Since tons of people are using internet on mobile devices, I suggest not paying too much attention to the title value in the image tag. On a desktop computer, that value is what people see on screen if they put their mouse pointer over the image for a set period of time (one second?). Once they move the mouse again, the title that appear will now disappear. I have used a few mobile devices and never seen the image title value pop-up on the screen.
What I do in order to lower HTML byte size and lower the chances of keyword spam is not even specify the title. Google hates it when the same set of keywords appear in a page over and over again. Here's an example:
<title>Yellow Chicken runny soup inside white chicken runny soup</title>
<p>Yellow chicken runny soup is made with white chicken runny soup mixed with light yellow chicken runny soup and one other chicken runny soup. See image of yellow chicken runny soup.</p>
<img src="/path/to/yellow/chicken/runny/soup.jpg" alt="yellow chicken runny soup" title="yellow chicken runny soup">
<p>See image of white chicken runny soup</p>
<img src="/path/to/white/chicken/runny/soup.jpg" alt="white chicken runny soup" title="white chicken runny soup">
<p>And that's all we have for white chicken runny soup and yellow chicken runny soup for today.</p>
<!-- copyright yellow and white chicken runny soup enterprises -->
As you can see, having the exact same title and alt value makes your keyword density for keywords higher, but if you don't watch it, you could go overboard to the point where search engines think your site is spam.
What is extremely important is having the alt value specified. This is a value that describes the image that google uses.
P.S. If someone manages to get my HTML posted above in top position in google's index, I'll throw that person in the guiness book of world records.