Kinect depth variance analysis

Here are the visualizations of absolute depth differences for each pixel for 40 frames using a Kinect. The setup is like this.

White color shows all pixels with absolute difference greater than 4mm

The high variance at the bottom right corner is due to the mouse which has a shiny surface and the Kinect does not work very well with shiny surfaces.  

White color shows all pixels with absolute difference greater than 2mm

White color shows all pixels with absolute difference greater than 1mm

Absolute depth variance shown as a heat map. The color changes from black, red, yellow and white as the value increases. The difference values are clipped between 0.8 and 2.

Music I like

One of the Pandora stations I listen all the time is based on Lux Aeterna by Clint Mansell on Requiem For A Dream. The music is usually instrumental with electronic string ensembles and has classical influences .

A review of smoothing techniques

Recently I need to smooth the Kinect-based finger tracking result. Without smoothing, there are a lot of jitters as shown in this demo video:

In searching for the best solution, I think it's good to have a review of different smoothing techniques. 

Simple moving average

$$s_t = \frac{1}{k}\sum_{n=0}^{k-1}x_{t-n}=\frac{x_t + x_{t-1} + ...+x_{t-k+1}}{k}=s_{t-1}+\frac{x_t-x_{t-k}}{k}$$

- Disadvantage: cannot be used on the first k-1 terms.

Weighted moving average

Give more weight to the recent terms in the time series. 

- Disadvantage: same as the simple moving average method, it cannot be used on the first k-1 terms. It also requires more complicated calculation at each step as it cannot be written as a inductive formula.

Exponential moving average

$$s_1 = x_0$$

$$s_t = \alpha x_{t-1} + (1 - \alpha)s_{t-1}$$

Exponential smoothing and moving average smoothing are similar in that they both assume a stationary, not trending, time series, therefore lagging behind the trend if one exists. Exponential smoothing also take into account all past data, whereas moving average only takes into account k past data points.

Double exponential smoothing

Double exponential smoothing can be used when there is a trend in the data.

Let {\(x_t\)} be the raw data sequence, {\(s_t\)} be the smoothed value for time t, and {\(b_t\)} be the best estimate of the trend at time t. The output of the algorithm is now written as \(F_{t+m}\). The formulae are:

$$s_1 = x_0$$

$$b_1 = x_1 - x_0$$

And for t>1

$$s_t = \alpha x_t + (1 - \alpha)(s_{t-1} + b_{t-1})$$

$$b_t = \beta(s_t - s_{t-1}) + (1 - \beta)b_{t-1}$$

where \(\alpha\) is the smoothing factor, \(0 < \alpha < 1\), and \(\beta\) is the trend smoothing factor, \(0 < \beta < 1\).

Bret Victor - Inventing on Pricinple

Bret Victor - Inventing on Principle from CUSEC on Vimeo.

Awesome WM configuration

Today I started to use Awesome on my desktop in the office. I've been using it for 3 months during my internship at Google and it was awesome! It requires a little bit of configuration at the beginning.

To make Awesome appear as a choice of WMs in the Ubuntu login screen, delete "NoDisplay=true" in /usr/share/xsessions/awesome.desktop. Apparently this is a bug in Ubuntu.

To create a user configuration file, copy the default one to the ~/.config folder:

$cd ~
$mkdir -p .config/awesome
$cp -r /etc/xdg/awesome/* .config/awesome

Note that there are some other files under /etc/xdg/awesome besides rc.lua, and you need to copy all the files. Otherwise there will be errors and the user configuration will be ignored (I tripped over this).

Configure screen locking
Install xscreensaver. Add the following lines to rc.lua.

# In globalkeys = ...
awful.key({ modkey }, "F12", function() awful.util.spawn("xscreensaver-command -lock") end)
# At the end of the file:
awful.util.spawn_with_shell("xscreensaver -no-splash")

Shortcuts

• Close dialog windows: meta+shift+c

Granola

Recently I've been obsessed with granola. It's so delicious! But it's very high in calories. One cup of granola can have 500-600 calories. Oatmeal is much better than granola. Oatmeal has soluble fiber  that slows down digestion, making you feel full longer (this is a good characteristic in food that I should look for). Oats contain photochemicals, which are antioxidants that help eliminate free radicals.

Granola also has oats as its base, but it has added sugar which increases its calories a lot. So should eat oatmeal instead!

Recycling etiquette

I've been wondering about whether we need to wash the bottles or the cartons before putting them into the recycling bin. I had a vague impression that we need to do that, but I feel that it's kind of a waste of water to do that. Today I found the answer to this question. So we should wash those containers before recycling to reduce contamination and improve recycling efficiency, but we can use washing-up water. This is in the spirit of reuse as well. In this way, we won't waste clean water and the recyclate does not need to be very clean anyways.