My initial thoughts on applications like this are to extend the included functionality already included. Apps like Ikea Place first show if a piece of furniture fits in with your home’s decor, but more importantly displays if a given piece of furniture will fit where you plan to place it. What would also be extremely useful would be a home renovation application. An application like this would allow you to see what the effects of different home renovations would be. It could show things like tearing down walls, changing your flooring, adding an island to your kitchen, etc. This tool would be useful in deciding how exactly you want to renovate your home before ever calling a contractor.
Another possibility that is slightly related would be a tool placement application. Many products today are made with proprietary tools, which are both hard to find and even harder to replace. With an application like this, you could show the application a specific part that you want to repair. The application would then walk you through the repair of the part as well as showing you the correct tools for each step of the process. If any repair requires a proprietary tool, the application would give you a list of alternative tools that are not proprietary. Also, if multiple tools can be used for any part of a repair, the application would also give you the option of choosing one of those tools. This would allow someone who may not have a lot of tools still be able to repair something.
Fashion is also a field that could be improved upon by an application like this. You could choose any given article of clothing and show your body in the camera. The application would then show you how you would look with that piece of clothing on. If you give the application your measurements it could also determine what size would look best on your body. The application could even be used to help create outfits for you. You could put on some pants and have the application generate the rest of the outfit for you based on how it would look in relation to those pants. A further extension would be to input all of the clothing items you currently own and have the application generate outfits from your wardrobe. This would be beneficial in two ways: the first is that the user saves time trying to decide on what to wear; the second would be that more parts of your wardrobe get worn more often. Personally, I know I have the tendency to stick to certain outfits because I like to wear specific articles and only a few things will match those articles well. By having my outfit decided for me I would feel more confident in branching out and wearing more of my own clothing and also trying different styles.
To go off of the fashion angle, an AR hairstyle application would also be very useful. Show your head in the camera and the application will show you best how to work with your hair texture in order to style your hair well. It could show simple things like how straightening or curling would look, and also things using different gels, cremes, pomades, etc. would look with your current hair. It could also show how different cuts/colors would look on you.