The human eye concentrates its color detection and high resolution into the fovea (center of the eye), leaving the rest of the eye to see only light and dark and motion. We compensate for this narrow focus by darting our eyes around to focus on one thing after another in rapid succession.

Computer images are the same resolution and color depth all the way
across, and it requires a lot more processing to integrate constantly shifting
views so that their objects can be seen as the same after the scene has
shifted. Even Fourier transforms are expensive.
Consequently, we are forced to make trade-offs in image resolution and
recognizing pattern variation in object detection. A pedestrian wearing
a patterned shirt will be much harder for the computer to see against a
complex background than for the human.

This is a color cube, with the three dimensions (red, green, and blue, RGB) explicitly shown. If you imagine the zero at the far end of the diagonal, then the three dimensions are CMY (cyan, magenta, and yellow). It's the same cube, only we have negated all the coordinates, so CMYK (for blacK, because most colored inks are not pure enough to get a good black, so they add black ink for that) is essentially merely a coordinate change from RGB. DigitalTutors has a video explaining the difference between RGB and CMY.

Except for sharp transitions in brightness, like the edge of a shadow (and sometimes even then), human vision tends to down-play differences in brightness not accompanied by differences in color or pattern. In normal RGB (red-green-blue) color images this is computationally difficult, because brightness dominates the differences. One way to deal with this issue is to convert the color space to luminance+hue+saturation (called YUV, or sometimes also HSB or LUV), then disregard most of the luminance. Marco Olivotto spends a lot of time in a video promoting PhotoShop explaining how their "Lab" color model (essentially YUV) lets you do interesting things with colors by deleting the luminance. Here are some other links you might find useful:

Jamie McCallister's video "RGB vs YUV Colour Space" explains YUV in video encoding.

Joe Maller: RGB and YUV Color (includes links)

Reddit neural nets discussion "Is there an advantage to encode images in YUV instead of RGB?"

BasslerAG FAQ "How does the YUV color coding work?"

StackExchange "Why do we use HSV colour space in vision ... processing?" is very relevant

Colored Object Detection, 6-second clip with luminance deleted

If
you imagine the Cartesian coordinate system of RGB
as an XYZ 3-space, a cube in one quadrant, black (0,0,0)
at the front bottom-left corner and white at the diagonally opposite corner,
and then you pick up this cube and rotate it so that black-white diagonal
is a vertical axis around which the other dimensions can spin, that's the
transformation.

Why is this important? It turns out that the representation we choose for our data can radically affect how we think about it. Newton (in England) and Leibniz (in Germany) both invented calculus about the same time, but Leibniz's notation is far more intuitive and easy to do other mathematical operations on, so we now use his work and ignore Newton's entirely -- except maybe to observe that Newton was probably first. There are various notational transformations that we can apply to our data to make it more tractable for different kinds of processing. One involves seeing the data in the frequency domain instead of time or space, which makes Fourier transforms (see the next paragraph) useful. Another notational transformation is spatial coordinate systems. We are familiar with "Cartesian coordinates" (named for Descartes, who invented it), which is useful for placing things in an absolute reference system based on perpendiculars. Pinning one or more of those coordinates to a particular point (often the observer) produces a numerical system more appropriate for things like ballistics, where you want to know where to point your cannon and how much powder to load in it in order to hit a particular target.

Color space is one of those systems where coordinates matter. Real light -- the photons we experience as visible light -- might be closer to YUV than RGB, where the wavelength of a particular photon = hue, how many photons there are at that wavelength = luminance, and how many photons there are at other wavelengths = saturation. The human eye has "cone" receptors for three bands of color, so (for us) three independent numbers can define any visible color (which makes it a 3-dimensional space, like the cube above), but different coordinate systems give us radically different abilities in terms of processing power. Even though human eyes detect light in the RGB color model, it is internally converted to luminance + hue + saturation for thinking about it (including object recognition). None of us ever thinks about a certain shade of orange as "um, yes, it has some green but more red than green" (unless we are specifically trained in RGB technology) because we do not see "green" in the color orange at all, we can only imagine that it's there.

For
our purposes, luminance (and to some degree also saturation) needs to be
deleted from the analysis, which is much easier in a YUV
color space. It's fairly easy computationally: luminance is the sum (average)
of red+green+blue samples, and saturation is the maximum difference; hue
and saturation together is a polar coordinate vector (seeing red, green,
and blue as three 120-degree thirds of a circle) where saturation is the
distance from the center (white vector length) while hue is the (pink)
angle of the vector. Luminance is the third dimension, black at one pole
and white at the other (the black center line in the image to the right).
The coordinate transformation consists of only adds and subtracts, which
are much faster and use less hardware than multiplies and divides.

The relationship between pressure over time compared to amplitude over frequency was investigated by the French mathematician Jean-Baptiste Joseph Fourier, and the conversion is something like a coordinate transformation, now called the "Fourier transform," except it's more complicated than converting Cartesian coordinates to polar. There are algorithms called "fast Fourier transform" (FFT) but they still involve trigonometric function calls on all the data, for example:

Overtones, harmonics, and additive synthesis

A gentle introduction to the FFT

The Scientist and Engineer's Guide to Digital Signal Processing

An Intuitive Explanation of Fourier Theory

Trig functions on 8-bit image data can be as fast as a table look-up,
so the computational cost is not as bad as it might at first appear. However,
the frequency analysis of the image data is not as useful for recognition
as the other features. Brayer
offers some recognition benefits, but mostly concentrates on other stuff.

Early small computers didn't even have a hardware multiply, everything
had to be done with adds and shifts, so programmers tended to favor algorithms
that minimize multiplications. I don't know of any fast divide hardware
(even today), the Intel chips tend to do it with Newton
approximations (a table look-up followed by a few steps of multiplication
and subtraction); with clever algorithm design, most of your divisions
can be converted into one table look-up and a single multiply. But none
of that is needed for simple Gaussian smoothing.

This video has a segment at 29 seconds where they are picking out people, but they don't say how they are doing it:

OpenCV GSOC 2015

For purposes of this project, we can make some simplifying assumptions,
like requiring the pedestrians we detect to be wearing solid, bright colors
(no detailed patterns, no bland colors that blend in with the background).
Thus it becomes a simple matter of finding blocks of solid color, and then
ignoring those blocks that are not credible pedestrians. That part is hard
enough, we don't need to add more difficulty on the first cut.

This project has the additional advantage that it's mostly computational. Other than acquiring the video stream, it can all be done in an average personal computer in a conventional programming language like Java.

Any questions or comments? This is your project.

Next time: What's Next?

Rev. 2017 April 29