Best Treatment for Sunken Eyes
I would correct the hollowness of your eyes with Restylane injections. The results are natural and last longer that Restylane in other more mobile areas of the face. It is very important that you choose your injecting physician most carefully for the treatment of the eye area as it is extremely delicate and unforgiving. Good luck and be well.
Botox & Fillers Vs Surgery
Thank you for your question and photos. The concerns you are expressing and showing in you photos would respond well to fillers such as Restylane and Botox/Dysport to the crow's feet area. This combination would work well for your but needs to be repeated. An extended blepharplasty is the surgical treatment of this problem. This has more longevity, but requires an operation. Hope this helps. Best wishes!
Restylane filling can make a very big difference here. Treatment lasts well over a year and can be easily adjusted, something that can't be said for grafted fat.
A proper evaluation in person will help determine solutions for your concerns. It is somewhat apparent in your photos.
Blepharoplasty for "Sunken Eyes"
I agree that your photos are difficult to interpret. It appears to me that there is not much hollowing directly beneath your eyes. The appearance of hollowing laterally is due to a prominent lateral fat pad. This pad is not usually used for fat transposition. Accordingly, a would perform a conservative fat removal laterally only.
Eyelid surgery often times repositions fat as well as removes it.
Volume restoration as well as volume reduction is part of modern blepharoplasty. The pictures are difficult to interpret. Nevertheless, there seems to be a good indication for lower lid blepharoplasty which would be specifically designed for the needs of the patient.
In select patients, lower lid rejuvenation may consist of conservative reduction (not removal) of the lower lid fat pads or 'bags', in combination with structural fat grafting of the 'tear trough' hollow immediately below. As with all aesthetic surgical procedures, it is absolutely essential to customize the surgical plan to the specific needs of every patient.
Sunken Rounded Eyes Corrected with Lower Eyelid Surgery
Tightening the lower lid or repositioning the lateral canthus can change the shape of the eye. This is a component of lower eyelid surgery. A physical exam and a frank discussion of what you do and do not want is imperative.