Obiage,Obijime

A piece of cloth that resembles a scarf in western fashion but has a fix size.
Usually made from silk but it has many kind of variatons, from very formal (used with fukuro obi) to casual (used with nagoya obi).
Obiage has the important function to cover the "obi makura" and its strings when wearing fukuro or nagoya obi.
From the front, you can see obiage on the top part of the obi.

A kind of cord made from silk or cotton that you use when you wear nagoya or fukuro obi. It's essential as you can't tie these kind of obi without an obijime.
Obijime has many variations, from very formal types (these are wider, always silk) to very casual (silk round types, cotton thinner types, etc).