I've taken a class on intellectual property law so let me give my interpretation. All original works become copyrighted by the creator at the time of creation, without the creator having to do anything.
This means any content you find on the internet is copyrighted by someone, regardless if they've posted a copyright notice on their page. Using said content without the permission of the copyright holder is illegal. (Although you're unlikely to be prosecuted.)
Exceptions apply to the quotation of written material, provided it is properly cited. This is why it's legal to re-print quotations (including the quoting posters on this site do of each other). This is also why scholarly journals can quote each other without asking for the author's permission.
Often websites will have blanket clauses on their sites enabling people to use their content (especially images) as long as they cite it's original location and give credit to the authors. As long as they follow the stipulated guidelines, they're in the clear.
Absent this authority, the legal course of action is to contact the copyright owner and obtain permission to use their image. Pain in the butt, but you can blame lawyers and the constitution for that.
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I've gotten around the permission part by having technical photo images worked into line art. That makes a second original image that is simply based on the first. There's a fine demarcation here, so be careful to make the line art obviously original.
It's not clear to me exactly what you are doing by the description above. I interperet this to mean you are re-creating the original work with line art and displaying your new creation. If this is true, your "new" art would be considered a derivative work under the law. To the extend it's content was based on another copyrighted piece of work, it would still belong to the original copyright holder, you would only own the rights to the additions or changes you made. Posting this new image doesn't get you around the legal hurdle. Making it obvious you re-created the image also doesn't get you anywhere legally. You still don't own the idea the image was originally based off of.
As for linking to the image's location on someone elses server, it's still using their image for your own purpose so beyond the bandwidth issues, it still violates their copyright assuming you don't have permission.