Putting parameters on a URL makes new URLs. Googlebot will see those two different URLs separately as separate images.
Should you minimize the variants? Not necessarily.
- Googlebot does duplicate content detection. It will likely figure out that the different image URLs have the same picture. When that happens it will likely choose one of them to rank and ignore the others. See What is duplicate content and how can I avoid being penalized for it on my site?
- Unlike web search, PageRank popularity isn't the most important factor for image rankings. The most important factor is "image quality". By which Google means "bigger is better". It is far easier to rank the biggest resolution version of your image compared to the anything scaled down.
In practical terms that means that I usually recommend disallowing Googlebot from finding all thumbnails and scaled down images, and direct Googlebot to the largest resolution image in most cases that it is used. For example your robots.txt could contain:
Disallow: *png?width=*
And when you use an image you could mark it up with a link like this:
<a href="123456.png"><img src="123456.png?width=250&height=200></a>
This would allow you to show the small image to users in the page, while still passing PageRank to the image. Google image search treats links to the image just as powerfully as an img tag usage.
You could even use JavaScript to intercept users that click on the image and show them the larger sized image in some sort of lightbox or popup instead of having their browser leave the page to view the image. As long as users can see the full sized image, Google wouldn't consider that to be manipulative or cloaking.
The only case in which you wouldn't want to link to the large image is when you link the image to something else instead. For example if you link a thumbnail to the product page, don't worry about the link to the large image there. Googlebot will find it on the product page.
