Image Registration

Astronomers often compare images taken at different times to search for comets, asteroids, variable stars, optical gamma-ray bursts, and supernovae. They also combine images to improve the signal-to-noise ratio over what they can obtain in a single integration, or to composite images into mosaics or color images. However, because telescope pointing is never exactly the same in two images, they must be brought into coincidence, or registered, before the images can be compared. Registration thus serves as a basic step in a variety of high-level processes.

Two images are said to be "in register" when corresponding features appear at the same pixel coordinates. Stars are ideal reference points for images, because they are both plentiful and fixed in space; but virtually any well-defined image feature can be used as a reference point. For precise registration, the image processing software must be able to compute a centroid for each reference point, under good conditions, to better than 0.05 of a pixel.

Registration requires a "master" image whose features can serve as reference points. In the "slave" image or images, the same reference points must also be visible. Images can be out of register in translation, rotation, scaling, or any combination.

• Translation means the reference points have shifted side to side or up and down because of tracking error and declination drift. If images are translated only, then one reference point is needed to register the images.

• Rotation usually occurs when a CCD camera is taken off the telescope, and with some focusing units, when the telescope is refocused. Severe field rotation occurs for CCD cameras mounted on alt-azimuth telescopes, except for a brief period when the object crosses the celestial meridian. Images taken with equatorially-mounted telescopes over a time span of hours are usually only translated, but those taken three or four hours apart or on different nights may be slightly rotated if the telescope is refocused. Polar alignment errors in an equatorial mounting also produce field rotation. It is rare to see field rotation without translation. To correct for rotation, it is necessary to measure two reference points.

Figure 16.11 These two images differ in translation, rotation, and scaling because they were taken with a Cookbook camera with different operating modes—yet after image registration, they will be aligned. To register images like these, it is necessary to mark the same two stars as reference points in each one.

Figure 16.11 These two images differ in translation, rotation, and scaling because they were taken with a Cookbook camera with different operating modes—yet after image registration, they will be aligned. To register images like these, it is necessary to mark the same two stars as reference points in each one.

• Scaling is usually a small effect for images taken with one telescope, but images taken with different instruments show large scaling differences. Images taken with different telescopes, filters, or CCD cameras are invariably also translated and rotated relative to one another. Two reference points are needed to correct for scaling differences.

16.4.1 Registration with Translation Only

Registration in translation only requires measuring one reference point in the master image, and measuring the same reference point in each slave image. If possible the reference points are isolated star images exposed to roughly half the full-well capacity of the CCD.

If the coordinates of the reference point on the master image are measured as vlnj, and the coordinates of the corresponding reference point on the slave image are measured as (xs, y J, then the translations, Ax and Ày, are:

Reference Coordinates for Registration

Master Image Slave Image

Figure 16.12 Solid dots are the reference points in these images, and the hollow dots, midway between each pair of reference points, are the centers for rotation and scaling. Astronomical images are easy to register because their star images make excellent reference points.

Ax and Ay describe the translation of the slave image relative to the master, in units of pixels. Positive values of x mean the reference point has moved to the right; negative values mean the reference point in the slave image is left of that in the master image. For registration, the slave image should be translated by -Ax and -Ay. Section 12.1 describes the mechanics of image translation.

16.4.2 Registration with Translation, Rotation, and Scaling

Two reference points are required to register images that are translated, rotated, and scaled relative to one another, plus you must have some way to select the center for rotating and scaling each slave image. In addition, if the CCD does not have square pixels, you must supply the pixel aspect ratio of the image (or images).

Registration begins by measuring coordinates for two points on the master image, (xml, yml) and (xm2, ym2), and two corresponding reference points on the slave image, (xsl, ysl) and (xs2, ys2). For good accuracy, the reference points should be located in diametrically opposite corners; failing that, as far apart as possible.

Although the centers for rotation and scaling could be either reference point, it is convenient to perform rotation and scaling at the midpoint of the two reference points. This location is the same regardless of the rotation or scaling of the original images, and is well suited as the reference point for translation. Accordingly, the equations for this "center" of the master are:

Figure 16.13 The slave image from Figure 16.11 is now registered to the master image.

Note that areas outside the original are black—the software cannot create data where there are none. Just for kicks, flip the page rapidly back and forth to see image blinking in action.

Figure 16.13 The slave image from Figure 16.11 is now registered to the master image.

Note that areas outside the original are black—the software cannot create data where there are none. Just for kicks, flip the page rapidly back and forth to see image blinking in action.

and the corresponding equations for the center of the slave image are:

and the image translations relative to (xm,.ym) in the master image are: Ax = xm-xs

We next find the rotational orientation between each pair of reference points in the master and slave images. Although their actual orientations are arbitrary, the difference between the orientations is the rotation of the slave image. The rotational orientation of the master image is:

- arctan

Xm I Xm2

and the rotational orientation of the slave image is:

\y,i -ysif so the rotational difference is:

Finally, we determine the image scales. The image scale is proportional to the distance between the pairs of reference points. In the master image, this distance is:

and in the slave image, the distance is:

so the scaling of the slave image relative to the master image is:

The final step is to translate, rotate, and scale the slave image to match the master, for which the translations are -Ax and -Ay, the rotation is -Ad, and the scaling factor is 1 Is. Algorithms for translation, rotation, and scaling are covered in Section 12.4.

For precise comparison between two images, they should be shifted equal amounts in opposite directions. For the master image, translations are Ax I2 and Ay/2, the rotation is Ad/2, and the scaling factor is Js . For the slave frame, the translations are -Ax / 2 and -Ay / 2, the rotation is -Ad / 2, and the scaling factor is

Astronomical CCD images are extremely well behaved in registration. They offer lots of reference points, and the resulting centroids are accurate to around 0.05 pixels. This means that the errors in translation due to errors in the centroids are roughly ±0.1 pixels. If the reference points are well spaced, the rotation errors are roughly ±0.01°, and scaling errors are roughly ±0.02%. Two-point registration guarantees that any mismatch between images will be considerably smaller than half a pixel at all points on the image. When large errors occur, they are almost always due to mis-identified reference points.

• Tip: In AIP4Win, access image registration through the Multi-Image I Registration tool Registration is also built into several other tools, where image registration is an essential step.

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