Analogue image zoom: comparing 6 megapixel images with 16 megapixel images

The problem

Let us say you have captured a shot of a test chart with a D40, and repeated the process (same lens) with a D7000. The D40 gives you a 6 megapixel image, and the D7000 gives you a 16 megapixel image. You would like to compare the sharpness of the one camera to that of the other.

There several options for executing this comparison:

1. Print both shots at the same size. This is probably the way to go if you intend to print a lot of uncropped photos.
2. Scale down the 16 MP image to 6 MP, and compare at 100% view.
3. Scale up the 6 MP image to 16 MP, and compare at 100% view.
4. Scale both images to some other resolution, e.g., 8 MP (like DxO labs do), or maybe 24 MP.

There is at least one sound reason why option 4 is the better choice amongst options 2 through 4: scaling artifacts. Performing an MTF analysis of an image upscaled with a popular cubic scaling algorithm (Mitchell) reveals that there is some effective contrast enhancement that takes places as part of the scaling process, visible as overshoot and undershoot in an edge profile plot. By scaling both images, you are at least trying to compare apples to apples, especially if you are unsure of exactly what sharpening algorithm your software will employ.

Of course, this entire post deals with visual interpretation of test chart images. If you are interested in other properties (e.g., MTF) then go ahead and use MTF Mapper to perform such measurements directly. The normal slanted edge MTF analysis does not really tell you what your aliasing will look like after dropping the OLPF from your sensor, nor how apparent sharpness is influenced by demosaicing algorithms. For such evaluations visual interpretation might prove useful still.

Another option: simulation

Once you embrace simulated images, such as those produced with mtf_generate_rectangle, you have a fifth option: directly produce a 16 MP (equivalent) image but keep the point spread function (PSF) of the 6 MP camera. I call this feature "analogue scaling", mostly because it effectively resamples the 6 MP image to 16 MP, but without using a discretized 6 MP image as the source. Instead, the usual "infinite precision" analytical description of the target scene is simply scaled down (relative to the photosite pitch), and the sample spacing of the rendered image is adjusted accordingly.

Here is a comparison between a simulated D40 (photosite pitch 7.8 micron, f/4, green light, 4-dot OLPF) and a D7000 (photosite pitch 4.73 micron, f/4, green light, 4-dot OLPF):

Simulated D40 image, effectively magnified by a factor of ~1.65 (click for full-size)

Simulated D7000 image (click for full-size)

These images were generated with the following commands:

mtf_generate_rectangle.exe --target-poly doc/pinch.txt -p airy-box -n 0 --analogue-scale 0.606410 --pixel-pitch 7.8 --aperture 4 -o pinch_d40.png

and

mtf_generate_rectangle.exe --target-poly doc/pinch.txt -p airy-4dot-olpf -n 0  --pixel-pitch 4.73 --aperture 4 -o pinch_d7k.png

respectively. Note that the analogue scale factor is ~0.606, which is 4.73/7.8, i.e., the ratio between the photosite pitch of the D7000 and D40. Specifying an --analogue-scale factor of greater than 1.0 will produce aliasing (and an apparent increase in sharpness), while a factor of less than 1.0 will produce smoothing, as would be expected from upscaling.

Note that the "-n 0" switch turns off simulated sensor noise. Since sensor noise is currently computed in the domain of the output image, this switch is required to produce a correct pair of images. If noise is left on, you would obtain a scaled D40 image with image noise appearing at the size of D7000 pixels, which will clearly cause the D40 image to appear better than it should. This can be fixed (in the mtf_generate_rectangle code) by scaling the "noise image" correctly, but I honestly only thought of this problem now as I am busy writing this blog post :)

Discusssion

Does this approach work? Well, take a look at the point where the converging lines blur into a gray mess in the D40 image (top image above). This appears to happen after the tick marked "2" in the horizontal set of lines --- maybe about one-third of the way from "2" to "1".

In the D7000 image, the extinction point (gray mess) appears almost exactly at the tick marked "1" in the horizontal set of converging lines. This appears about right, since we know the linear resolution of the D40 is about 0.606 that of the D7000. Not really a rigorous proof, but at least reassuring.

To summarize: the --analogue-scale option of mtf_generate_rectangle will allow you to produce a pair of synthetic images of a test chart to simulate two different cameras, with different photosite pitch values, but without the hassle or potential artifacts introduced by upscaling the discrete image produced by the lower-resolution camera.

Of course, this type of simulation will allow you to investigate potential future sensors too. How would a 50 MP APS-C camera render a resolution test chart .... ?

ps: MTF Mapper version 0.4.16 is finally available here --- this is the first version to support all the required features to produce the results found in this post.