Convert a Photograph into an Illustration

I'd start in PSD, using a "Threshold" adjustment layer on photo. The photo could be converted to a Smart Object and a Gaussian Blur Effect applied, to smooth out the edges. This method allows you to play with the amount of blur vs. Threshold to use to get the effect you're after. The resulting image can then be auto-traced in AI.

Can you show the photo in question?

It would then be easier to provide possible ways.

Any automatic functions will only be as good as the source image. Even by editing in Photoshop you can only improve what's already there.

A manual approach would be best.

You could try various settings in Image Trace to see if something works, but most likely you'll have better results if you take your image into Photoshop first. Adjust your curves/levels/contrast until the features you want highlighted are the ones that remain. Then take that image into Illustrator and use Image Trace.