Up to about 2013, this was a much-discussed question, mainly due to LinkedIn users having the mindset that the website is an online bank of resumés (CVs) and generally we don't put photos on a resumé. That has changed - we DO put a photo on LinkedIn. In fact we have now reached a point where you look at a photo-less profile and think that this person either thinks they don't look business-like, or they haven't figured out how to add a photo - and thus potentially missing out on networking and business opportunities.
Your profile photo is more important in LinkedIn than many social media sites as this is your best chance of making a business connection - someone who wants to do business with you wants to look at you in the eye, and they will judge your suitability for working with them on the basis of your profile photo. One recent survey suggested that 80% of your time looking at someone's LinkedIn profile is looking at their profile photo.
If I am at the point of considering a meeting with someone I haven't met before, I will always do my prep work beforehand. Checking their LinkedIn profile will form part of my assessment, which connections we both know (good icebreaker), along with what they want to talk about, how we would each benefit from working together, and so on.
BASIC RULE - You need a clear profile photo which gives the mood of who you are, and how you would like to be seen when working with others.
ACTION POINT - Ensure you have a clear head-and-shoulders photo filling most of the area. If you cannot see your eyes, you are too far away. No sunglasses, dudes! If you focus on a particular aircraft type, consider having that unobtrusively in the background.
If you put your business logo in here instead, you have failed to understand LinkedIn, but look out for a future blog post on LinkedIn company pages.