The actual scientific paper is:
C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, D. Rugar Nanoscale magnetic resonance imaging PNAS 2009, doi: 10.1073/pnas.0812068106.

The abstract:

We have combined ultrasensitive magnetic resonance force microscopy (MRFM) with 3D image reconstruction to achieve magnetic resonance imaging (MRI) with resolution <10 nm. The image reconstruction converts measured magnetic force data into a 3D map of nuclear spin density, taking advantage of the unique characteristics of the 'resonant slice' that is projected outward from a nanoscale magnetic tip. The basic principles are demonstrated by imaging the 1H spin density within individual tobacco mosaic virus particles sitting on a nanometer-thick layer of adsorbed hydrocarbons. This result, which represents a 100 million-fold improvement in volume resolution over conventional MRI, demonstrates the potential of MRFM as a tool for 3D, elementally selective imaging on the nanometer scale.

I think it's important to emphasize that this is a nanoscale magnetic imaging technique. The summary implies that they created a conventional MRI that has nanoscale resolution, as if they can now image a person's brain and pick out individual cells and molecules. That is not the case! And that is likely to never be possible (given the frequencies of radiation that MRI uses and the diffraction limit that applies to far-field imaging.

That having been said, this is still a very cool and noteworthy piece of science. Scientists use a variety of nanoscale imaging tools (atomic force microscopes, electron microscopes, etc.), but having the ability to do nanoscale magnetic imaging is amazing. In the article they do a 3D reconstruction of a tobacco mosaic virus. One of the great things about MRI is that is has some amount of chemical selectivity: there are different magnetic imaging modes that can differentiate based on makeup. This nanoscale analog can use similar tricks: instead of just getting images of surface topography or electron density, it could actually determine the chemical makeup within nanostructures. I expect this will become a very powerful technique for nano-imaging over the next decade.

The image analysis question is interesting. You are trying to read dial positions, so conventional OCR is probably useless (unless there is a package to do exactly that?).

What you can do is use image processing commands (in your favorite programming language; a shell script, Python, etc.) to crop the image to generate a small image for each dial. Then convert to grayscale (and maybe increase the contrast to highlight the dial). To then calculate the preferred orientation in the image, you calculate gradients along different directions. There will be a much higher value for the gradient along directions perpendicular to the preferred axis. This procedure is described very briefly in this paper:
Harrison, C.; Cheng, Z.; Sethuraman, S.; Huse, D. A.; Chaikin, P. M.; Vega, D. A.; Sebastian, J. M.; Register, R. A.; Adamson, D. H. "Dynamics of pattern coarsening in a two-dimensional smectic system" Physical Review E 2002, 66, (1), 011706. DOI: 10.1103/PhysRevE.66.011706

This is easiest to do if you use a graphics package that has directional gradients built-in (but coding it yourself probably wouldn't be too hard). Basically you create copies of the image and on one you do a differentiation in the x-direction, and for the other one a differentiation in the y-direction. Let's call these images DIFX and DIFY. Then you compose two new images:
NUMERATOR = 2*DIFX*DIFY
DENOMINATOR = DIFX^2-DIFY^2

Then you calculate a final image:
ANGLES = atan2( NUMERATOR, DENOMINATOR )

(All the above calculations are done in a pixel-by-pixel mode.) The final image will have an angle map (with values between -pi to pi) for the image. It should be easy to then use the avg or max over that image to pull out the preferred direction. You may also improve results by tweaking the initial thresholding, or by adding an initial "Sharpen Edges" step, or by blurring the NUMERATOR and DENOMINATOR images slightly before doing the next step.

In any case, the above procedure has worked for me when coding image analysis for orientation throughout an image (coding was done in Igor Pro in my case). So maybe it is useful for you.

As a chemist and practicing scientist, I can attest to the phenomenal costs of doing modern science (much of which comes from safety regulations, and associated "certified" equipment). So I do agree that it is very difficult in the modern age for a hobbyist in their garage to make a groundbreaking discovery... That having been said, i think there are many reasons why hobbyist chemistry (and hobbyist science in general) is a good thing:

1. The combinatorial space in science (and in the production of chemicals especially) is absolutely massive. There is no practical way for chemists to explore it all, so of course they make educated guesses about what is both (a) reasonably easy to make; and (b) of some practical value. However because the combinatorial space is large, there is still plenty of uncharted territory for others to explore. Random fortuitous discoveries are certainly a part of science.

2. Hobbyists can afford to do research that is risky and has no obvious application (I mean "risky" in the sense of "it might not work or lead anywhere" and not in the sense of "it might be dangerous"). They don't have to satisfy funding agencies or pragmatic concerns. They can just explore. Thus they can sometimes pursue crazy lines of inquiry that established scientists wouldn't touch.

3. There is such a thing as having your creativity inhibited by institutionalized concepts. A hobbyist isn't as restricted by the "well-established-rules" of the field, and thus may make creative discoveries others would have missed. (This is rare, by the way: the vast majority of science comes from pushing along using well-established procedures and concepts... but rare "out of the box" discoveries are also important in science.)

4. Doing chemistry (or science in general) on a budget, using only commonly-available equipment, can actually force specific kinds of discoveries. Specifically, it helps to discover things that are cheap (which industry loves!) since it can be done with commodity chemicals and tools. (Who knows, there may be a cheap way to make a better antifreeze using only what is in your house and back-yard.) So hobbyists actually have a chance to discover things that will actually make an impact on industry (whereas the chance that they discover something fundamentally new, without modern diagnostic tools, is slimmer).

5. Finally, even if the hobbyist doesn't actually discover anything new or interesting (which is, by far, the most likely outcome), it has a positive effect on the participants. The people doing it are doing so for fun (presumably), and that in itself is reason enough. Moreover it may be the catalyst for someone to go into science professionally. The ability to make kids enthusiastic about science should not be overlooked. Like most hobbies, hobby-science is more about the process than the end result.

As a chemist, I definitely like the idea of hobby chemists, and/or home laboratories. People should be free to do science at home if they are so inclined. But this is in some sense a bad example:

You should never use the same equipment for your chemistry as for your other household things. If you're going to do chemistry at home, do it safely. This means having a separate (well-ventilated) room for your work, and using separate ovens, microwave, glassware, and other equipment for your work. Chemical contamination is a real threat. You may look at a chemical reaction and deem all the reactants and products to be safe... but if you make a mistake you may contaminate a room/oven/glassware with a more dangerous side-product. And you do not want to be then ingesting these contaminants (worse, you do not want to expose your family and friends).

So, like I said, be safe and use dedicated equipment for your experiments. (And don't brush your teeth with the toothbrush you use to clean your test tubes.)