and Vision Egg so far. 

Problem for OpenCV, no SGI support; minimum GUI - no even radio button
Problem for VisionEgg, need this Python language that I had no idea
before. Is it efficient?

Probably a perfect thing doesn't exist. In this case, please provide
the popular libraries that are close to the requirement with
explaination of pros and cons.

Take a look at these software lists:

http://www-2.cs.cmu.edu/~cil/v-source.html

http://www.cs.uwa.edu.au/~cheng/myresearch.html

I have experience with Tina and Vista, both of which are very popular,
and I know the main developer of Gandalf and I'm sure it's very good.

You'll find that there's lots of fast, robust open-source code out
there that does what you want, since implementing the algorithms is
the fun part. However, the sticking points are going to be the need
for cross-platform support and a GUI, since providing these is largely
drudge work and rarely gets done by developers who aren't getting
paid.

Hope this helps.

Eadfrith

Thanks for the comment and I will definitely take a good look. 

I just found wxWindows today from SourceForge that can do the GUI part
pretty good. Maybe the only thing is it's a little too complex.