Image Size Best Practices for Mobile Application

For Android, I think the best place for you to start would be here, it has a lot of information including standard screen sizes and how to display images while keeping them in the best possible quality.

http://developer.android.com/guide/practices/screens_support.html

I'd also suggest doing as much image manipulation as possible on your server. Images are a pain to work with on Android due to memory constraints and fragmentation. Two phones may store pictures taken the same way with different orientations, and there is no simple way to handle rotations, though it can be done (thankfully, I've yet to encounter a phone that incorrectly records Exif data, but I wouldn't be surprised if they existed...). The more you rely on the phone to do, the more chances you have for error due to manufacturers putting wrappers around and otherwise customizing how it handles media.

As for how to display, ideally if your back end is already doing a bunch of different resizes, you can include your screen density when you request the images and send the best size based on the dev guide. If you want to keep differences to a minimum, at least support med or high density for phones, and extra high density for tablets.

Just my two cents, I'm sure you'll have a lot of opinions. Good luck.

I don't have a full answer for you, but I do have some thoughts...

1) I'd suggest reducing the image sizes before uploading. If I were using your application and I had to upload a 4 meg photo, everytime I wanted to use your application, I'd probably pass. And as we venture forward, we're hitting much better technology in terms of camera phones; Nokia has released a 41 megapixel camera, which I'm guessing will create rather large images. Users having to download a 4-6 MB image is also not a great idea. Just some thoughts from a user point of view.

2) I wouldn't cut the images. You don't necessarily know what parts of the image aren't important, so how would you know where to crop it? Let the phone size the pictures accordingly and rely on the ability to zoom into pictures to see things at a larger size.

3) You could try to make a UI that hides buttons. If you have something really simple (like just going forward or backwards) you could rely on gesture controls (swiping) to move around your application. You can implement sliding drawers and menus that take up space temporarily, when in use, but give you the space back when you want to look at the main content (pictures, in your case). I've typically found that hiding buttons doesn't work well and people seem to want/search for buttons that let them navigate, but the Android gallery works just fine with menu + swiping only, so who really knows.