Home Page       Mon Dec 1 02:11:21 JST 1997

Star detection in PIXY system

The way to detect stars in PIXY system ([1]) is quite simple, it regard those pixels whose value is more than some threshold from the background level as part of a star. But generally photos are inclined to be brighter in center and darker in circumference, and so are the astronomical images. Therefore, the background level is not constant all over an image but becomes a curved surface which heaps up in center. In [2], the curved surface is resembled by a quadratic function of x,y, coordinates on the image, and called flatfield function. And twice of the standard deviation of differences between the background level and each pixel value is regarded as a threshold, then stars are detected.

By the way, the inclination that the center is brighter and the circumference is darker also appears in case of CCD imaging. In this case, people prepare a homogeneous flat light source in some way, let each pixel be lightened equally and obtain a flat image called flatfield previously. Then every image is flattened by division by the flatfield. For example, let's see the case that the flatfield value is 20 in center and 10 in circumference. It means that the center has double sensitivity of that in circumference. So a star in center whose value is 1000 and a star in circumference whose value is 500 have in fact same brightness. Dividing the image wholly by the flatfield makes the value of the star 50 equally in center and circumference, so the image becomes flat.

In a case supposed in this article, the system has only the image itself and cannot obtain the flatfield actually and flatten the image by division. However the background level of an image reflects the sensitivity variance in positions. So the background level may seem to be in place of flatfield in case of CCD imaging and division by the background may seem to flatten the image as flatfield does. This way actually flattens raw CCD images. However, it cannot work on level corrected images. For example, let's see the case that the sensitivity in center is twice than in circumference and the background level is 100 in center and 50 in circumference. After subtracting 40 from each pixel, the background level becomes 60 and 10 respectively. Then the ratio is 6:1, which no longer reflects the ratio of sensitivity. In addition, the PIXY system treats with various images of many people, such as images which is a normal photo originally and scanned with a film scanner or scanned printed pictures, etc. The situation of those images is same as that of level corrected images even if they are not corrected deliberately. The background level is sometimes nearly 0 in those images, so simple division causes excessive correction. For example, in the case above, two stars with same brightness is in center and circumference, and the original value is 500 and 250 respectively. After subtracting 40, the value becomes 460 and 210. Because the ratio of the background becomes 6:1, a simple division makes the value of the two stars 77 and 210 respectively. In this case the difference between the two stars of same brightness increases on the contrary. Therefore, I did not adopt the correction by division in [2].

However, the way mentioned above has some faults. First of all, the problem that stars with same brightness do not look equal in brightness depending on the position. There is also another problem that faint stars in circumference cannot be detected by a threshold determined in order to reject noises in center. That is because the center is more sensitive, the noises also appear more in center. The following example shows this problem. The middle image shows the detected stars from the top image. The bottom image also shows the detected stars after the threshold is decreased. Only the center of the image becomes noisy with a threshold.

Nova Cas 1995
Photo: Seiichi Yoshida
Dec. 21, 1995, 19:02 JST (1 min)
Fujishiro Town, Ibaraki Pref. Japan
25-cm f/6.3 Schmidt-Cassegrain
Konica color GX3200

The next section describes the way of flattening by division to avoid this problem.

By the way, I called the background level flatfield function in [2] because I have tried to cancel the influence of the sensitivity variance by regarding the background level as a curved surface. But I call the function for correction by division flatfield function, the background level sky field, and distinguish each other after this.