Similarity Plots

I started to follow the Cutler-Davis paper by generating similarity matrix plots. These plots are essentially recurrence matrices.

The similarity matrix was generated by using an absolute difference match metric:

(1)
Where is an image pixel value at time .

For this application, I used the buffered image created by grabbing a horizontal slice that overllaped the region where the radar was rotating. (See the Spatial-Temporal II posting)

This changes the match metric to be:

(2)
Where is all pixel coordinates in an image.
is a pixel value from the scanline buffer at time . This is simply a match metric between two scanlines separated by time. is a constant because it is just a single horizontal scanline slice at time t.

The similarity matrix, , should have a constant valued main diagonal component () which is the match of image to itself. () The diagonal is just a self-matching indicator.

If there is periodicity, there should also be a pattern of values outside the main diagonal. This is from the image matching itself a period of time later. For example, suppose you take a snapshot of a clock with the second hand over the 6. Take another snapshot 60 seconds later and the second hand is in the exact same orientation.

I also noticed that since the radar is mainly in the center column region of the temporal/spatial buffer I should probably do a weighted version of the absolute difference to attempt to ignore the irrelevant data. I did this by applying a Hanning window on each horizontal slice. This gave more weight to the region where the radar is located and does improve the similarity plots. This changes (2) into

(3)
where

(4)

and is width of the image.

In all these plots, notice the blue main diagonal running from top-left down to the bottom-right corner. Also, the lobes or peaks coincide with the periodic rate of the radar.

The best of these similarity images is the stabilized and weighted version. It has a more uniform appearance. This shows that stabilization and weighting can improve the similarity plots.