How to quickly estimate file sizes of resized images on iOS?

Question

In Mail, when I add an image and try to send it, it quickly asks me which size I want to send the images as. See screenshot:

I want to do something similar in an app where I will be uploading an image and want to enable the user to resize the image before it is uploaded. What is the best way to estimate the file size as Apple does here?

It seems that it would take too long to actually create each of the resized images only to check them for sizes. Is there a better way?

I did find this Apple sample code which helps a little bit but to be honest is a bit overwhelming. :)

Answer 1

The single biggest factor in determining the final compressed image size is not image size or JPEG compression quality, but image complexity (lit. entropy). If you know that you're always going to be dealing with highly-detailed photos (as opposed to solid color fields or gradients), that somewhat reduces the variance along that dimension, but...

I spent a fair amount of time doing numerical analysis on this problem. I sampled the compressed image size of a detailed, high-resolution image that was scaled down in 10 percentage point increments, at 9 different JPEG quality levels. This produced a 3-dimensional data set describing an implicit function z = (x, y) where x is the scaled image size in pixels (w*h), y is the JPEG compression quality, and z is the size of the resulting image in bytes.

The resulting surface is hard to estimate. Counterintuitively, it has oscillations and multiple inflection points, meaning that a function of degree 2 in both x and y is insufficient to fit it, and increasing the polynomial degrees and creating custom fitting functions didn't yield significantly better results. Not only is it not a linear relation, it isn't even a monotonic relation. It's just complex.

Let's get practical. Notice when Apple prompts you for the image size: when you hit "Send", not when the image first appears in the mail composition view. This gives them as long as it takes to compose your message before they have to have the estimated image sizes ready. So my suspicion is this: they do it the hard way. Scaling the image to the different sizes can be parallelized and performed in the background, and even though it takes several seconds on iPhone 4-calibur hardware, all of that work can be hidden from the user. If you're concerned about memory usage, you can write the images to temporary files and render them sequentially instead of in parallel, which will use no more than ~2x the memory of the uncompressed file in memory.

In summary: unless you know a lot about the expected entropy of the images you're compressing, any estimation function will be wildly inaccurate for some class of images. If you can handle that, then it's fairly easy to do a linear or quadratic fit on some sample data and produce a function for estimation purposes. However, if you want to get as close as Apple does, you probably need to do the actual resizing work in the background, since there are simply too many factors to construct a heuristic that gets it right all of the time.