Author profile image will not be displayed in SERPs. In my opinion, most of authors had created their Google Plus Profile because of the fact that their G+ profile photo would be shown in the Google Web search results as a rich snippets in both Desktop as well as mobile. However, those people who has not created a profile in Google Plus, their photo will obviously not shown in search results.
The main reason behind Google Authorship was to increase in Click-Through Rate (CTR) for the articles and blog posts shown as a rich snippets in search results. Obviously, people would click on those Web Search Results which displays an image of author who have written or published that particular webpage article or blog post.
Google removing Author Photo from Search Results
As per John Mueller (Webmaster Trends Analyst) G+ Post, Google removing the profile photo and circle count from search results for simplifying the way authorship is shown in all devices.
“As a part of this, we’re simplifying the way authorship is shown in mobile and desktop search results, removing the profile photo and circle count.”
Does this mean Google Authorship will no longer exist? Will you not able to see the Author Stats i.e. search statistics (Impressions, clicks and CTR) for pages for which you are the verified author in Google Webmaster Tool?
Authorship in search results is nothing but the way to inform people searching their query in Google Search Engine that they may choose the website or blog posts which are written or posted by their relied authors. Thus they may find more reliable, great and original contents based on their previous experiences on particular site or blog authors.
Note that John Mueller clearly states that Google Authorship markup will still work without being active on Google+ and you can also use Google+ without using authorship markup.
Accordingly, you can see the name of a webpage’s author next to your results provided you are a verified author for that particular webpage article or blog post. In other words, if you want to see your name as author in Google search results then you must verify authorship of your content by creating G+ profile and link it to that contents.