Where is the minefield?

Detecting a minefield in coastal and inshore waters may rely on supposed detections, and many spurious or clutter detections. A representative image of such point detections is shown, with the greater density shown as a horizontal band near the bottom of the image. The other two images in this animation are the 4th and 5th wavelet transform scales. They can be used to demarcate the minefield.

Commands used

The point pattern set was generated in S-Plus using 1500 points for the Poisson clutter, and 200 points for the "stochastic bar" which were also distributed as a Poisson distribution but with an additive Gaussian component. Thus the problem is one of finding 200 "interesting" points among 1500 uninteresting points. The points' coordinates were read into IDL, an image produced, and this was written to a FITS file.

The significance limits for detection were set up with mr_abaque -d. This was followed by the determining of the support image at each of 6 resolution scales, mr_psupport -I c.fits -s xxx -p cout. The support images were extracted using mr_extract -x cout.mr cout. Finally the support images were converted to GIF, following color-coding (13 rainbow) in IDL.

Another important command is mr_detect which not only detects the clusters, with support for lots of noise models, but also calculates and outputs parameters for all objects or `blobs' found. The objects or blobs can be at different resolution scales, or a combination of them.

To probe further

Working Group on Model-Based Clustering for Marked Spatial Point Processes, sponsored by Office of Naval Research.

Image and Data Analysis: The Multiscale Approach, J-L Starck, F Murtagh and A Bijaoui, Cambridge University Press, 1998.