After enduring the math and tedium of developing our own corrections for images with vignetting, geometric distortion, and chromatic aberration, it's worth looking at some alternatives not involving such a high pain level.
First, if you're a user of a recent version of Photoshop, you have the Lens Correction filter available. This filter has adjustments for the 3 areas we've been exploring. It works fine for estimating simple adjustments in any of these 3 areas but it doesn't have any kind of built in knowledge of adjustments required for particular lens/camera combinations. If you only need approximate corrections and like the easy-to-use interface, this is a good way to go. If, on the other hand, you have stricter requirements or you have short focal length lenses with complex mustache distortion or other more complex problems, the Lens Correction filter won't handle it.
Another option to consider is DxO Optics Pro which is a sophisticated product handling a number of image problems including those we've been discussing plus many others. This software is tied directly to your camera/lens combination by way of modules that have very specific correction parameters built in that are the result of DxO's expert lab testing. Results can be very good, the product comes with standalone and Photoshop plugin versions, and can be used to batch process large quantities of images fairly easily. On the minus side, it's not inexpensive (although certainly not overpriced for what it does), it's a bit daunting to learn the quirky interface, and it only supports a subset of camera and lens combinations. For example, at the time of this writing, it doesn't support the Canon G9 we've been using as our example in this series.
Finally, there's PTLens which is a much less ambitious effort in terms of functionality but which has a much broader camera/lens coverage than DxO. It comes with a standalone version (handling only JPEG and TIFF images) and a Photoshop plugin. In terms of cost (about 10% of DxO), simplicity, and effectiveness for its strong point, geometric distortion correction, this is a gem. It also handles vignetting and chromatic aberration but you must make those adjustments manually, unlike the corrections for geometric distortion which cover a very broad range of cameras and lenses. PTLens had its genesis from Panorama Tools roots and handles geometric distortion under the covers in the same way that we discussed using the third-order polynomial radial corrections—except you don't have to be aware of it. By the way, the manual corrections for chromatic aberration in PTLens are also analogous to what we developed using corrections for the red and blue channels. In fact, the PTLens sliders show the numeric radial deviation from 1.0 (no change) as you visually tweak the image to your satisfaction. You can interchangeably use the PTLens numbers and the d coefficients we used in hugin parameters. I routinely will use PTLens to get in the ballpark and then transfer the corrections to hugin to refine the correction to as close as I can get to eliminating transverse chromatic aberration. The PTLens Photoshop plugin can be used to handle large numbers of images simply by making a Photoshop Action to run during ACR processing for example. The one thing I don't like about PTLens is it doesn't handle very large images well, having a tendency to bomb out with memory errors. But, other than that, you'll have a hard time finding a bigger "bang for the buck".
Both DxO Optics Pro and PTLens have free trial versions which should be exploited if you're at all interested in looking at their capabilities.
Given you can buy good solutions for correcting image problems we've been discussing, you may wonder why all the trouble doing it ourselves with all those measurements and mathematical manipulations. There are a few reasons. First, none of the products mentioned above handles all camera/lens combinations. For example, DxO doesn't handle the Canon G9 and PTLens doesn't handle the Canon G9 with the Raynox wide angle adapter we mentioned back in the post about geometric distortion. Second, by doing your own measurements you can be more confident that your custom-built corrections are as accurate as possible for your particular images. And third, there's nothing like grinding your nose into the pixel-level image flaws to get a real understanding of what your equipment capabilities and limitations are.
Next up, some final thoughts on compact consumer cameras generally and the Canon G9 in particular, given what I've learned going through these image correction exercises. After that, maybe we'll get back to some real photography discussion instead of all this techie pixel-bending stuff.
Showing posts with label geometric distortion. Show all posts
Showing posts with label geometric distortion. Show all posts
Monday, August 25, 2008
Monday, August 18, 2008
Part 5: Putting It All Together
In previous posts, we've looked at the Canon G9 point-and-shoot camera's vignetting, geometric distortion, and chromatic aberration. We've also looked at strategies for addressing these issues, primarily using the fulla command from the hugin panorama photo stitcher package.
The fulla command doesn't have a nice friendly GUI interface but it does allow us to put together arbitrary corrections to be applied to large numbers of images without a great deal of effort. Each of the fulla corrections we've explored in previous posts can be combined into a single command addressing vignetting, geometric distortion, and chromatic aberration.
Your workflow sequence is very important. The corrections we've been discussing should be applied to the images before any cropping, resizing, etc. have been done. I always shoot raw so I use ACR or some other tool for "developing" the image to set the correct initial tonality, color temperature, etc. and then export the image in 16-bit TIFF format (lossless unlike JPEG). I apply the image corrections and then bring the corrected version into Photoshop for subsequent processing.
Let's start with a hypothetical file shot on the Canon G9 at 7.4 mm and f/4, and processed from the raw CR2 file into a 16-bit TIFF file called example.tif. To apply my standard corrections for vignetting, geometric distortion, and chromatic aberration, I would use the following command:
(The '\' characters indicate arbitrary line breaks for formatting here. This is actually all one command line.)
The "-c" option gives the polynomial coefficients for correcting vignetting, the "-g" option gives the polynomial coefficients for geometric distortion correction, and the "-r" and "-b" options provided the polynomial coefficients for transverse chromatic aberration correction. (But you already knew that.)
When fulla is done crunching the numbers, it outputs a file with a "_corr" filename suffix. So our example correction would create a new file called example_corr.tif. It will look substantially better than the original with the corrections applied.
Naturally you don't want to have to type in that command every time you process a file so you can create a MSDos batch command file (on Windows) or a Bash script (on Unix systems) to generalize it. Let's say we want to correct arbitrary numbers of files with one command. We can create a batch file like this:
(Once again, this should be all on one line in the real batch file.) Assuming you named this something like G9_74_4.bat (because it's only useful for the G9's 7.4 mm f/4 images), you can process all the TIFF files in a directory with a single command:
Unix, Linux, Mac users can create analogous script files using for iterations to do precisely the same thing.
I must mention something about the fulla command here: it's flaky and not mature in some regards. One frustration is that, when it outputs a corrected image, that corrected image has its metadata stored in an unconventional way that is not visible to Photoshop and many other applications. If you're running any kind of responsible workflow, this is not good, but there is a way around the problem.
ExifTool by Phil Harvey is a superbly-done high-function image metadata management tool. It has an extraordinary number of capabilities and it handles them well. If you download the tool, you can use it to save your EXIF (and other metadata) from your image, apply your fulla corrections, and then restore the original metadata in standard format. For example, you can save the metadata for all TIFF files in a subdirectory with this command:
Process your files using the fulla corrections and then restore the metadata to the corrected files.
You can even skip the intial save to MIE file (Meta Information Encapsulation) and simply rewrite the original file's metadata over the fulla output file:
Finally, if you're really ambitious and have Perl programming skills, you could use the Perl Image::ExifTool package to determine the focal length and f-stop for the image and then do a table lookup to determine which of the fulla option parameters to use. I've done a rudimentary job of this just for the subset of camera settings I almost always use for the Canon G9.
If all these seems like a lot of trouble to correct the occasional image, you're right. It's most worthwhile if you routinely have large numbers of images you wish to optimize; then the use of fulla in batch or script files makes more sense.
If you only do occasional corrections, want something a bit easier to deal with, or want a commercial solution, stay tuned. Next up we'll glance at a couple of alternatives for correcting images that don't require all the up-front work we've been slogging through here.
The fulla command doesn't have a nice friendly GUI interface but it does allow us to put together arbitrary corrections to be applied to large numbers of images without a great deal of effort. Each of the fulla corrections we've explored in previous posts can be combined into a single command addressing vignetting, geometric distortion, and chromatic aberration.
Your workflow sequence is very important. The corrections we've been discussing should be applied to the images before any cropping, resizing, etc. have been done. I always shoot raw so I use ACR or some other tool for "developing" the image to set the correct initial tonality, color temperature, etc. and then export the image in 16-bit TIFF format (lossless unlike JPEG). I apply the image corrections and then bring the corrected version into Photoshop for subsequent processing.
Let's start with a hypothetical file shot on the Canon G9 at 7.4 mm and f/4, and processed from the raw CR2 file into a 16-bit TIFF file called example.tif. To apply my standard corrections for vignetting, geometric distortion, and chromatic aberration, I would use the following command:
fulla -c 1.0398:-0.1155:0.1954:-0.1605 \
-g 0.028:-0.0871:0.0521:1.007 \
-r 0:0:0:1.00024 -b 0:0:0:1.00041 example.tif
(The '\' characters indicate arbitrary line breaks for formatting here. This is actually all one command line.)
The "-c" option gives the polynomial coefficients for correcting vignetting, the "-g" option gives the polynomial coefficients for geometric distortion correction, and the "-r" and "-b" options provided the polynomial coefficients for transverse chromatic aberration correction. (But you already knew that.)
When fulla is done crunching the numbers, it outputs a file with a "_corr" filename suffix. So our example correction would create a new file called example_corr.tif. It will look substantially better than the original with the corrections applied.
Naturally you don't want to have to type in that command every time you process a file so you can create a MSDos batch command file (on Windows) or a Bash script (on Unix systems) to generalize it. Let's say we want to correct arbitrary numbers of files with one command. We can create a batch file like this:
for %%f in (%1) do \
fulla -c 1.0398:-0.1155:0.1954:-0.1605 \
-g 0.028:-0.0871:0.0521:1.007 \
-r 0:0:0:1.00024 -b 0:0:0:1.00041 %%f
(Once again, this should be all on one line in the real batch file.) Assuming you named this something like G9_74_4.bat (because it's only useful for the G9's 7.4 mm f/4 images), you can process all the TIFF files in a directory with a single command:
g9_74_4 *.tif
Unix, Linux, Mac users can create analogous script files using for iterations to do precisely the same thing.
I must mention something about the fulla command here: it's flaky and not mature in some regards. One frustration is that, when it outputs a corrected image, that corrected image has its metadata stored in an unconventional way that is not visible to Photoshop and many other applications. If you're running any kind of responsible workflow, this is not good, but there is a way around the problem.
ExifTool by Phil Harvey is a superbly-done high-function image metadata management tool. It has an extraordinary number of capabilities and it handles them well. If you download the tool, you can use it to save your EXIF (and other metadata) from your image, apply your fulla corrections, and then restore the original metadata in standard format. For example, you can save the metadata for all TIFF files in a subdirectory with this command:
exiftool -o %f.mie -ext tif .
Process your files using the fulla corrections and then restore the metadata to the corrected files.
exiftool -overwrite_original -tagsfromfile %-.5f.mie \
-ext tif .
You can even skip the intial save to MIE file (Meta Information Encapsulation) and simply rewrite the original file's metadata over the fulla output file:
exiftool -overwrite_original -tagsfromfile %-.5f.%e \
example_corr.tif
Finally, if you're really ambitious and have Perl programming skills, you could use the Perl Image::ExifTool package to determine the focal length and f-stop for the image and then do a table lookup to determine which of the fulla option parameters to use. I've done a rudimentary job of this just for the subset of camera settings I almost always use for the Canon G9.
If all these seems like a lot of trouble to correct the occasional image, you're right. It's most worthwhile if you routinely have large numbers of images you wish to optimize; then the use of fulla in batch or script files makes more sense.
If you only do occasional corrections, want something a bit easier to deal with, or want a commercial solution, stay tuned. Next up we'll glance at a couple of alternatives for correcting images that don't require all the up-front work we've been slogging through here.
Monday, July 28, 2008
Part 3: Geometric Lens Distortion Correction
All lenses, particularly cheaper mass-produced lenses have some amount of geometric distortion. Some primary lenses, particularly expensive ones, can be highly corrected. Others, particularly with large zoom ranges, are characterized by mixes of barrel or pincushion distortion (or both). The result is images where straight lines appear curved, particularly noticeable in the outer portions of the images.
In 1998 Helmut Dersch created a set of software tools that could be used to, among other things, correct lens distortions so that they could be more effectively stitched together in panoramas. His library of tools caused a cottage industry to grow with many GUI front-ends developed to use the tools. Not everyone is interested in creating panoramas, but many are interested in correcting noticeable distortions for things like ocean horizons, architectural features, and many other distortion-sensitive subjects.
The Canon G9, which we've been using as the guinea pig for our series discussion, has a zoom range of 7.4 mm to 44.4 mm (equivalent to roughly 35 - 210 mm in 35 mm terms). At the short end of the range, it has moderate inner barrel and outer pincushion distortion (the combination commonly called mustache distortion). As the lens zooms out, images acquire slight pincushion distortion. The compound distortions in the lens don't correct well using simplistic generic tools so we'll develop specific corrections to flatten the images at the various zoom settings.
We need to apply a corrective distortion to the image to compensate for the lens-induced distortions. The image distortions are radially symmetric so we'll use a function that determines image distortion based on radial distance from the center of the image. In short, we'll be using a 3rd-order polynomial to correct the radial distance each part of the picture needs to be moved, based on its original radial distance from the center:
Our goal is to find the values for a, b, and c to correct for our lens's distortion at a specific focal length. The d value is only used to adjust the total image size to compensate for the other corrections. It has a value of
There are a few approaches to finding the coefficients for the polynomial. One way is to shoot several images and stitch them together into a panorama using one of the commonly-available tools and then note the corrections the software made to fit the images together. In essence, the process of stitching the images accurately requires the software to correct for distortions to complete its job.
We'll use a more targeted approach using one image. In this technique, you shoot an image that contains several horizontal and vertical lines that you know are straight. A large office building is ideal. The objective is to have several lines available in the image at varying distances from the center of the image and stretching all the way to the edges of the image. You then use a panorama stitching tool such as the freely-available hugin panorama photo stitcher package. Using hugin to do this, you load the target image twice, cancel the automatic control point detection, and manually add control points along the lengths of each of the lines you know should be straight. All control points on a line must belong to the same line labeled tn where n is a line number starting at 3 for the first line. (Lower numbers are reserved for other types of lines.)
Once you go through the tedium of identifying a few hundred control points on 6 to 12 lines covering various parts of the image, you run the optimizer to determine what the coefficients should be to cause the distorted lines to become straight.
For the G9, I created test images through the zoom range and here are the corrections I came up with which give me images with the lens distortions largely removed.
To apply corrections to an image, you can use the hugin fulla command we've mentioned previously. This time we use the -g option to pass our correction coefficients:
The output will be our distortion-corrected image. (In this case the image of the building was shot with the G9 set at its shortest focal length, 7.4 mm, so we use the coefficients corresponding to that focal length.)
This technique will go a long way toward correcting obvious geometric distortion but it's not perfect. It doesn't correct to perfection although in most cases it's nearly impossible to tell without careful measurements of the resulting image. It also doesn't handle radially asymmetric distortions such as might occur in misaligned lenses.
Next up, we'll take a look at chromatic aberration and see how we can correct one type of it.
In 1998 Helmut Dersch created a set of software tools that could be used to, among other things, correct lens distortions so that they could be more effectively stitched together in panoramas. His library of tools caused a cottage industry to grow with many GUI front-ends developed to use the tools. Not everyone is interested in creating panoramas, but many are interested in correcting noticeable distortions for things like ocean horizons, architectural features, and many other distortion-sensitive subjects.
The Canon G9, which we've been using as the guinea pig for our series discussion, has a zoom range of 7.4 mm to 44.4 mm (equivalent to roughly 35 - 210 mm in 35 mm terms). At the short end of the range, it has moderate inner barrel and outer pincushion distortion (the combination commonly called mustache distortion). As the lens zooms out, images acquire slight pincushion distortion. The compound distortions in the lens don't correct well using simplistic generic tools so we'll develop specific corrections to flatten the images at the various zoom settings.
We need to apply a corrective distortion to the image to compensate for the lens-induced distortions. The image distortions are radially symmetric so we'll use a function that determines image distortion based on radial distance from the center of the image. In short, we'll be using a 3rd-order polynomial to correct the radial distance each part of the picture needs to be moved, based on its original radial distance from the center:
a * r3 + b * r2 + c * r + d
Our goal is to find the values for a, b, and c to correct for our lens's distortion at a specific focal length. The d value is only used to adjust the total image size to compensate for the other corrections. It has a value of
d = 1 - (a + b + c)
There are a few approaches to finding the coefficients for the polynomial. One way is to shoot several images and stitch them together into a panorama using one of the commonly-available tools and then note the corrections the software made to fit the images together. In essence, the process of stitching the images accurately requires the software to correct for distortions to complete its job.
We'll use a more targeted approach using one image. In this technique, you shoot an image that contains several horizontal and vertical lines that you know are straight. A large office building is ideal. The objective is to have several lines available in the image at varying distances from the center of the image and stretching all the way to the edges of the image. You then use a panorama stitching tool such as the freely-available hugin panorama photo stitcher package. Using hugin to do this, you load the target image twice, cancel the automatic control point detection, and manually add control points along the lengths of each of the lines you know should be straight. All control points on a line must belong to the same line labeled tn where n is a line number starting at 3 for the first line. (Lower numbers are reserved for other types of lines.)
Once you go through the tedium of identifying a few hundred control points on 6 to 12 lines covering various parts of the image, you run the optimizer to determine what the coefficients should be to cause the distorted lines to become straight.
For the G9, I created test images through the zoom range and here are the corrections I came up with which give me images with the lens distortions largely removed.
| Focal Length | a | b | c | d |
|---|---|---|---|---|
| 7.4 mm | 0.028 | -0.0871 | 0.0521 | 1.007 |
| 8.2 mm | 0.0313 | -0.089 | 0.0474 | 1.0103 |
| 9.0 mm | 0.0082 | -0.0186 | -0.0046 | 1.015 |
| 12.7 mm | 0.0187 | -0.0558 | 0.0528 | 0.9843 |
| 16.8 mm | -0.0172 | 0.0541 | -0.0477 | 1.0108 |
| 22.0 mm | -0.0053 | 0.0196 | -0.0201 | 1.0058 |
| 25.0 mm | -0.0038 | 0.0131 | -0.0133 | 1.004 |
| 29.2 mm | -0.0065 | 0.0184 | -0.0111 | 0.9992 |
| 36.8 mm | 0.0102 | -0.0355 | 0.0391 | 0.9862 |
| 44.4 mm | -0.0159 | 0.0626 | -0.0674 | 1.0207 |
| Special bonus: 7.4 mm with Raynox 0.7X wide angle conversion lens attached: | ||||
| 5.2 mm | 0.0513 | -0.1509 | 0.0835 | 1.0161 |
To apply corrections to an image, you can use the hugin fulla command we've mentioned previously. This time we use the -g option to pass our correction coefficients:
fulla -g 0.028:-0.0871:0.0521:1.007 image_file_name
The output will be our distortion-corrected image. (In this case the image of the building was shot with the G9 set at its shortest focal length, 7.4 mm, so we use the coefficients corresponding to that focal length.)
This technique will go a long way toward correcting obvious geometric distortion but it's not perfect. It doesn't correct to perfection although in most cases it's nearly impossible to tell without careful measurements of the resulting image. It also doesn't handle radially asymmetric distortions such as might occur in misaligned lenses.
Next up, we'll take a look at chromatic aberration and see how we can correct one type of it.
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