Variance updating

Variance adaptation by online cumulative average (Feb. 2004 - )

§We found that the variances are not independent of (i) the level of illumination (brightness) and of (ii) the surface color.
§However, assume that the illumination change is not all sudden, sx2 and sm2 could be assumed to be the same as s .
Let’s update the variance s by online cumulative average.
For obtaining a learning rate b for variance updating, I did not include a Gaussian since I know the mean but obtaining its variance is not clear. I believe the variance s we are updating is not the one of the Gaussian, S, here. So I just set the learning rate as a constant temporarily.
All resultant images are rescaled for display accordingly.

EXPERIMENTAL RESULTS

No learning (alpha = 1/3 in common)

Assuming all pixels are background events, they are all accepted to the pixel's codeword. The codeword mean and variance are updated accordingly as we discussed.

Fixed illumination

b = 0.02 (VS. Euclidean distance only )

b = 0.1

Variable illumination

b = 0.02

b = 0.1

Codeword learning

Set a critical value t* as 4, 3, 2, ... to see how this codeword learning affects the variance adaptation. Multiple codewords are allowed.

NOTES:

The images are resized (80x60 by sub-sampling) to accelerate the learning process.

In the codeword, variance, F, and t images, white pixels mean no codeword matched. However, in the variance image, some pixels having high variance show white pixels.

The variance plot is showing the change of variances of selected 5 sample pixels. Since some pixels have multiple codewords, there may be several plot for those codewords.

The 'cumulative count of new codewords' is what we discussed last time.

Fixed illumination

s2_init = 9.0 (alpha = 0.3333, beta=0.1)

t*=4

t*=3

t*=2

s2_init = 2.5

t*=3.5 (alpha=0.3333, beta=0.1)

t*=3.5 (alpha=0.1, beta=0.1)

t*=3.5 (alpha=0.04, beta=0.04)

New one-minute sequences

There are three sequences 'lowfixed', 'highfixed', and 'variable' which were recorded for one minutes. TD = threshold for detection, TC = threshold for coding.

Old algorithm (TD=TC)

                    Low fixed

s2_init = 2.5, alpha = 0.1, beta=0.1, t*=3.5

                    High fixed

s2_init = 2.5, alpha = 0.1, beta=0.1, t*=3.5

                    Variable

s2_init = 2.5, alpha = 0.1, beta=0.1, t*=3.5

s2_init = 2.5, alpha = 0.3, beta=0.3, t*=3.5

New algorithm (separate TD and TC)

                    Low fixed

s2_init = 2.5, alpha = 0.1, beta=0.1, TD=3.5, TC=5.5

                    High fixed

s2_init = 2.5, alpha = 0.1, beta=0.1, TD=3.5, TC=5.5

                    Variable

s2_init = 2.5, alpha = 0.3, beta=0.1, TD=3.5, TC=5.5

Non-parametric Variance Estimation with Single Exponential Smoothing

                    Variable

TD=3.5, TC=5.5

Apr 8, 2004

Non-para / No MeanAdj / No MeanDBL / No VarDBL

Non-para / No MeanAdj / No MeanDBL / Yes VarDBL

Non-para / Yes MeanAdj / No MeanDBL / No VarDBL

Non-para / Yes MeanAdj / No MeanDBL / Yes VarDBL