What Technique To Get Almond Shaped Asian Eyes? (photo)

This is exactly the purpose and goal of medial epithcanthoplasty.  When it is good it can be very, very good.  However, when it is bad it is very, very bad.  It must be considered a high risk surgery.  The reason for this is simple.  The surgery must be performed in a very visible location of your face.  If it does not heal well then the scars are obvious.  Because this is where people look when they talk to you, it is highly distracting to be scarred in this location.  It is my opinion that only 30% of people attempting to have an inside fold taken to an outside fold have an acceptable result.  For this reason most very experienced Asian eyelids surgeons, and I include myself in this category, do not encourage taking this surigical risk.  This is more than sharing an "asesthetic vision."  This is a matter of knowing what is reasonable and what is not reasonable.  I do agree that  there is no substitute for a personal assessment and detailed consultation with the right surgeons.  By the way you have exquisite aesthetic tastes, both women who you have chosen as your models are very beautiful.

Some Asians have a well defined epicanthic fold while others have less of one.  I try not to change the epicanthic fold when I perform eyelid surgery. It is difficult to achieve a natural result and it would require scars in an area of the eyelid where you really wouldn't want one.

First of all, names can be confusing so let's sort that out.
Canthopexy is when your edge of your eyes is fixed usually only with sutures, sometimes with a small hole made in the bone to reposition your lateral eyelid position.
CanthoPLASTY is when you manipulate the lateral eyelid so that you are not only changing the position usually with a stitch also but doing something else to it, refine it by cutting some tissues out, shortening the lower eyelid amongst other things. But hey, what's in a name because in Asian eyelid surgery it gets more complex.
In Asian eyelid surgery the Almond eyes shape you're talking about is achieved via Epicanthoplasty- stay with me here- epicanthoplasty is surgical technique to modify and improve the shape of your eyelid that is closest to your nose but can also be to the outside aspect closer to your ears. In Korean you called this a "Front opening" and "Back opening".
These epicanthoplasty procedures, "Front +/- back opening" procedures can be a addition to the typical double eyelid surgery where it aims to create a more Almond shaped eyes like you describe. A lot of Asian eyelids have what's known as medial epicentral fold and by "opening" this up you get a more of an Euroasian look which is what most of my patients come to me to request. It's still your eyes, not a Western eyes but a subtle change that still identify you as an Asian person,
Wish you the best in your journey.
Dr Leo Kim, Specialist Plastic Surgeon in Sydney

You are right in not wanting to “Americanize” or “Europeanize” your eyelids as that would result in a very unnatural appearance.

Asian eyes require delicate finesse with the typical epicanthal fold that lies in front of the eye so that proper surgery does not mar the natural beauty of this type of eye. These surgeries are often referred to as Double Eyelid Surgery as approximately half of Asians have a “single fold” and half have a “double fold”.  If you do internet research, you will many different styles and techniques for Asian Eyelid Surgery.

Creating a natural appearance in the Asian eyelid is complex, so I take into account the age and gender of the patient. I avoid removing too much skin or fat which is a common technical error made by surgeons less familiar with Asian eyes.  Proper surgery begins with a design which is drawn prior to the procedure. Many of my Asian patients fly to New York from all over the world asking me to do revisional surgery on their Asian Eyelid surgery because they are not happy with scars which go outside the natural crease and are difficult to manage.

To recreate your crease and fold like the second one may not be possible completely. Actually the eye on the right is very much like many caucasian peoples. They are just associated with dark eyes and features. The fold on the right is also less distinct. This is hard to recreate. Both eyes have type one epicanthal folds but the fold in Natalie Portman is more distinct, deeper and goes more medially. You will have to know that getting the results exactly as you would like them is not an easy task but go to someone that has a lot of experience in Asian Blep

It's hard to answer the question of what specific surgical procedures you need to achieve a similar appearance with the photos you've posted without knowing what you look like to begin with.  Asians generally like to preserve their ethnicity while improving the appearance of their eyes.  

For example, when Asians get a double eyelid surgery, they don't want a crease that Westernizes them or makes them look Caucasian.  They want to preserve their ethnicity while achieving the double eyelid.

The best thing is to seek out a board certified specialist who shares your same aesthetic vision and can help you achieve the results you seek.