Lattice Match

I had to decipher jargon in the Cutler-Davis paper a little bit more to figure out how they developed the algorithm to measure the periodic rate.

The following are the match measure requirements for :

(1)

(2)

The trick was to develop the matrix containing the peaks from the autocorrelation matrix,
This was achieved by gaussian filtering the autocor. matrix and then running through each pixel and label it a peak if it is a strictly maximum value within some local neighborhood radius N.

The above image is the autocorrelation matrix of the stabilized and weighted similarity matrix.

Below is image illustrating the peaks found from the autocor. matrix. where there are 7 white pixels indicating the peak locations. A neighborhood radius of 11 was chosen


The next step was to create synthetic lattice matrices parameterized by a distance value which directly relates to the periodic rate. A square lattice and a 45 degree rotated lattice are used. These lattices are labeled as in the match metric conditions in equations (1) and (2). Below is an illustration of the square and rotated lattice structures overllapping the autocorr. matrix.
The results from this technique measures a distance value of 71 frames which is very accurate. I have noticed the parameters used for selecting the peaks (such as neighborhood radius) can make the estimation way off. For instance, the minimum value a peak can have was set to 0.25 to generate the 72 frame estimate. If I changed the peak value to 0.2 then a distance of 61 frames was chosen. I will need more data sequences to test this algorithm more to see how sensitive it is to the parameters chosen.