(From the Mira MX User's Guide).
This tutorial shows you how to register an image set using Mira's Image Registration package. If the alignment involves correcting a simple field drift or a wobble, then you can align them using a simple "shift" alignment on 1 or more points. However, in this example we will need the full power of the Register Images command because one of the images has has a serious parallelogram distortion. The pictures below show the 4 images averaged to show the same stars at various locations in the images. Within each picture, each group of points shows the same star from each of the images. It is clear that the images cannot be brought into alignment using any combination of shifting, scaling, and rotation. However, Mira has the tools that will solve this problem.
To register this set of images requires using a 6-coefficient Shear transformation, which requires using at least 3 reference points per image. But relax! Even though this sounds complicated, Mira handles most of the details behind the scenes. You simply click some points on one image, let Mira copy them to the other images, and click two other buttons to calculate and apply the corrections. The Shear method corrects for image shift, field rotation, non-perpendicular axes, and unequal directional image scale. As you will see at the end of this tutorial, that is sufficient to correct the images so that features overlap with positional uncertainties near the 0.01 pixel level.
Open the Images and Inspect Them
To begin, open 4 images of the Comet Hyakutake that are supplied with the Mira installation. These images were acquired using a CCD camera with a 105mm lens, which makes them severely under-sampled with an image scale of 48 arcseconds per pixel. As you can see, point sources (stars) are typically 1 or 2 pixels wide.
Use the File > Open command or Ctrl+O to open the Open dialog, then select the 4 images as shown. Be sure that the Options box shows Open as Image Set so that the images open into the same window.
On the Open dialog, click [Open] and the images quickly appear in an Image Window as shown below.
As shown here, we have de-magnified the image and shrunk the window to keep the pictures small. You may choose to use a large window with a magnified image or to shrink the image or window. The display has no effect on the registration quality since the reference markers use coordinates computed from the image pixel data, not from the display.
Examining the Images
Before starting to register the images, it is a good idea first to examine the images you have opened. Perhaps some images are poor quality or you have other reasons not to align them. You need to do any image set adding, deleting, or re-ordering before starting Image Registration (or Photometry) since these adjustments are not allowed while the image registration package is active. To examine the images, move the red thumb on the track bar in the Animation Toolbar at the bottom of the Image Window. If you need to change the images in the image set, see Changing the Image Set.
After making any necessary changes to the image set, we are ready to register the images. From the pull-down menus, select Process > Register. This opens the Registration Toolbar, as shown below (note: the Register command is also available as the left-most button on the Animation Toolbar). When you are finished with Image Registration, you close the Registration Toolbar using the Process > Register command that opened the toolbar.
Choosing Image Registration Settings
Image registration involves many complex mathematical operations that can be applied in different ways for different situations. This means that many different settings are involved in getting the best results. Typically, you will use the same settings so you will not need to change them each time you do registration. However, you should have a sense of what adjustments and settings are available and how they affect the results. Since this is your first time doing image registration, we will describe these settings in detail, even though you will most often just allow them to operate silently, behind the "front end" of the simple toolbar user interface.
On the Image Registration Toolbar, click to open the Alignment Marker Preferences dialog. This is a standard dialog for setting "marker preferences" used by numerous Mira commands. This dialog contains the two pages shown below.
The pictures above show the Drawing and Centroid pages that control how registration markers are located and displayed on the images. The Drawing page shows that the markers are red and 1.5 points (about 2 screen pixels) wide. The Centroid page settings are more important because they are somewhat sensitive to the size of the alignment points on the images. These settings may change for different image sets. In this case, the images are severely under-sampled and the stars are only 1 to 2 pixels wide. We use a small centroid Sample Radius of 3 pixels. The tracking Search Radius should be 20 to allow for 20 pixel jumps between images. You should seldom use a value larger than around 40. In addition, these are positive images with brighter things having higher signal, so the centroiding should be done on Positive objects, not Negative ones. You should be using the centroid positions near where you click the mouse on the image. You do not have to use centroiding; instead Mira can use the exact coordinate where you click the mouse. But the Centroid First Point box must be checked if you intend to use centroid positions. When you are finished changing the settings, click [OK] or [Apply] to save your changes.
Next we need to check the method used to align the images. Click the button on the Registration Toolbar to open the Registration Preferences dialog. This dialog has 2 pages, as shown below.
Settings in the Registration Preferences dialog control the way image pixels are aligned and how the pixel values are adjusted to fall at new coordinates in the output images.
- Settings on the Resampling page relate to "resampling", which is the mathematical prescription for how the pixel values are shifted and adjusted to align the images.
- Settings on the Background page control the "background" (empty image) into which the r-sampled images are saved. For example, you can choose to make the registered images larger than the original ones or have all the aligned images offset as a group.
For the purposes of this tutorial, make all settings like those shown above. After making changes, click [OK] or [Apply] to save them and close the dialog. We are now ready to mark registration points.
Marking Reference Points
Enter marking mode by clicking the button on the Registration Toolbar and use the Animation Toolbar to go to the first image. Now click on each of the 6 stars shown in the picture below. As you move onto each point, notice how the magnified view on the Image Toolbar shows you a detailed view, despite the lack of detail in the de-magnified image. You can adjust the tracker magnification by double-clicking on it to cycle between 1, 3, 5, and 9x the original data (this picture shows Mira AL).
Seldom do you ever need more than 5 to 6 reference points on a CCD image. So long as the markers are well separated and placed all around the image, the alignment should be excellent. But you must choose "good" points. The points we have marked were chosen using these guidelines:
- right, but not saturated.
- fairly round.
- well isolated from nearby stars.
- distributed around the image, rather than clumped in one area.
At any time when marking points, you can change your mind about using a point. For example, you can delete a point and re-mark it elsewhere, or just delete it. To delete a point, press the [Shift] key and click on it. In Marking Mode, the [Shift] key is a toggle in marking mode: up=mark, down=delete), or you can click the button on the Registration Toolbar to enter Delete mode. Using the [Shift] key is usually easiest.
With 6 points marked on the first image, we now need to transfer them to the other images. There are 2 ways to do this:
Change to the next image and click on all the same objects, repeating this for each image in the stack. This requires knowing or remembering which ones you chose, and perhaps flipping back and forth between images. However, it will be necessary if the images are misaligned in rotation.
If each successive image is within 10 to 20 pixels of alignment with the previous one, Mira can track the points through the remaining images. Tracking computes a new centroid position in each image based on its location in the previous image.
The Tracking method is best if the images are not far out of alignment. To track the objects marked in the current image, click the button on the Registration Toolbar. There are now reference points in all images, but how well matched are they? The only way to answer this is to look through the image set. Using the Animation Toolbar, step through each image and check if it found the correct point in all images. Actually, in this crowded field of under-sampled stars, you will find that some of the markers locked onto the wrong star which is nearby the correct one. This is easily fixed! In Marking mode, click on the correct point to mark it, then press [Shift] and click on the misplaced marker to delete it. Repeat this for any incorrectly placed markers that you find. When you have scanned through all the markers on all images, you are ready to compute the mathematical equations that will be used to shift the pixels around and bring the images into alignment.
Computing the Registration Equations
To compute the registration equations, click on the Registration Toolbar. This matches all the patterns of markers to figure out which marker goes with which one in all other images and then calculated the coefficients of the equations that match them. This produces a listing of results in a Text Editor window:
The "Reference Image" chosen on the Resampling page is considered to be perfect and the other images are matched to it (by default, the reference image is the first image). For each of the other images Mira reports "x terms" and "y terms" plus RMS errors. For example, the x terms are x0, dCx, and dCy and the RMS error in the x axis is labeled x rms. Since the registration is optimal but not exact, there will be a small difference between the position of same detail in a pair of images. In this case, the RMS errors are typically around 0.02 to 0.03 pixels. That's extremely good! If any of the values were unusually large, it would probably indicate an erroneously marked point. You could go back through the images and find the bad point(s), delete and re-mark them, and click again to repeat the calculation. If you find that this does not help, use the button to open the Resampling page and click the [Residuals] button. The table of residuals shows the difference in calculated position and actual position for each registered point. A bad point has a residual that is very high or very low. Identify the bad points, close the dialog, and delete those points from the images. Then re-calculate.
You can copy, save, or print the Residuals table using commands in its menu. To open its menu, right click on the table. For example, you might copy the table, close the dialog, and then paste the table into a Mira Text Editor.
Now that the transformation equations are known, we perform the alignment. Click to do this and you are done with image registration. Use the Animation Toolbar to scan through the image set and view the results. If everything is well aligned (and it should be because the RMS errors were small), then you may wish to save or combine the images (or do whatever you wanted to do with registered images). If you don't like the result, Undo the alignment and try again.
Assessing the Results
Let's look at how well aligned the images have become. Stars in the original images were tiny but mostly round. Therefore, the image of a star should also be round if all the images are added together. If not, then one or more of the images is not well aligned. Use the Process > Combine command in the pull-down menu (or on the Animation Toolbar) to combine the images using the Mean method. The picture below shows a region magnified 16x. Notice that the combined stars are extremely round, which means excellent alignment.
As a final step, let us assess the quality of the alignment in a quantitative way. Measure the centroid position for a nicely isolated star that was not one of the registration points. The positions should be very similar. In this example, use the star at coordinate (661,603). Move the Image Cursor to near this point and click the (Centroid) button to compute the centroid positions in all images. The result looks like this:
The X and Y centroid positions are intensity weighted coordinates of high precision. How do they compare? Actually, they are in good agreement for all 4 images. The typical difference, or scatter among them, gives an estimate of the exactness of the alignment. You can use your hand calculator to compute the mean and error of the mean position for each of the X and Y coordinates. We will quote the error of the mean, which is the uncertainty in the mean value; it is the standard deviation of the mean divided by the square root of the number of values (4 images gives 4 points). Here are the results:
Mean X = 660.982 +/- 0.0069
Mean Y = 602.995 +/- 0.0053
The x and y coordinates agree to better than 1/100-th of a pixel. That is good enough to write a book about!
In this tutorial we have taken a grand tour of image registration. We have examined all the factors that can affect the quality of the outcome. Typically, registration can be done much faster than in this case. If the images are of good quality and not far out of alignment, most of the detailed examination shown here can be bypassed and the results will be excellent.