The Story of Digital Color

Earlier this year, I did some work on digital color management for a project. During my readings for the project, I accumulated a lot of interesting articles that I thought I could share. The festive colors around inspired me to finally write about them (and also in case I need to refer them again :D). In this post, I have presented a collection of articles, papers, wikis, comics, podcasts …, that you may refer to find out more about the subject. Let’s then begin our story, starting from all the way back to how we see and perceive colors:

I. The background

Dispersion of light - Prism experiment.
The ‘splitting of white light into seven colors’ experiment. In reality, you see more of a continuous spectrum than the discrete seven colors shown above.

Before we get started on digital color, let’s refresh some  high-school science topics. It is kind of mind-boggling to think about it, but the concept of colors is something that you make up in your own head. Fundamentally they are electromagnetic radiation with frequencies in the visible range. Our eye’s retina is layered with mainly two types of photoreceptor cells: the rods (black-and-white vision) and the cones. The cones enable us to see color and are of three types: rho (more sensitive to longer wavelengths), gamma (medium) and beta (short). At this point I would like to introduce you to the applets designed by Prof. Mark Levoy. I’d strongly recommend you to play around with them, at least the ones on the Introduction to color theory page.

Radiation with different wavelengths (or frequencies) excite these color receptors in our eyes to varying levels which is then processed by the brain to give us a perception of seeing color. This phenomenon is known as metamerism or the tri-stimulus response in humans.  Such type of color reproduction is cheaper to process and is easier to control. IA similar technique is also exploited in building displays for our computer screens and mobile phones as well – the objects that we cherish the most and spend most of our time staring at. They also use three types of sources to produce all the colors on the display.

There may be differences in how we see the world by adding more types of color receptors. Most men have 3 types of cones (8% have even fewer types and are color-blind), while women can have up-to four due to genetic factors. This Oatmeal comic beautifully illustrates how the number of colors affects color vision in erm.. the Oatmeal way. As a bonus, you also get to find out about how Mantis Shrimp’s vision is powered by technology superior to humans. [1] All of this and the search for a tetra-chromat woman, can be found in this Radiolab podcast on colors.

Now that you understand that the beauty is indeed in the eye, let’s get a little further into the color theory and move on to our next topic.

II. Color Theory Basics

In the previous section, we learned that the illusion of color can be created by three primary colors. Based on this we have two types of color systems:

a) Additive: We add varying quantities of primaries to get other colors. If we are using R, G and B as our primaries: we can have R+G = yellow, R+B = magenta and B+G = cyan. This kind of color mixing is used in digital displays when we have individual sources for each primaries.

b) Subtractive: A paint or ink based medium would follow such a system. It is named so because of the fact that we perceive the color of object as the kind of light that it reflects back, while absorbing the rest of the colors. This can be imagined to be like subtracting color by reflecting it. An example of this system could have Cyan, Magenta and Yellow as the primaries. We also add black to increase contrast and for other practical concerns in the popular CMYK color format.

The other type of system that you may have heard about deals with Hue, Saturation and Value (HSV). These three dimensions are supposed to describe how we actually understand colors:

200px-Munsell-system.svg
Representation of a HSV color system. Hue is depicted as an angle of of the circle, saturation along the radial line and value along the vertical axis through the center.
  1. Hue: name of the color – red, yellow, blue
  2. Saturation:  a color’s ‘strength’. A neutral gray would have 0% saturation while saturated, apple red would be 100%. Pink would be an example of something in between – an unsaturated red.
  3. Value: It deals with the intensity of light. You can kind of understand it as seeing colors in dark and bright light. You don’t see any color in very dim environments and also when it is blinding bright.

This color system is more suited for image processing and manipulation uses.

III. Color Spaces

Finally we have arrived at the computer science portion of our discussion. Since computer displays have to process and present all of these different types of colors, we must find a good way to represent them as well. Most color spaces have 3 to 4 components (or channels or dimensions). A complete digital image reproduction system would involve three phases: 1) acquiring the image (say using a camera), 2) transmitting it (saving it in an image format / using an A/V cable etc.) and finally 3) displaying it (on a screen, printing or projecting it). Some color formats are more suited for a particular phase in this system. These color spaces would be based on one of the color systems that we learned about in the section above.

The simplest of the color spaces would be a Gray color space. It only has a single channel with values varying from black to white. The common 3-channel color space families are:

RGB family: These are mainly used in displays and scanners. Members of this family included sRGB, Adobe RGB color formats etc. These formats are defined by international standards defined by various organizations.

YUV / YCbCr / YCC family: These are the most unintuitive types of color spaces. They were designed keeping in mind the transmission efficiency and for efficient storing.

Device Independent Colors: All the colors spaces that we have discussed till now may produced varied results on different output devices unless calibrated. Different devices have different ranges of colors that they can produce. [2] As a result they are called device dependent colors. To counter this, some clever folks at CIE developed imaginary color formats (although not useful for any making output devices [3] ) that specify color as perceived by a ‘standard’ human. Examples of these colors spaces include CIE XYZ, L*a*b and L*u*v.

The Apple developer article on color management is a good source to read more on this topic.

IV. Color Display: Techniques and Terminologies

Now that we have covered most of the basic stuff. Let’s talk about the other common terms in brief that you may have encountered about color reproduction.

  • Color Depth and Bits per pixel (BPP)
    These parameters define the number of bits used to define a single pixel’s color. If you are using 8 bit color, you will use 3 bits (or 8 levels) for R & G and 2 for B. This is assuming that your 3 channels are red, green and blue. Similary you can have other color depths like 16-bit and 24-bit (True color) which can represent 256 shades of red, green and blue. Modern displays support something known as deep color (up to 64-bit) with gamut comprising of a billion or more colors. Although our human eye can not distinguish between so many colors, we need this bigger gamuts for high dynamic range imaging. This also affects image perception by the humans as we do perceive red, green and blue in equal capacities. So even though we may be producing more colors on the screen, we may not have sufficient number of shades for the colors we are more sensitive to. Having a larger gamut takes care of all those shades to which our eyescan distinguish but need more information in order to be represented in the digital space.
  • Color Temperature
    Color temperature is derived from the color of radiation emitted by a black body when heated to a particular temperature. Hence, it is commonly specified in units of Kelvin. Our main interest here is adjusting the white point or the chromaticity of the color reproduced by equal red, green and blue components in an output device. This allows us to adjust the colors appear “warmer” or “cooler”.
  • Dynamic Range and Quantization
    You may have heard about the newer camera phones having an HDR mode. These phones are able to process a photograph so that it can have both clear shadows and also brighter regions in the frame. The dynamic range of the image is what they are referring to here. Dynamic range is the ratio of the brightest to the darkest light levels. These levels are quantized into several intensity levels in this range. An 8-bit device would have 256 such intensity levels.
  • Gamma
    Gamma
    We are able to better distinguish between colors intensities at lower levels.

    Our eye is sensitive to the various intensities of colors in a non-linear or power relationship. This allows us to see clearly both indoors (or at night) and outdoors in bright daylight. [4] This leads us to have something known as gamma correction in computer graphics.  You can map the linear levels of your images to a curve of your choice. This must be done according to the characteristics of the output device like the monitor. When you adjust the brightness, contrast or gamma settings on your display, you are essentially manipulating this curve. This GPU Gems article from the Nvidia’s Developer zone tells you more about Gamma that you need to know.  I think, I’ll probably stop here but this topic probably deserves more space than a short paragraph. There are a couple of excellent articles by Charles Poynton on this such as The Rehabilitation of Gamma and the Gamma FAQ.

  • Dithering
    Our eyes tends to smear adjacent pixel colors together. This phenomenon is exploited to simulated higher color depth images than what that could be supported by an output device or possible in an image format. You can see some examples of dithering here. In another type of dithering known as temporal dithering, colors are changed in consecutive frames to create a similar illusion.

V. The sRGB color format

Although now a bit dated, most of the consumer devices still use sRGB as the default color spaces. When you see sRGB content on compatible devices, you will enjoy the same colors. You can find out more about what goes into making a standard color space here: http://www.w3.org/Graphics/Color/sRGB.html. After reading about the fundamentals of digital color, I hope that you’d have a good understanding of how to read a specification like that.

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This is a very short post considering the breadth of topics that it deals with. I have tried to highlight the human factors that influenced the development of color theory and technologies throughout this post. They sure were able to piqué my curiosity to find out more. I hope that you’d also like this collection of resources to read about color. I would be glad if you could point out any errors and typos here.

Image Credits: Munsell System. © 2007, Jacob Rus

Footnotes

  1. Update: Study reveals that Mantis shrimp uses color to communicate! http://www.livescience.com/42797-mantis-shrimp-sees-color.html?cmpid=514636 ^
  2. More info here: http://graphics.stanford.edu/courses/cs178-10/applets/colormatching.html ^
  3. Device independent colors are useful for studying the color theory. They are also used as intermediaries when converting between different colors spaces. ^
  4. This could be similar to other psychometric curves: http://en.wikipedia.org/wiki/Psychometric_function ^

The Stroop Test

The Stroop task is among the popular research tools used in experimental psychology. It involves creating a conflict situation using words and colors. The original experiment was conducted by John Ridley Stroop way back in 1935. The participants are asked to do an oral reading of color words – like “red“, “green“, “blue” etc. in these tasks. In his first experiment, Stroop compared the reading times of words in two conditions: a) the neutral condition: words are presented in a normal black ink on a white background; and b) Incongruent condition: having incompatible color combinations e.g. “red“. It was during his second experiment that he found the reading times were much faster when using colored rectangles as compared to incongruent color-word combinations.

Other Stroop paradigms have also compared incongruent with congruent conditions. The Wikipedia article on the subject summarizes their results:

Three experimental findings are recurrently found in Stroop experiments:

  1. A first finding is semantic interference, which states that naming the ink color of neutral stimuli (e.g. when the ink color and word do not interfere with each other) is faster than in incongruent conditions. It is called semantic interference since it is usually accepted that the relationship in meaning between ink color and word is at the root of the interference.
  2. Semantic facilitation, explains the finding that naming the ink of congruent stimuli is faster (e.g. when the ink color and the word match) than when neutral stimuli are present (e.g. when the ink is black, but the word describes a color).
  3. The third finding is that both semantic interference and facilitation disappear when the task consists of reading the word instead of naming the ink. It has been sometimes called Stroop asynchrony, and has been explained by a reduced automatization when naming colors compared to reading words.

I needed a mobile (Yay, HTML5!) Stroop task as one my experiments in a class project. First, I tried using the Google Speech API but it was failing to recognize my own speech inputs, so I resorted to using regular buttons instead. I also wanted to vary the difficulty of the task, so I added an option of adding more color variations (More buttons, more targets, Fitts’ law …). Here’s what I could come up with in a couple of hours:

A Symphony of Drums

I spent my afternoon today at Tablaphilia – a tabla symphony composed by Pt. Samir Chatterjee. It was incredible to listen to 22 drummers playing together on a single stage in harmony and conducted in a symphony. Do you find it strange when I talk about harmonics while describing something performed on drums? A lot of people new to Tabla certainly do. You could sense the confusion in the audience as they watched the band “tune” their drums. Most drums, such as the ones used in a rock performance produce only in-harmonic vibrations. You’d probably prefer a dry sound without any ‘ring’ on these drums contrary to what you get from a Tabla.

tabla
A tabla is usually played as a set of two drums. The one on the left is the bass drum while the right one has a pitch and can produce harmonic overtones.

Tabla is part of a family of musical drums including Mridangam and Pakhawaj, which can produce harmonic overtones. In fact, tabla featured relatively much later in Indian music. There are several theories about its origins, such as the legend involving the famous musician – Amir Khusro [1] , and how he invented tabla when a jealous competitor broke his drum. Many also believe that Tabla may have more ancient roots in the instrument known as Tripushkara, which had three different parts like a drum kit: horizontal, vertical and embraced. I find this theory more convincing but the absolute beginnings of tabla remain unclear. However, we do know that Tabla became popular in the 17th century, when there was a need to have a drum that could give faster and complex rhythm structures required for the then emerging Sufi music style. The “finger and palm” technique used on the Tabla was much more suited for it than the heavier sounding Pakhawaj.

Alright, coming back to the central theme of the post: what allows a drum to produce harmonics? Without going into its mathematics (read, I can’t :D), allow me to refresh your memory about some concepts in harmonics. Perhaps you remember the experiments performed with the sound column and a tuning fork in your Physics lab. [2] You’d recall that a string vibrates at some fundamental frequency and its integer multiples are known as harmonics. Stringed instruments can vibrate in a harmonic series, and a unique combination of these harmonics make them sound the way they do. But what about a membrane such as the ones that used on these drums? Turns out that the drum-head on the pitch drum (the right one; See picture.) can also produce five such harmonics giving its musical effect. These are responsible for the different bols that are played on the tabla. There are two papers by the Nobel prize-winning physicist CV Raman, who has explored them in a lot of detail: "Musical drums with harmonic overtones" (C.V. Raman and S. Kumar, 1920)  and "The Indian musical drums" (C.V. Raman, 1934)

Unlike most drums, tabla has a sophisticated mechanism to alter its pitch. All tablas are designed to have a pitch that can vary between a certain range. This is done by beating along the sides of the head and adjusting the tension in the straps on the side with wooden blocks. By carefully tuning several tablas, you can derive different notes used in music and have something as amazing like this:

It was exhilarating to hear the “notes” played by the drummers during the concert piece today  as the tablas provided both rhythm and melody. As I was enjoying the music, I couldn’t help but wonder about the engineering skills and knowledge required to build these instruments. Most artisans responsible for building them have no formal training about the theory behind it. All the ingredients that go into making the drum, its shape, the three layers of membrane on the head and even the placement of the black spot (or syahi) contribute to the unique sounds of the instrument. Some of the techniques for building the drum have been passed within families over hundreds of years. The exact recipe for making the syahi, is still kept as a closely guarded secret in these families. This loading of the membrane with the syahi allows the tabla to produce overtones. Did you notice that it is placed off the center on the bass (the left drum) though? The membrane also has different regions which when struck in a certain manner produce the overtones. When you go about counting the different parameters and factors, it makes you wonder about how by mere experience, the makers of tabla could design it.

Listening to Tablaphilia was an incredibly unique experience. I always enjoy when students play together in a tabla class while learning a piece but having a complete performance like this was very new for me. Usually, tabla performances are either done solo or they give company to a melody instrument but never as an ensemble. Some connoisseurs of Indian music would argue that a format like this doesn’t offer any room for improvisations. Agreed; but then what is music without variety and experimentation. I look forward to more such symphonies and concerts.

References

  1. C.V. Raman (1934), The Indian musical drums. Available: http://www.ias.ac.in/jarch/proca/1/179-188.pdf.
  2. C.V. Raman and S. Kumar (1920), Musical drums with harmonic overtones. Available: http://www.nature.com/nature/journal/v104/n2620/abs/104500a0.html.

Footnotes

  1. Amir Khusro, the second; as I am told, but I couldn’t find a reference online ^
  2. The Wikipedia article on Harmonics has some really neat illustrations. ^

Talk: The Signal Processing Approach to Biomarkers

A biomarker is a measurable indicator of a biological condition. Usually it is seen as a substance or a molecule introduced in the body but even physiological indicators may function as dynamic biomarkers for certain diseases. Dr. Sejdić and his team at the IMED Lab work on finding innovative ways to measure such biomarkers. During the ISP seminar last week, he presented his work on using low-cost devices with simple electronics such as accelerometers and microphones, to capture the unique patterns of physiological variables. It turns out that by analyzing these patterns, one can differentiate between healthy and pathological conditions. Building these devices requires an interdisciplinary investigation and insights from signal processing, biomedical engineering and also machine learning.

Listening to the talk, I felt that Dr. Sejdić is a researcher who is truly an engineer at heart as he described his work on building an Asperometer. It is a device that is placed on the throat of a patient to find out when they have swallowing difficulties (Dysphagia). The device picks up the vibrations from the throat and does a bit of signal processing magic to identify problematic scenarios. Do you remember the little flap called the Epiglotis that guards the entrance to your wind pipe, from your high school Biology? Well, that thing is responsible for directing the food into the oesophagus (food pipe) while eating and preventing it from going into wrong places (like the lungs!). As it moves to cover the wind pipe, it records a characteristic motion pattern on the accelerometer. The Asperometer can then distinguish between regular and irregular patterns to find out when should we be concerned. The current gold standard to do these assessments involve using some ‘Barium food’ and X-Rays to visualize its movement. As you may have realized, the Asperometer is not only unobstrusive but also appears to be a safer method to do so. There are a couple of issues left to iron out though, such as removing sources of noise in the signal due to speech or even breathing through the mouth. We can, however, still use it in controlled usage scenarios in the presence of a specialist.

The remaining part of the talk briefly dealt with Dr. Sejdić’s investigations of gait, handwriting processes and preference detection, again with the help of signal processing and some simple electronics on the body. He is building on work in biomedical engineering to study age and disease related changes in our bodies. The goal is to explore simple instruments providing useful information that can ultimately help to prevent, retard or reverse such diseases.

Talk: Look! New stuff in my room!

Yesterday, I attended a talk by Prof. David Forsyth. One of the perks of being a student is to be able to attend seminars like these. The talk was mostly about his work on understanding pictures of rooms and inserting objects into them. It was a light talk and he did not go too much into the details of his paper. Apart from that he gave an overview of the current work done by the computer vision researchers and his vision (pun intended) for the future. Overall, it was a fun talk to attend and a Friday evening well spent :D.

Here is a video showing a demo of the method, in case you are curious:

Talk: Understanding Storytelling

This week I attended a very interesting talk by Dr. Micha Elsner. Yes, this was one of those full-house ISP seminars. I was glad that I reached the venue a bit earlier than the usual. Dr. Elsner started his talk by giving us an overview of the bigger goals he is looking at. His work is helping us formally understand storytelling and develop computational methods for it. If you have ever used Auto Summarize in Word, you’ll have an intuitive idea about how it works: It finds sentences with frequently used words to make a summary of the document. It can generate satisfactory summaries for articles that merely state some facts, but would fail miserably in trying to understand and summarize a story.

Dr. Elsner’s approach focuses on observing social relationships between characters as the story unfolds, to understand the high level plot. He uses two basic insights about common plots in a story: a) it has an emotional trajectory, i.e. over time, we see a variation in negative and positive emotions, and b) characters interact with each other and have a social network just like in real life.

To begin his analysis, Dr. Elsner would first parse the text to identify characters from the noun phrases in the sentences. This step itself is not an easy one. For example, one character may be referred to by several different names through the chapters like – Miss Elizabeth Bennet, Miss Bennet, Miss Eliza, Lizzy and so on. Once we have that, we could try understanding the relationships between different characters over course of time. Simple functions measuring nearby mentions (co-occurrence) of the characters and their emotional trajectory curves are used to build a complex similarity measure. Emotion trajectory is plotted by finding words with “strong sentiment” cues. This makes up the first-order character kernel for measuring similarity. Now, he adds social network features to build the second order kernel. Characters are more similar if they each have close friends who are also similar.

I think that the method for testing the similarity the proof of concept was also an ingenious one. Dr. Elsner artificially re-orders the chapters of a book, and attempts to distinguish it from the one in the original form. Success here would imply that we indeed been able to gather some understanding about a plot by using this method. A corpus of novels from Project Gutenberg is used as a training data for this purpose. Do go through the links in the section below to find out more!

Further Reading

  1. Micha Elsner. Character-based Kernels for Novelistic Plot Structure. Proceedings of the Conference of the European Chapter of the Association for Computational Linguistics (EACL 2012), Avignon, France. Available: http://aclweb.org/anthology-new/E/E12/E12-1065.pdf
  2. Presentation slides are also available on Dr. Elsner’s page: http://www.ling.ohio-state.edu/~melsner/slides/novelpres.pdf

Talk: ISP Seminar

Turn-Taking Behavior in a Human Tutoring Corpus by Zahra Rahimi

In their research, Zahra and Homa, analyze turn-taking behavior between students in a human-human spoken tutoring system. This analysis could be helpful in understanding how users from different demographics interact with a tutor. In this study, they use sequences of speech and silence over time to mark ‘Active’ and ‘In-active’ states the dialogues between the tutor and the student. Considering both the tutor and student together we have four different combinations of these states, in which each one of them being active or inactive. The next step is to learn (using a semi-Markov process) a model from the dialogues. Using this model, they are able to measure the association of these models with features such as gender, scores obtained in the pre-test etc. The experiments provide some interesting results such as female students speak simultaneously longer with the tutor than male students; while their activities are less than their male counterparts. Also, for the students with a lower pre-test scores, the tutor tended to speak for longer time.

Content-Based Cross-Domain Recommendations Using Segmented Models by Shaghayegh Sahebi

Sherry presented her work on the job recommendation systems in her talk. This was done as part of her internship at LinkedIn last summer. The site originally used a single model to make job recommendations to the users by selecting features from their profiles. But, these profiles tend to vary a lot according to the job function the users play and the industry they are in. Professionals in academia, for example, may put a very different set of information on their resume as opposed to a banking executive. With this new study, they wish to segment users using these very features (current job function and industry etc.) before sending them to the recommender systems. This allows them to develop an efficient method of feature augmentation and adapt their algorithms.

The model was built and evaluated based on some pre-collected data. They evaluated the accuracy of the system in recommending the jobs that the users applied to. This, however, restricted them to a certain extent and an online A/B testing is still under process. We’ll have to wait and watch for the results to find out if they do better than the one-size-fits-all model that is currently in place.

Further Reading

  1. Z. Rahimi, Homa B. Hashemi “Turn-Taking Behavior in Human Tutoring Corpus.” AIED 2013. Available: http://link.springer.com/chapter/10.1007%2F978-3-642-39112-5_111