How important is the following in purchasing a laptop that will be used for image editing:
- processor speed
- amount of RAM
- integrated vs. dedicated graphics card
- HD speed (SSD; or 5400/7200/10000 rpm)
They are all important. But they are all inter-related, so it is best to have a balanced system.
For example, if you have a lot of RAM, you will hold more in memory, and do less paging (to disk), so the HD will be in use less often, and so HD speed would be less important. If you skimp on RAM, and don't have enough, the HD will be used more, data will be fetched more slowly to the processor, so having a super fast processor may be wasted because you have a bottleneck in your memory/storage and the processor is idle waiting on data.
Similarly, if you have a good graphics card it may take some of the workload off the processor, making raw processor speed less important.
On a laptop, I think the main place you can gain performance improvement is in a good dedicated graphics card.
Next most important would probably be RAM. I have 8GB and doing heavy editing in CS6 that seems to be enough. 16GB might give some incremental improvement, but I expect 8GB is enough.
The HD speed will help files/thumbnails load more quickly, and speed up paging, but I think it's the least important, especially if you have sufficient RAM.
Processor speed I think depends on the software you use. Some make better use of multiple cores than others. The speed (GHz) isn't as important as how many cores, and whether you can take advantage of them.
There is an in-depth discussion of these on the Adobe site: How to tune Photoshop CS6 for peak performance
Processor and Ram are most important. Both are in the category of "you can never have too much", when it comes to image processing.
For the processor, on the minimal side, you want at least a mid-range Core i5 (assuming you're going the PC route), with a midrange Core i7 being ideal. All things (or clock speeds) being equal a Core i7 will have smp multiprocessing enabled, which can offer some small gains over the Core i7, but a faster Core i5 will be more beneficial to Photoshop (etc), than a slower Core i7, if it comes to that.
With RAM, get at least 8GB, with 16GB being ideal. Unfortunately laptop ram always costs a bit more than a desktop, but a good tip is to order to order a laptop with the minimal amount of memory and add more yourself. Laptop vendors charge way more than market price for RAM upgrades.
The next most important thing is hard drive speed. Laptops are limited here as 7200rpm drives (still standard on desktops) get too hot and noisy for typical laptop usage. So it often comes down to the choice between a slow 5400rpm drive (which will be a bottleneck for image editing), or a solid state drive (which is great, but won't hold enough data). Optimally, you get get/afford a system with both a fast ssd and a slower, larger drive. Next best would be a hybrid drive with an ssd cache mixed with a standard drive. But the 2 drive solution is the best bet, in my opinion.
As far as graphics card goes, you don't need much. Pretty much any low-to-mid range amd or nvidia 3d accelerated platform will work. Photoshop only uses 3d acceleration for certain operations, so adding a lot of video card won't necessarily get you big gains in performance.
What processing application do you use ? Its worth checking that it actually uses GPU (graphics processor), not all do.
If it doesn't, dedicated graphics is only worthwhile for the dedicated memory, because it'd mean its not using RAM from the main system.
Lightroom for example does not use the GPU.
RAM and CPU are the most important things. CPUs are complex things nowadays, you can't just rely on clock speeds. I use http://www.cpubenchmark.net/ to compare them.
I recently got a new laptop and went for a matte screen, I think its far better for photo editing.
I know everyone always hates "it depends" answers, but that's true to some extent here. If, in this case, you're talking specifically about processing a single image when you say "image editing", then I'd agree with Mike's answer wholeheartedly, including his reference to speeding up CS6.
If, on the other hand, you're talking about processing lots of images with a package like Lightroom, your disk speed becomes so important that an SSD really becomes a must-have -- even more-so than a dedicated video card, in some cases (see Adobe's help page and performance tips pages, as well). Since SSD's remain fairly expensive compared to traditional HDD's, consider a laptop that will let you mount both. A few laptops actually give you two bays for disks, but another option is to look for a laptop that supports a HDD adapter for the multibay so that you can replace your optical drive with a HDD. Two drives working at once, by the way, is also a great way to improve I/O speed. The Adobe docs will help you locate caches and so forth on one drive and data on the other.
Finally, be sure your laptop is running at top speed. Since laptops need to manage battery life and some challenging cooling constraints, they may throttle CPU performance or turn off your dedicated GPU in some situations. My Lenovo W510, for instance, not only throttles the CPU on battery power, it will also throttle back if you're using a power supply that doesn't pump out enough juice.