Multiscale contrast enhancement

The latest print issue of Optical Engineering (June 2007) has an interesting paper on color image contrast enhancement based on mathematical morphology.

The authors use the CIE 1976 UCS diagram to convert the images to a luma-chroma representation. They use mathematical morphology on the Y plane, applying open and close operators to find the image's principal regions according to a morphological contrast criterion. They also have a second approach based on retinex theory, but using morphological operations instead of the usual family of Gaussian transformations. In the color channels they use the gravity center law to boost the contrast.

This paper can be found online in the SPIE Digital Library under the title "Morphological multiscale contrast approach for gray and color images consistent with human visual perception" or doi:10.1117/1.2749711.

Limits of visual awareness

When we briefly examine a scene visually, we can pay attention only to one color at a time. However, we can see it in multiple locations.

New research by Liqiang Huang et al. proves the unexpected fact that our rich visual experience appears to be a substantial overestimation of what we are actually perceiving. We think we are aware of a complex world of varied colors, shapes, and directions of motions, etc. but in fact in any given instant we can see only one color.

What we see is what we can retrieve from visual memory, which does not contain a single image or frame, but what we have perceived in a number of different instants. For example, if we consider a small number of colored monochrome disks on a neutral surface, then if they disks have all the same color, in an instant we can determine that color and the disk's position. If the disks are in more than a single color, then in an instant we can see the disk's locations, but not their colors.

The two experiments required to prove this are not simple and are reported in Science Magazine of 10 August 2007: Vol. 317. no. 5839, pp. 823 - 825. They require to determine what the informational content of any single momentary act of conscious perception is.

Links from the comments:

• Press release … http://web.mit.edu/newsoffice/2007/clutter-0821.html
• Matlab code … http://dspace.mit.edu/handle/1721.1/37593
• Associated paper … http://www.journalofvision.org/7/2/17/Rosenholtz-2007-jov-7-2-17.pdf

Mini review. Without conscience

As mortgage investments are in crisis, I'll offer you my second mini review in the 301.7—terrorism @ home series, because you indicated in my post on risk management that all that is necessary is to understand the risks and hedge against them. Today's book among others briefly discusses the Savings & Loans crisis and what you learn from that may help you develop a proper risk management strategy for the current crisis, which has many similarities.

Dr. Robert D. Hare is the foremost expert in the antisocial personality disorder syndrome and his book Without conscience is accessible to us non-specialists. Dr. Hare wrote his book ten years before Dr. Stout wrote hers (see my previous post), so while the latter was influenced by the events of September 11, 2001, the former was written after the Desert Storm war in Iraq.

However, the books are completely different for more fundamental reasons. While Dr. Stout works with APD victims, Dr. Hare researches the psychopaths themselves, and therefore offers a diametrically opposite perspective. Again, also with this book you should not draw any quick conclusions about any person; instead you should read the book slowly and carefully so you can learn to protect yourself. [As a CYA, I am citing actual text in block quotes instead of paraphrasing it in a few words. For your convenience, each block quote has an anchor.]

Dr. Hare starts with electroencephalograms (EEG) that do not look human:

Everybody has met these people, been deceived and manipulated by them, and forced to live with or repair the damage they have wrought. These often charming—but always deadly—individuals have a clinical name: psychopaths. Their hallmark is a stunning lack of conscience; their game is self-gratification at the other person's expense. Many spend time in prison, but many do not. All take far more than they give.

Like Dr. Stout, also Dr. Hare is flabbergasted by the high incidence rate of this condition and by how physically close they are to us.

The most obvious expressions of psychopathy —but by no means the only ones—involve flagrant criminal violation of society's rules. Not surprisingly, many psychopaths are criminals, but many remain out of prison, using their charm and chamaleonlike abilities to cut a wide swath though society and leaving a wake of ruined lives behind them.

He then asks

is the psychopath mentally ill or simply a rule breaker who is perfectly aware of what he or she is doing?

The question is not just a semantic one; posed another way, it has immeasurable practical significance: Does the treatment or control of the psychopath rightly fall to mental health professionals or to the correctional system? Everywhere in the world, judges, social workers, lawyers, schoolteachers, mental health workers, doctors, correctional staff, and members of the general public need—whether they know it or not—the answer.

One important criterion is that

unlike psychotic individuals, psychopaths are rational and aware of what they are doing and why. Their behavior is the result of choice, freely exercised.

In other words, these individuals are not sick or insane and the correctional system has to deal with them.

By the way, the terms sociopath and psychopath are often used interchangeably. Some people prefer the former because it is less easy to be confused with psychotism or insanity. However, Dr. Hare makes a clear distinction between the two terms and does not consider them to be synonyms:

"antisocial personality disorder" refers primarily to a cluster of criminal and antisocial behaviors. The majority of criminals easily meet the criteria for such a diagnosis. "Psychopathy," on the other hand, is defined by a cluster of both personality traits and socially deviant behaviors. Most criminals are not psychopaths, and many of the individuals who manage to operate on the shady side of the law and remain out of prison are psychopaths. Keep this in mind if you have occasion to consult a clinician or counselor about a psychopath in your life. Make sure that he or she knows the difference between antisocial personality disorder and psychopathy.

Dr. Hare has developed a complex clinical diagnostic tool, the Psychopathy Checklist (PCL). The diagnosis is difficult, because psychopathy is a syndrome—a cluster of related symptoms. Anyway, the symptoms are:

Emotional/Interpersonal	Social deviance
glib and superficial egocentric and grandiose lack of remorse or guilt lack of empathy deceitful and manipulative shallow emotions	impulsive poor behavior controls need for excitement lack of responsibility early behavior problems adult antisocial behavior

As for lack of remorse or guilt, Dr. Hare notes

In an ironic twist, psychopaths frequently see themselves as the real victims.

And regarding shallow emotions he notes that

Laboratory experiments using biomedical recorders have shown that psychopaths lack the physiological responses normally associated with fear.

Given these two facets of the psychopath—feelings & relationship and social deviance—one could assume these people could not only become our neighbors next door but also terrorists who are jealous of our freedom and democracy. However, Dr. Hare notes that

it is […] unlikely that psychopaths would make good spies, terrorists, or mobsters, simply because their impulsiveness, concern only for the moment, and lack of allegiance to people or causes make them unpredictable, careless, and undependable—likely to be "loose cannons."

Thus psychopaths usually do not get along well with one another and operate individually. However, occasionally they can become partners in crime, and then

generally, one member of the pair is a "talker" who gets his or her way through charm, deceit, and manipulation, whereas the other is a "doer" who prefers direct action—intimidation and force. As long as their interests are complementary, they make a formidable pair.

An interesting perspective is how psychopaths see the PCL:

Recently, an ex-con offered me his opinion on the Psychopathy Checklist: he wasn't to impressed! Now middle-aged, he had spent most of his early adult life in prison, where he was once diagnosed as a psychopath. Here are his responses:

Glib and superficial—"What is negative about articulation skills?"

Egocentric and grandiose—"How can I attain something if I don't reach high?"

Lack of empathy—"Empathy toward an enemy is a sign of weakness."

Deceitful and manipulative—"Why be truthful to the enemy? All of us are manipulative to some degree. Isn't positive manipulation common?"

Shallow emotions—"Anger can lead to being labeled a psychopath."

Impulsive—"Can be associated with creativity, living in the now, being spontaneous and free."

Poor behavioral controls—"Violent and aggressive outbursts may be a defensive mechanism, a false front, a tool for survival in a jungle."

Need for excitement—"Courage to reject the routine, monotonous, or uninteresting. Living on the edge, doing things that are risky, exciting, challenging, living life to its fullest, being alive rather than dull, boring, and almost dead."

Lack of responsibility—"Shouldn't focus on human weaknesses that are common."

Early behavior problems and adult antisocial behavior—"Is a criminal record reflective of badness or non-conformity?"

Interestingly, he had nothing to say about Lack of remorse or guilt.

The main trait is, however, the lack of a conscience, hence the book's title.

We don't know why the conscience of the psychopath—if it exists at all—is so weak. However, we can make some reasonable guesses:

• Psychopaths have little aptitude for experiencing the emotional responses—fear and anxiety—that are the mainsprings of conscience.
• The "inner speech" of psychopaths lacks emotional punch.
• Psychopaths have a weak capacity for mentally "picturing" the consequences of their behavior

Like Dr. Stout, also Dr. Hare is very concerned of contemporary American society encouraging and glorifying many of these symptoms. He concludes

Are we unknowingly allowing a society to evolve that is the perfect breeding ground, and perhaps even a "killing field," for psychopaths? As our morning newspaper tells us, this question grows more pressing every day.

Some numbers he quotes are;

• On average, about 20% of male and female prison inmates are psychopaths.
• Psychopaths are responsible for more than 50% of the serious crimes committed.

A recent study by the FBI found that 44% of the offenders who killed a law enforcement officer on duty were psychopaths.

In a chapter on white-collar psychopaths, the author writes:

Grambling's ability to rationalize his behavior is typical of the attitude psychopaths have towards their victims. In addition to his wish to be "liked by everyone," his euphemistic view of himself as a "financial architect," and his "fear of losing face," he considered his crimes logical responses to frustration and pressure, or more the victim's fault than his own. "In Grambling's mind, anyone who is stupid enough to trust or believe him deserves the consequences," said [New York Assistant District Attorney] Rosner.

Your homework: reflect on the above paragraph every time you say "risk management."

To illustrate how difficult it is to diagnose a psychopath, Dr. Hare relates an anecdote of a personal experience he had with the organizer of a conference on crime here in California, who stole his honorarium:

Ironically, I had spent quite a bit of time with this man, at a luncheon held just before my talk and later in a bar. I detected nothing unusual or suspicious about him; my antenna failed to twitch in his presence. Would I have lent him money? Possibly. I do recall insisting that I pick up the bar tab. He wasn't wearing a bell around his neck!

In fact,

many psychopaths never go to prison or any other facility. They appear to function reasonably well—as lawyers, doctors, psychiatrists, academics, mercenaries, police officers, cult leaders, military personnel, businesspeople, writers, artists, entertainers, and so forth—without breaking the law, or at least without being caught and convicted. […]

Rather than refer to these individuals as successful psychopaths—after all, their success is often illusory and always at someone else's expense—I prefer to call them subcriminal psychopaths. Their conduct, although technically not illegal, typically violates conventional ethical standards, hovering just on the shady side of the law. Unlike people who consciously adopt a ruthless, greedy, and apparently unscrupulous strategy in their business dealings but who are reasonably honest and empathetic in other areas of their lives, subcriminal psychopaths exhibit much the same behaviors and attitudes in all areas of their lives. If they lie and cheat on the job—and get away with it or are even admired for it—they will lie and cheat in other areas of their lives.

Dr. Hare then elaborates on the victims of these white-collar psychopaths—victims who live in fear of retributions—and notes how only few of them become visible, like the tip of an iceberg. The others suffer in the dark.

Tragically these victims often cannot get other people to understand what they are going through. Psychopaths are very good at putting on a good impression when it suits them, and they often paint their victims as the real culprits. As one woman—the third wife of a 40 year old high school teacher—recently told me: "For five years he cheated on me, kept me living in fear, and forged checks on my personal bank account. But everyone, including my doctor and lawyer and my friends, blamed me for the problem. He had them so convinced that he was a great guy and that I was going mad, I began to believe it myself. Even when he cleaned out my bank account and ran off with a 17 year old student, a lot of people couldn't believe it, and some wanted to know what I had done to make him act so strangely."

Writing then about the corporate psychopath, Dr. Hare then goes into the S & L crisis, which

at the time of this writing, the projected cost to U.S. taxpayers of what has become known as the S & L bail-out approaches $1 trillion—more than the entire cost of the Vietnam War.

He then finally starts writing about what all this means for us average people who are just living a normal life and try to make a contribution to society.

The sad fact is that we are all vulnerable. Few people are such sophisticated and perceptive judges of human nature that they cannot be taken in by the machinations of a skilled and determined psychopath. Even those who study them are not immune; as I've indicated in previous chapters, my students and I are sometimes conned, even when aware that we're dealing with a probable psychopath.

In an analogy that is easy to understand for us color scientists, he notes that

the psychopath is like a color-blind person who sees the world in shades of grey but who has learned how to function in a colored world. He has learned that the light signal for "stop" is at the top of the traffic signal. When the color-blind person tells you he stopped at the red light, he really means he stopped at the top light. He has difficulty in discussing the color of things but may have learned all sorts of ways to compensate for this problem, and in some cases even those who know him well may not know that he cannot see colors.

Like the color-blind person, the psychopath lacks an important element of experience—in this case, emotional experience—but may have learned the words that others use to describe or mimic experiences that he cannot really understand. As Cleckley put it, "He can learn to use ordinary words … [and] will also learn to reproduce appropriately all the panthomime of feeling … but the feeling itself does not come to pass."

Recent laboratory research provides convincing support for these clinical observations.

However, there is a twist:

Psychopaths are notorious for not answering the questions posed to them or for answering in a way that seems unresponsive to the question. […] Psychopaths also sometimes make it difficult for their listeners to understand parts of their narrative.

And

We are sucked in not by what they say but by how they say it and by the emotional buttons they push while saying it.

As for the moral stance we should take, Dr. Hare writes

psychopaths do meet current legal and psychiatric standards for sanity. They understand the rules of society and the conventional meanings of right and wrong. They are capable of controlling their behavior, and they are aware of the potential consequences of their acts. Their problem is that this knowledge frequently fails to deter them from antisocial behavior.

[…] In my opinion, psychopaths certainly know enough about what they are doing to be held accountable for their actions.

About their modus operandi he then teaches us

Psychopaths tend to see any social exchange as a "feeding" opportunity, a contest, or a test of wills, in which there can be only one winner. Their motives are to manipulate and take, ruthlessly and without remorse.

[…] Although psychopaths may talk a lot, they are not necessarily skilled wordsmiths. It is primarily the "show," not eloquent use of language, that attracts our attention and cons us. Good looks, a touch of charisma, a flood of words, contrived distractions, a knack for knowing which buttons to press—all these can go a long way toward obscuring the fact that the psychopathic presentation is nothing more than a "line." A good-looking, fast-talking psychopath and a victim who has "weak spots" is a devastating combination. If the psychopath's "show" is not enough, the adroit use of "stage props"—phony credentials, flashy car, expensive clothes, a sympathy-inducing role, and so forth—will usually complete the job.

Pondering on how our American culture is encouraging more and more the traits of psychopaths, Dr. Hare envisions a dark future reminiscent of A Clockwork Orange.

If, as I believe, our society is moving in the direction of permitting, reinforcing, and in some instances actually valuing some of the traits listed in the Psychopathy Checklist—traits such as impulsivity, irresponsibility, lack of remorse, and so on—our schools may be evolving into microcosms of a "camouflage society," where true psychopaths can hide out, pursuing their destructive, self-gratifying ways and endangering the general student population. […] our society may be not only fascinated but increasingly tolerant of the psychopathic personality. Even more frightening is the possibility that "cool" but vicious psychopaths will become twisted role models for children raised in dysfunctional families of disintegrating communities where little value is placed on honesty, fair play, and concern of the welfare of others.

[…] today our streets, our schools, and even our homes might afford the psychopath the chance to blend in undetected, undiagnosed, and actively encouraged. I hope that this book will draw attention to this frightening possibility by putting psychopathy in children into bold relief.

Eventually Dr. Hare discusses therapies for psychopaths. Unfortunately there aren't any and the only possibilities are to either teach them to use cognitive skills not to do harm—after all they are sane—or must outcast them.

With few exceptions, the traditional forms of psychotherapy, including psychoanalysis, group therapy, client-centered therapy, and psychodrama, have proved ineffective in the treatment of psychopathy. Nor have the biological therapies, including psychosurgery, electroshock therapy, and the use of various drugs, fared much better.

Psychopaths don't feel they have psychological or emotional problems, and they see no reason to change their behavior to conform to societal standards with which they do not agree.

To elaborate, psychopaths are generally well satisfied with themselves and with their inner landscape, bleak as it may seem to outside observers. They see nothing wrong with themselves, experience little personal distress, and find their behavior rational, rewarding, and satisfying; they never look back with regret or forward with concern. They perceive themselves as superior beings in a hostile, dog-eat-dog world in which others are competitors for power and resources. Psychopaths feel it is legitimate to manipulate and deceive others in order to obtain their "rights," and their social interactions are planned to outmaneuver the malevolence they see in others.

Dr. Hare then suggest we should refrain from sending them into therapy, because

unfortunately, programs of this sort merely provide the psychopath with better ways of manipulating, deceiving, and using people. As one psychopath put it, "These programs are like a finishing school. They teach you how to put the squeeze on people."

To conclude, Dr. Hare gives a survival guide teaching you how to protect yourself.

• Know what you are dealing with.
• Try not to be influenced by "props." (Don't pay too much attention to any unusually captivating characteristic of people you meet—dazzling looks, a powerful presence, mesmerizing mannerisms, a soothing voice, a rapidfire verbal pitch, and so forth. […] Close your eyes or look away and carefully listen to what the person is saying.)
• Don't wear blinkers. (Ask the individual about his or her friends, family, relatives, employment, place of residence, plans, and so forth. Psychopaths usually give vague, evasive, or inconsistent replies to queries about their personal lives. Be suspicious of such replies, and try to verify them.)
• Keep your guard up in high-risk situations.
• Know yourself. (Psychopaths are skilled at detecting and ruthlessly exploiting your weak spots, at finding the right buttons to press. Your best defense is to understand what your weak spots are and to be extremely wary of anyone who zeros in on them.)
• Obtain professional advice.
• Don't blame yourself.
• Be aware of who the victim is. (Psychopaths often give the impression that it is they who are suffering and that it is the victims who are to blame for their misery. But they are suffering a lot less that you are, and for different reasons. Don't waste your sympathy on them; their problems are not in the same league as yours. Theirs stem primarily from not getting what they want, whereas yours result from a physical, emotional, or financial pounding.)
• Be careful about power struggles. (Keep in mind that psychopaths have a strong need for psychological and physical control over others. They must be in charge, and they will use charm, intimidation, and violence to ensure their authority. In a power struggle a psychopath will usually focus on winning. This doesn't mean you shouldn't stand up for your rights, only that it will probably be difficult to do so without risking serious emotional or physical trauma.)
• Set firm ground rules. (Although power struggles with a psychopath are risky at best, you may be able to set up some clear ground rules—both for yourself and for the psychopath—to make your life easier and begin the difficult transition from victim to a person looking out for yourself.)
• Don't expect dramatic changes. (To a large extent, the personality of psychopaths are "carved in stone.")
• Cut your losses. (The psychopath may succeed in shattering your self-confidence and may convince you—and your friends—that you are unworthy of his or her time or even that you are "losing it." The more you give in, the more you will be taken advantage of by the psychopath's insatiable appetite for power and control. Rather than make fruitless attempts to adapt to a hopeless situation—usually by giving in, accepting your lot in life, or losing your self-identity—it may be better to recognize that your emotional and physical survival requires that you take charge of your life. This can be a tricky move—even a dangerous one—and it requires good professional advice, both clinical and legal.)
• Use support groups.

The book concludes with

The social and financial costs to society of failing to solve the daily mystery of the psychopath will be staggering. It is imperative that we continue to search for clues.

Take action, read one of the books in this review series, and build your risk management strategy. And do not forget you are a member of this society, so when you spot a psychopath, write your Congress Person.

In the next mini review I will review a book about our workplace.

Mini review. The sociopath next door

This mini review is the first in a series that I would call 301.7—terrorism @ home. In Europe the Seventies brought IRA, ETA, RAF, and BR and with them terrorism in our immediate environment. In the USA, 30 years later, after 11 September 2001, we also have to deal personally with terrorism. As a society, we have entities like military strategists, politicians, covert agencies, and historians to study the phenomenon; and we have institutions like the Secret Service, police, and army to deal with it.

Informally, we label the agents of terrorism with terms like sociopaths and psychopaths. However, for the past 60 or so years (actually, since Cleckley wrote The Mask of Sanity in 1941) these terms have been associated by the medical profession with an actual disease. The medical name of this disease is antisocial personality disorder and it is described in section 301.7 on page 706 in the Diagnostic and Statistical Manual of Mental Disorders IV of the American Psychiatric Association.

It turns out that antisocial personality disorder, or APD for short, is a quite common disease—4% of the population are affected by it. For comparison, here in California, according to the Centers for Disease Control and prevention, the "alarmingly high" colorectal cancer incidence rate is 0.045%. Therefore APD has pandemic proportions and you should be aware of it, because you might have to deal with a sociopath living next door.

A good starting point is Dr. Martha Stout's book The sociopath next door. Dr. Stout has served on the Harvard Medical School for 25 years and is also in private practice, specializing in the victims of sociopaths. The book is easy to read and gives you an overview of the disease and some guidance on how to recognize and deal with APD sufferers.

Diagnosing and treating a disease is complex and requires a trained physician. For example, if you checked out section 301.7 above, you will have noticed that page 705 is all about when the symptoms are not those of APD, and the diagnostic criteria requires you to have some anamnesis prior to age 15 of the diseased.

If you think your friend has a heart attack, you do not take out your Swiss Army knife and perform a bypass on him; similarly, if you think you are the victim of a sociopath, seek immediate help from your family doctor, who can then refer you to a specialist. With this caveat, Dr. Stout teaches you some symptoms of this disease, namely

1. failure to conform to social norms
2. deceitfulness, manipulativeness
3. impulsivity, failure to plan ahead
4. irritability, aggressiveness
5. reckless disregard for the safety of self or others
6. consistent irresponsibility
7. lack of remorse after having hurt, mistreated, or stolen from another person

But she teaches you also that there is little you can do, other than avoid any contact with sociopaths. In fact she elaborates on these 13 rules for dealing with sociopaths in everyday life:

1. the first rule involves the bitter pill of accepting that some people literally have no conscience
2. in a contest between your instincts and what is implied by the role a person has taken on—educator, doctor, leader, animal lover, humanist, parent—go with your instincts
3. when considering a new relationship of any kind, practice the Rule of Threes regarding the claims and promises a person makes, and the responsibilities he or she has. Make the Rule of Threes your policy
4. question authority
5. suspect flattery
6. if necessary, redefine your concept of respect
7. do not join the game
8. the best way to protect yourself from a sociopath is to avoid him, to refuse any kind of contact or communication
9. question your tendency to pity too easily
10. do not try to redeem the unredeemable
11. never agree, out of pity or for any other reason, to help a sociopath conceal his or her true character
12. defend your psyche
13. living well is the best revenge

So far I have not told you what this disease is. Dr. Stout explains that we have 7 senses. You know about about the first 5. The 6^th is intuition and the 7^th is conscience. A person with APD is a person completely lacking the 7^th sense. Like some people are born blind, some persons are born without a conscience. Because the incidence is so high—1 in 25, like for color blindness—you sooner or later will have to deal with a sufferer, although at first sight it is not obvious.

Like color blindness, APD is a genetic disease. Comparing monozygotic with dizygotic twins, scientists researching the Texas Adoption Project have estimated that APD is 54% inherited, the rest being acquired. Worse than many color blind people not being aware of their disease, the sociopaths cannot be aware of their disease because they do not have the conscience that is necessary to detect a conscience.

If you recall the research published early 2003 about Genghis Khan's propagating his APD-carrying genes to some 16 million men living between Afghanistan and northeastern China—almost one in every 200 men alive—you would expect this disease to be prevalent in Central Asia.

This is not so, because of the acquired component, which in this case should be qualified as "demonically nurtured." In fact, the Asian cultures focus on the relation among people, therefore sociopaths tend to be outcast or even executed, like the Inuit do with the kunlangeta, as they call the sociopaths. In America's Judeo-Christian culture of individualism, instead, many traits of sociopathy are praised and reinforced, such as impulsivity, irresponsibility, and lack of remorse.

In conclusion, right here is where you can become the victim of a sociopath. If you live here, slowly and carefully reading Dr. Stout's book is a must.

Stiles Two-Degree Pilot Data

As I was poking on the Internet for the interpolated 2º pilot color-matching data as functions of wavelength at intervals of 1 nm, I could not find it. As it is always nice to be able to go back to the "book" instead of converting from wavenumber and interpolating by oneself, I quickly scanned Table I(5.5.3) in Wyszecki and Stiles on the trusty old Digital Sender with the Kamakura engine I conceived back in 1991 and OCRed it with ABBYY FineReader 8.0 Professional and here it is:

% The Stiles & Burch 2-deg CMFs are based on measurements made in 10
% observers. The data are referred to as pilot data, but probably represent
% the best estimate of the 2 deg CMFs, since, unlike the CIE 2 deg
% functions (which were reconstructed from chromaticity data), they were
% measured directly.
%
% From Table I(5.5.3) of Wyszecki & Stiles (1982). (Table 1(5.5.3) of
% Wyszecki & Stiles (1982) gives the Stiles & Burch functions in 250
% cm^{-1} steps, while Table I(5.5.3) of Wyszecki & Stiles (1982) is gives
% them in interpolated 1 nm steps.)
%
% These CMFs differ slightly from those of Stiles & Burch (1955). As noted
% in footnote a on p. 335 of Table 1(5.5.3) of Wyszecki & Stiles (1982),
% the CMFs have been "corrected in accordance with instructions given by
% Stiles & Burch (1959)" and renormalized to primaries at 15500 (645.16),
% 19000 (526.32), and 22500 (444.44) cm^{-1} (nm).
%
cmf = [390, 0.18397*10^-2, -0.45393*10^-3, 0.12152*10^-1;
391, 0.22070*10^-2, -0.53474*10^-3, 0.14604*10^-1;
392, 0.26451*10^-2, -0.62941*10^-3, 0.17534*10^-1;
393, 0.31672*10^-2, -0.74019*10^-2, 0.21033*10^-1;
394, 0.37890*10^-2, -0.86974*10^-2, 0.25208*10^-1;
395, 0.46153*10^-2, -0.10464*10^-2, 0.31110*10^-1;
396, 0.54135*10^-2, -0.11995*10^-2, 0.36165*10^-1;
397, 0.62593*10^-2, -0.13528*10^-2, 0.41145*10^-1;
398, 0.72015*10^-2, -0.15386*10^-2, 0.46652*10^-1;
399, 0.83035*10^-2, -0.17975*10^-2, 0.53472*10^-1;
400, 0.96264*10^-2, -0.21689*10^-2, 0.62371*10^-1;
401, 0.11208*10^-2, -0.26695*10^-2, 0.73827*10^-1;
402, 0.13000*10^-2, -0.32299*10^-2, 0.87262*10^-1;
403, 0.14934*10^-2, -0.37616*10^-2, 0.10186;
404, 0.16943*10^-1, -0.41784*10^-2, 0.11682;
405, 0.18979*10^-1, -0.44304*10^-2, 0.13161;
406, 0.21071*10^-1, -0.46185*10^-2, 0.14684;
407, 0.23269*10^-1, -0.48824*10^-2, 0.16337;
408, 0.25621*10^-1, -0.53580*10^-2, 0.18206;
409, 0.28156*10^-1, -0.61520*10^-2, 0.20358;
410, 0.30803*10^-1, -0.72048*10^-2, 0.22750;
411, 0.33450*10^-1, -0.83929*10^-2, 0.25297;
412, 0.35991*10^-1, -0.95963*10^-2, 0.27918;
413, 0.38326*10^-1, -0.10704*10^-1, 0.30538;
414, 0.40459*10^-1, -0.11689*10^-1, 0.33172;
415, 0.42459*10^-1, -0.12579*10^-1, 0.35897;
416, 0.44398*10^-1, -0.13405*10^-1, 0.38787;
417, 0.46342*10^-1, -0.14194*10^-1, 0.41914;
418, 0.48282*10^-1, -0.14977*10^-1, 0.45284;
419, 0.50098*10^-1, -0.15786*10^-1, 0.48810;
420, 0.51662*10^-1, -0.16651*10^-1, 0.52396;
421, 0.52851*10^-1, -0.17603*10^-1, 0.55953;
422, 0.53564*10^-1, -0.18649*10^-1, 0.59396;
423, 0.53789*10^-1, -0.19688*10^-1, 0.62676;
424, 0.53542*10^-1, -0.20593*10^-1, 0.65752;
425, 0.52837*10^-1, -0.21240*10^-1, 0.68586;
426, 0.51690*10^-1, -0.21512*10^-1, 0.71140;
427, 0.50160*10^-1, -0.21404*10^-1, 0.73438;
428, 0.48348*10^-1, -0.21029*10^-1, 0.75560;
429, 0.46357*10^-1, -0.20502*10^-1, 0.77588;
430, 0.44287*10^-1, -0.19936*10^-1, 0.79604;
431, 0.42209*10^-1, -0.19414*10^-1, 0.81667;
432, 0.40065*10^-1, -0.18875*10^-1, 0.83746;
433, 0.37751*10^-1, -0.18212*10^-1, 0.85779;
434, 0.35168*10^-1, -0.17320*10^-1, 0.87703;
435, 0.32220*10^-1, -0.16097*10^-1, 0.89459;
436, 0.28888*10^-1, -0.14518*10^-1, 0.91025;
437, 0.25318*10^-1, -0.12711*10^-1, 0.92446;
438, 0.21671*10^-1, -0.10821*10^-1, 0.93780;
439, 0.18104*10^-1, -0.89882*10^-2, 0.95080;

440, 0.14763*10^-1, -0.73457*10^-2, 0.96395;
441, 0.11643*10^-1, -0.58873*10^-2, 0.97687;
442, 0.85576*10^-2, -0.44508*10^-2, 0.98815;
443, 0.53193*10^-2, -0.28691*10^-2, 0.99635;
444, 0.17441*10^-2, -0.97985*10^-3, 0.10001*10;
445, -0.23392*10^-2, 0.13690*10^-2, 0.99814;
446, -0.69620*10^-2, 0.42191*10^-2, 0.99033;
447, -0.12038*10^-1, 0.75200*10^-2, 0.97759;
448, -0.17481*10^-1, 0.11219*10^-1, 0.96083;
449, -0.23206*10^-1, 0.15266*10^-1, 0.94092;
450, -0.29130*10^-1, 0.19610*10^-1, 0.91875;
451, -0.35208*10^-1, 0.24189*10^-1, 0.89561;
452, -0.41419*10^-1, 0.28932*10^-1, 0.87310;
453, -0.47746*10^-1, 0.33770*10^-1, 0.85281;
454, -0.54170*10^-1, 0.38634*10^-1, 0.83625;
455, -0.60677*10^-1, 0.43464*10^-1, 0.82487;
456, -0.67291*10^-1, 0.48303*10^-1, 0.81815;
457, -0.74083*10^-1, 0.53311*10^-1, 0.81348;
458, -0.81124*10^-1, 0.58651*10^-1, 0.80820;
459, -0.88482*10^-1, 0.64481*10^-1, 0.79972;
460, -0.96224*10^-1, 0.70954*10^-1, 0.78554;
461, -0.10434, 0.78117*10^-1, 0.76479;
462, -0.11270, 0.85807*10^-1, 0.73987;
463, -0.12113, 0.93840*10^-1, 0.71354;
464, -0.12947, 0.10203, 0.68846;
465, -0.13759, 0.11022, 0.66723;
466, -0.14535, 0.11825, 0.65182;
467, -0.15284, 0.12620, 0.64089;
468, -0.16017, 0.13420, 0.63201;
469, -0.16747, 0.14239, 0.62281;
470, -0.17486, 0.15088, 0.61098;
471, -0.18247, 0.15981, 0.59430;
472, -0.19025, 0.16916, 0.57222;
473, -0.19801, 0.17875, 0.54617;
474, -0.20553, 0.18840, 0.51769;
475, -0.21260, 0.19794, 0.48829;
476, -0.21903, 0.20720, 0.45941;
477, -0.22465, 0.21603, 0.43234;
478, -0.22953, 0.22444, 0.40726;
479, -0.23386, 0.23255, 0.38389;
480, -0.23780, 0.24042, 0.36195;
481, -0.24153, 0.24816, 0.34118;
482, -0.24521, 0.25585, 0.32131;
483, -0.24896, 0.26359, 0.30216;
484, -0.25281, 0.27155, 0.28379;
485, -0.25674, 0.27993, 0.26634;
486, -0.26076, 0.28889, 0.24990;
487, -0.26485, 0.29862, 0.23458;
488, -0.26901, 0.30928, 0.22050;
489, -0.27319, 0.32095, 0.20767;

490, -0.27727, 0.33353, 0.19593;
491, -0.28109, 0.34686, 0.18509;
492, -0.28453, 0.36081, 0.17498;
493, -0.28744, 0.37526, 0.16541;
494, -0.28969, 0.39008, 0.15622;
495, -0.29125, 0.40521, 0.14730;
496, -0.29228, 0.42078, 0.13865;
497, -0.29298, 0.43696, 0.13031;
498, -0.29354, 0.45390, 0.12232;
499, -0.29415, 0.47173, 0.11470;
500, -0.29500, 0.49060, 0.10749;
501, -0.29616, 0.51059, 0.10071;
502, -0.29734, 0.53148, 0.94295*10^-1;
503, -0.29813, 0.55298, 0.88199*10^-1;
504, -0.29816, 0.57482, 0.82358*10^-1;
505, -0.29706, 0.59673, 0.76714*10^-1;
506, -0.29446, 0.61845, 0.71209*10^-1;
507, -0.29004, 0.63975, 0.65792*10^-1;
508, -0.28387, 0.66063, 0.60468*10^-1;
509, -0.27628, 0.68127, 0.55274*10^-1;
510, -0.26759, 0.70184, 0.50248*10^-1;
511, -0.25812, 0.72251, 0.45426*10^-1;
512, -0.24816, 0.74344, 0.40844*10^-1;
513, -0.23802, 0.76478, 0.36537*10^-1;
514, -0.22781, 0.78656, 0.32523*10^-1;
515, -0.21725, 0.80852, 0.28781*10^-1;
516, -0.20600, 0.83037, 0.25287*10^-1;
517, -0.19374, 0.85179, 0.22016*10^-1;
518, -0.18014, 0.87252, 0.18945*10^-1;
519, -0.16488, 0.89226, 0.16050*10^-1;
520, -0.14768, 0.91076, 0.13309*10^-1;
521, -0.12848, 0.92793, 0.10717*10^-1;
522, -0.10745, 0.94384, 0.82893*10^-2;
523, -0.84777*10^-1, 0.95857, 0.60380*10^-2;
524, -0.60631*10^-1, 0.97221, 0.39763*10^-2;
525, -0.35184*10^-1, 0.98482, 0.21170*10^-2;
526, -0.86031*10^-2, 0.99650, 0.47268*10^-3;
527, 0.18950*10^-1, 0.10073*10, -0.94755*10^-3;
528, 0.47338*10^-1, 0.10172*10, -0.21657*10^-2;
529, 0.76441*10^-1, 0.10261*10, -0.32223*10^-2;
530, 0.10614, 0.10339*10, -0.41574*10^-2;
531, 0.13633, 0.10405*10, -0.50101*10^-2;
532, 0.16688, 0.10459*10, -0.58186*10^-2;
533, 0.19770, 0.10499*10, -0.66202*10^-2;
534, 0.22868, 0.10525*10, -0.74487*10^-2;
535, 0.25981, 0.10538*10, -0.83032*10^-2;
536, 0.29116, 0.10542*10, -0.91612*10^-2;
537, 0.32277, 0.10539*10, -0.10001*10^-1;
538, 0.35471, 0.10531*10, -0.10799*10^-1;
539, 0.38702, 0.10521*10, -0.11536*10^-1;

540, 0.41976, 0.10512*10, -0.12191*10^-1;
541, 0.45298, 0.10507*10, -0.12742*10^-1;
542, 0.48676, 0.10505*10, -0.13188*10^-1;
543, 0.52121, 0.10504*10, -0.13543*10^-1;
544, 0.55645, 0.10502*10, -0.13822*10^-1;
545, 0.59259, 0.10498*10, -0.14039*10^-1;
546, 0.62973, 0.10489*10, -0.14210*10^-1;
547, 0.66800, 0.10473*10, -0.14348*10^-1;
548, 0.70748, 0.10448*10, -0.14468*10^-1;
549, 0.74822, 0.10413*10, -0.14579*10^-1;
550, 0.79004, 0.10368*10, -0.14681*10^-1;
551, 0.83271, 0.10312*10, -0.14770*10^-1;
552, 0.87603, 0.10245*10, -0.14845*10^-1;
553, 0.91978, 0.10168*10, -0.14901*10^-1;
554, 0.96376, 0.10080*10, -0.14936*10^-1;
555, 0.10078*10, 0.99826, -0.14947*10^-1;
556, 0.10516*10, 0.98745, -0.14931*10^-1;
557, 0.10953*10, 0.97574, -0.14888*10^-1;
558, 0.11391*10, 0.96338, -0.14819*10^-1;
559, 0.11834*10, 0.95066, -0.14727*10^-1;
560, 0.12283*10, 0.93783, -0.14613*10^-1;
561, 0.12743*10, 0.92515, -0.14480*10^-1;
562, 0.13215*10, 0.91287, -0.14328*10^-1;
563, 0.13702*10, 0.90123, -0.14160*10^-1;
564, 0.14206*10, 0.89044, -0.13978*10^-1;
565, 0.14727*10, 0.88039, -0.13782*10^-1;
566, 0.15262*10, 0.87070, -0.13575*10^-1;
567, 0.15807*10, 0.86100, -0.13357*10^-1;
568, 0.16360*10, 0.85095, -0.13129*10^-1;
569, 0.16917*10, 0.84018, -0.12893*10^-1;
570, 0.17476*10, 0.82835 -0.12650*10^-1;
571, 0.18034*10, 0.81513, -0.12401*10^-1;
572, 0.18589*10, 0.80020, -0.12147*10^-1;
573, 0.19138*10, 0.78362, -0.11888*10^-1;
574, 0.19680*10, 0.76573, -0.11625*10^-1;
575, 0.20214*10, 0.74686, -0.11356*10^-1;
576, 0.20739*10, 0.72735, -0.11082*10^-1;
577, 0.21254*10, 0.70752, -0.10803*10^-1;
578, 0.21757*10, 0.68770, -0.10518*10^-1;
579, 0.22247*10, 0.66819, -0.10228*10^-1;
580, 0.22724*10, 0.64930, -0.99317*10^-2;
581, 0.23186*10, 0.63117, -0.96303*10^-2;
582, 0.23635*10, 0.61365, -0.93258*10^-2;
583, 0.24069*10, 0.59659, -0.90203*10^-2;
584, 0.24489*10, 0.57981, -0.87159*10^-2;
585, 0.24896*10, 0.56317, -0.84148*10^-2;
586, 0.25289*10, 0.54649, -0.81188*10^-2;
587, 0.25668*10, 0.52963, -0.78300*10^-2;
588, 0.26034*10, 0.51245, -0.75502*10^-2;
589, 0.26387*10, 0.49480, -0.72812*10^-2;

590, 0.26725*10, 0.47675, -0.70210*10^-2;
591, 0.27044*10, 0.45842, -0.67665*10^-2;
592, 0.27344*10, 0.43993, -0.65146*10^-2;
593, 0.27620*10, 0.42143, -0.62622*10^-2;
594, 0.27871*10, 0.40302, -0.60062*10^-2;
595, 0.28093*10, 0.38484, -0.57437*10^-2;
596, 0.28286*10, 0.36699, -0.54718*10^-2;
597, 0.28445*10, 0.34961, -0.51875*10^-2;
598, 0.28570*10, 0.33277, -0.48896*10^-2;
599, 0.28660*10, 0.31647, -0.45831*10^-2;
600, 0.28717*10, 0.30069, -0.42743*10^-2;
601, 0.28742*10, 0.28539, -0.39696*10^-2;
602, 0.28734*10, 0.27056, -0.36751*10^-2;
603, 0.28695*10, 0.25615, -0.33970*10^-2;
604, 0.28625*10, 0.24215, -0.31410*10^-2;
605, 0.28525*10, 0.22853, -0.29132*10^-2;
606, 0.28397*10, 0.21526, -0.27191*10^-2;
607, 0.28240*10, 0.20233, -0.25626*10^-2;
608, 0.28055*10, 0.18975, -0.24398*10^-2;
609, 0.27842*10, 0.17755, -0.23441*10^-2;
610, 0.27601*10, 0.16575, -0.22693*10^-2;
611, 0.27333*10, 0.15438, -0.22092*10^-2;
612, 0.27037*10, 0.14347, -0.21577*10^-2;
613, 0.26714*10, 0.13305, -0.21090*10^-2;
614, 0.26365*10, 0.12313, -0.20572*10^-2;
615, 0.25989*10, 0.11373, -0.19966*10^-2;
616, 0.25586*10, 0.10489, -0.19220*10^-2;
617, 0.25158*10, 0.96593*10^-1, -0.18328*10^-2;
618, 0.24707*10, 0.88810*10^-1, -0.17319*10^-2;
619, 0.24235*10, 0.81516*10^-1, -0.16223*10^-2;
620, 0.23743*10, 0.74682*10^-1, -0.15069*10^-2;
621, 0.23234*10, 0.68282*10^-1, -0.13883*10^-2;
622, 0.22708*10, 0.62289*10^-1, -0.12695*10^-2;
623, 0.22169*10, 0.56679*10^-1, -0.11532*10^-2;
624, 0.21617*10, 0.51426*10^-1, -0.10418*10^-2;
625, 0.21054*10, 0.46504*10^-1, -0.93822*10^-3;
626, 0.20483*10, 0.41892*10^-1, -0.84426*10^-3;
627, 0.19904*10, 0.37578*10^-1, -0.75965*10^-3;
628, 0.19320*10, 0.33553*10^-1, -0.68351*10^-3;
629, 0.18733*10, 0.29807*10^-1, -0.61496*10^-3;
630, 0.18145*10, 0.26333*10^-1, -0.55316*10^-3;
631, 0.17557*10, 0.23120*10^-1, -0.49727*10^-3;
632, 0.16972*10, 0.20162*10^-1, -0.44648*10^-3;
633, 0.16390*10, 0.17448*10^-1, -0.39998*10^-3;
634, 0.15815*10, 0.14972*10^-1, -0.35697*10^-3;
635, 0.15247*10, 0.12724*10^-1, -0.31668*10^-3;
636, 0.14687*10, 0.10695*10^-1, -0.27849*10^-3;
637, 0.14137*10, 0.88722*10^-2, -0.24217*10^-3;
638, 0.13596*10, 0.72418*10^-2, -0.20760*10^-3;
639, 0.13065*10, 0.57899*10^-2, -0.17465*10^-3;

640, 0.12543*10, 0.45033*10^-2, -0.14319*10^-3;
641, 0.12030*10, 0.33688*10^-2, -0.11310*10^-3;
642, 0.11527*10, 0.23734*10^-2, -0.84268*10^-4;
643, 0.11033*10, 0.15045*10^-2, -0.56564*10^-4;
644, 0.10550*10, 0.74966*10^-3, -0.29873*10^-4;
645, 0.10076*10, 0.96611*10^-4, -0.40831*10^-5;
646, 0.96114, -0.46618*10^-3, 0.20896*10^-4;
647, 0.91577, -0.94692*10^-3, 0.45000*10^-4;
648, 0.87149, -0.13524*10^-2, 0.68102*10^-4;
649, 0.82835, -0.16894*10^-2, 0.90080*10^-4;
650, 0.78642, -0.19645*10^-2, 0.11081*10^-3;
651, 0.74574, -0.21840*10^-2, 0.13018*10^-3;
652, 0.70637, -0.23544*10^-2, 0.14807*10^-3;
653, 0.66835, -0.24819*10^-2, 0.16437*10^-3;
654, 0.63174, -0.25727*10^-2, 0.17897*10^-3;
655, 0.59659, -0.26327*10^-2, 0.19175*10^-3;
656, 0.56294, -0.26679*10^-2, 0.20261*10^-3;
657, 0.53081, -0.26828*10^-2, 0.21149*10^-3;
658, 0.50018, -0.26796*10^-2, 0.21842*10^-3;
659, 0.47099, -0.26601*10^-2, 0.22343*10^-3;
660, 0.44320, -0.26262*10^-2, 0.22656*10^-3;
661, 0.41679, -0.25797*10^-2, 0.22784*10^-3;
662, 0.39172, -0.25224*10^-2, 0.22731*10^-3;
663, 0.36793, -0.24560*10^-2, 0.22501*10^-3;
664, 0.34541, -0.23822*10^-2, 0.22096*10^-3;
665, 0.32410, -0.23027*10^-2, 0.21520*10^-3;
666, 0.30398, -0.22192*10^-2, 0.20776*10^-3;
667, 0.28502, -0.21332*10^-2, 0.19868*10^-3;
668, 0.26716, -0.20460*10^-2, 0.18809*10^-3;
669, 0.25035, -0.19581*10^-2, 0.17630*10^-3;
670, 0.23455, -0.18700*10^-2, 0.16361*10^-3;
671, 0.21971, -0.17822*10^-2, 0.15033*10^-3;
672, 0.20576, -0.16950*10^-2, 0.13675*10^-3;
673, 0.19267, -0.16090*10^-2, 0.12317*10^-3;
674, 0.18037, -0.15247*10^-2, 0.10988*10^-3;
675, 0.16884, -0.14424*10^-2, 0.97164*10^-4;
676, 0.15801, -0.13625*10^-2, 0.85290*10^-4;
677, 0.14784, -0.12856*10^-2, 0.74535*10^-4;
678, 0.13829, -0.12120*10^-2, 0.65168*10^-4;
679, 0.12930, -0.11420*10^-2, 0.57370*10^-4;
680, 0.12086, -0.10755*10^-2, 0.51033*10^-4;
681, 0.11294, -0.10124*10^-2, 0.45981*10^-4;
682, 0.10549, -0.95247*10^-3, 0.42045*10^-4;
683, 0.98510*10^-1, -0.89554*10^-3, 0.39058*10^-4;
684, 0.91958*10^-1, -0.84145*10^-3, 0.36853*10^-4;
685, 0.85811*10^-1, -0.79004*10^-3, 0.35271*10^-4;
686, 0.80044*10^-1, -0.74116*10^-3, 0.34151*10^-4;
687, 0.74630*10^-1, -0.69463*10^-3, 0.33338*10^-4;
688, 0.69544*10^-1, -0.65030*10^-3, 0.32676*10^-4;
689, 0.64762*10^-1, -0.60803*10^-3, 0.32017*10^-4;

690, 0.60260*10^-1, -0.56765*10^-3, 0.31211*10^-4;
691, 0.56019*10^-1, -0.52909*10^-3, 0.30183*10^-4;
692, 0.52029*10^-1, -0.49231*10^-3, 0.28963*10^-4;
693, 0.48282*10^-1, -0.45733*10^-3, 0.27587*10^-4;
694, 0.44769*10^-1, -0.42414*10^-3, 0.26090*10^-4;
695, 0.41480*10^-1, -0.39274*10^-3, 0.24508*10^-4;
696, 0.38408*10^-1, -0.36311*10^-3, 0.22876*10^-4;
697, 0.35543*10^-1, -0.33526*10^-3, 0.21228*10^-4;
698, 0.32878*10^-1, -0.30917*10^-3, 0.19597*10^-4;
699, 0.30405*10^-1, -0.28486*10^-3, 0.18018*10^-4;
700, 0.28114*10^-1, -0.26231*10^-3, 0.16521*10^-4;
701, 0.25999*10^-1, -0.24151*10^-3, 0.15140*10^-4;
702, 0.24051*10^-1, -0.22247*10^-3, 0.13905*10^-4;
703, 0.22261*10^-1, -0.20514*10^-3, 0.12833*10^-4;
704, 0.20620*10^-1, -0.18940*10^-3, 0.11911*10^-4;
705, 0.19117*10^-1, -0.17512*10^-3, 0.11124*10^-4;
706, 0.17740*10^-1, -0.16218*10^-3, 0.10457*10^-4;
707, 0.16481*10^-1, -0.15046*10^-3, 0.98953*10^-5;
708, 0.15329*10^-1, -0.13983*10^-3, 0.94242*10^-5;
709, 0.14273*10^-1, -0.13018*10^-3, 0.90293*10^-5;
710, 0.13305*10^-1, -0.12140*10^-3, 0.86965*10^-5;
711, 0.12415*10^-1, -0.11336*10^-3, 0.84120*10^-5;
712, 0.11593*10^-1, -0.10595*10^-3, 0.81621*10^-5;
713, 0.10829*10^-1, -0.99062*10^-4, 0.79333*10^-5;
714, 0.10116*10^-1, -0.92590*10^-4, 0.77125*10^-5;
715, 0.94092*10^-2, -0.85760*10^-4, 0.74351*10^-5;
716, 0.87394*10^-2, -0.79184*10^-4, 0.71463*10^-5;
717, 0.81190*10^-2, -0.73128*10^-4, 0.68695*10^-5;
718, 0.75441*10^-2, -0.67550*10^-4, 0.66041*10^-5;
719, 0.70114*10^-2, -0.62412*10^-4, 0.63497*10^-5;
720, 0.65177*10^-2, -0.57677*10^-4, 0.61057*10^-5;
721, 0.60599*10^-2, -0.53313*10^-4, 0.58718*10^-5;
722, 0.56354*10^-2, -0.49290*10^-4, 0.56474*10^-5;
723, 0.52417*10^-2, -0.45580*10^-4, 0.54322*10^-5;
724, 0.48765*10^-2, -0.42159*10^-4, 0.52258*10^-5;
725, 0.45377*10^-2, -0.39003*10^-4, 0.50277*10^-5;
726, 0.42232*10^-2, -0.36091*10^-4, 0.48377*10^-5;
727, 0.39313*10^-2, -0.33403*10^-4, 0.46553*10^-5;
728, 0.36600*10^-2, -0.30921*10^-4, 0.44728*10^-5;
729, 0.24081*10^-2, -0.28628*10^-4, 0.42952*10^-5;
730, 0.31742*10^-2, -0.26511*10^-4, 0.41251*10^-5];

Snap, match, shop

It appears I have not been on HP's home page for a month, because I totally missed a color related story, one that got a high reader score of 4.78 out of 5. This story, Snap, match, shop, is about the practical solution to a very difficult problem, namely finding the best shade of foundation for one's complexion.

As can be appreciated from the technical report, this is not the kind of problem that can be solved in a Silicon Valley garage. It requires a good research laboratory that can synergistically leverage deep expertise in color science, imaging and mobile communications.

The research team was led by Principal Scientist Dr. Nina Bhatti portraited below.

In the picture at below, Nina Bhatti holds the specially designed color chart near her skin while using a mobile phone camera to capture and send the photo via MMS to the advisory service for a color recommendation.

The full HP Labs team that helped to create the Color Match technology is presented in the picture below. Top row (left to right) Harlyn Baker, Sabine Susstrunk, Nina Bhatti, Nic Lyons. Bottom row: Mike Harville, John Schettino, Scott Clearwater.

Instead of sitting down with a consultant at a beauty counter, a shopper photographs herself using a mobile phone camera and while holding a specially designed color chart. The person then sends the photo as an MMS (multimedia message) to an advisory service. That system locates the person’s face within the image and color corrects the image for camera and lighting discrepancies.

Skin pixels are extracted from the color corrected image of the person’s face, and then compared to an existing database of previously captured and analyzed images of skin tones of real people. In a matter of seconds, people using the service receive a text message response with a recommendation on the shades of makeup that are best suited to their complexion.

The technology can work with any mobile operator and on any mobile phone equipped with a camera.

The photograph below illustrates that using the specially designed color chart and a mobile phone camera, a shopper can receive an expert recommendation on what shades of make-up are best suited for their complexion.

The photograph below illustrates how the system locates the consumer's face within the image and color-corrects the image for camera and lighting discrepancies.

The image is then compared to an existing database of previously captured and analyzed images of skin tones of real people. In a matter of seconds, the consumer receives a text message response, with a recommendation on the shade of foundation that best matches her complexion.

HP's Jhilmil Jain holds a newer version of the specially designed color chart near her skin while someone uses a mobile phone camera to capture and send the image via MMS to the advisory service for a color recommendation.

A common mobile phone equipped with a camera can help shoppers identify the make-up shades that best suit their complexion. Users receive a text message, suggesting the appropriate shade of make up for their skin tone.