7 Multiscale entropy as a measure of relevant information in an image

Since the multiscale entropy extracts the information from the signal only, it was a challenge to see if the astronomical content of an image was related to its multiscale entropy.

Figure 10: Region of a simulated image containing an undetectable source at the center

For this purpose, we studied the astronomical content of 200 images of 1024 $\times$ 1024 pixels extracted from scans of 8 different photographic plates carried out by the MAMA digitization facility (Paris, France) (Guibert 1992) and stored at CDS (Strasbourg, France) in the Aladin archive (Bonnarel et al. 1999). We estimated the content of these images in three different ways:

1.

By counting the number of objects in an astronomical catalog (USNO A2.0 catalog) within the image. The USNO (United States Naval Observatory) catalog was originally obtained by source extraction from the same survey plates as we used in our study. (A catalog is the term commonly applied in astronomy to a relational table, or a tabular array, of coordinate positions followed by object feature measurements;)

2.

By counting the number of objects estimated in the image by the Sextractor object detection package (Bertin & Arnouts 1996). As in the case of the USNO catalog, these detections are mainly point sources (i.e. stars, as opposed to spatially extended objects like galaxies);

3.

By counting the number of structures detected at several scales using the MR/1 multiresolution analysis package (MR/1 1999).

Figure 11 show the results of plotting these numbers for each image against the multiscale signal entropy of the image.

Figure 11: Multiscale entropy versus the number of objects: the number of objects is, respectively, obtained from (top) the USNO catalog, (middle) the Sextractor package, and (bottom) the MR/1 package

The best results are obtained using the MR/1 package, followed by Sextractor and then by the number of sources extracted from USNO. The latter two basically miss the content at large scales, which is taken into account by MR/1. Unlike MR/1, Sextractor does not attempt to separate signal from noise.

Sextractor and multiresolution methods were also applied to a set of CCD (charge coupled detector, i.e. digital, as opposed to the digitized photographic plates used previously) images from CFH UH8K, 2MASS and DENIS near infrared surveys. Results obtained were very similar to what was obtained above. This lends support to (i) the quality of the results based on MR/1, which take noise and scale into account, and (ii) multiscale entropy being a good measure of content of such a class of images.