Why Google Changes Your Titles in Search Results

Everyone knows that page title takes a major role in the Google search results.
A significant title can get high number of clicks and also more traffic to your site, whereas a poor title can cause people to skip over your website and visit another site of your competitors.
Hence in search results, how does Google choose exactly what they will use for the title of your page? Is it determined by schema? Or else, Is this determined by particular heading tags (H1s or H2s)?
Google's honored Engineer Matt Cutts illustrates that why Google changes your titles? in webmaster help video.
Many of the webmasters don't understand that Google doesn't display exactly the title tag for particular page. It is not new that Google always change the title tags. There are a less number of reasons to why Google will choose a title apart from webmaster’s title tag.
"When we try to select the title to display in the search results, we are looking for a succinct description of the page that's also relevant to the query," Cutts explained.
Google looks for three things, which are:

1. Something relatively short.
2. A high-quality description of the page and perfectly the site that the page is on.
3. That it's somehow related to the query.

"Hence if your existing HTML title fits those principles, then often times the default will be to just use your title" Cutts said.
"In an ideal world it will exactly illustrate the page and the site, it would be related to the query and also be short."
All webmasters doesn’t write high quality titles for search engines. In some cases you wonder why Google choose an odd or even completely wrong title for a webpage, when it isn't in the title tag or the page's title.
There are the different ways Google selects a title for a page in their search results, Cutts said.
"Now if your present title doesn't match to user’s query, then a user who types in something and doesn't see something related to their query or doesn't have a better idea about exactly what this page is going to be, is less likely to click on it. So in those different cases we might dig a little bit deeper," Cutts said. "We might use content on your web page," he said.
"We might look at the links that point to your page and include some text from those links. We might even use the Open Directory Project to evaluate what a good title would be. We are searching for the high quality title that will help the user or else that's what they are looking for." Cutts also said how you can try and change your titles for particular keywords you feel a searcher is going to search for.