We’ve been hearing a whole lot of this lately, both from real people and from disinfo. I admit, I have been a little curious myself as to what effect angles can affect ear alignment. I decided to try a little experiment using photos of Mark, and photos I found on the internet to help us measure as close as possible what percentages we should expect.
The concept is this: I will have a picture of the subject at a level position. I will measure the pixel distance from the person’s trichion (hairline) to the bottom of the chin. Then I will align that image with the same person angling their head up or down at a certain angle. I will measure the pixel distance of the top and bottom of the ears and divide that by their head size to get a percentage. That is the ballpark percentage we should then expect the same person’s ears to be misaligned at that angle degree. If they are misaligned to a much larger degree, it is likely not the same person (not considering all other variables, which I will get into).
For the scientists here, you may instantly realize a flaw in this experiment. In order to turn this into a reliable formula:
Expected Ear Alignment Percentage Variance (EEAPV) = Ear Differential / Face Length
We need to know the exact angle degree the face is tilted up or down. That is difficult to come by since the photos are from the front and not the side. We need to trust our eyes to calculate the degree of the head tilt. Here is a helpful image so you can better understand what certain degrees look like:
Let’s take a look at what approximately 45-60 degrees angled upwards does to a person’s ear alignment (note that in all of these matches, I aligned them by pupils).
According to the pixel ruler on MS paint, the size from her hairline to the bottom of her chin is 64 points. Here are the percentages I got:
Top of the ear – 14/64 – 21.8% Variance
Bottom of the ear – 10/64 – 15.6% Variance
Now let’s try 60 degrees angled down.
Again, the pixel length of her face is 64 points.
Top of the ear – 18/64 – 28.125% Variance
Bottom of the ear – 21/64 – 32.8% Variance
Downward angle has a higher variance. I think that is because she has her head at a more severe degree facing downward since humans have more mobility to turn their head down rather than up.
Now let’s try a 30 degree angle to compare.
In this case, there is a similar variance to the earlier upward angle photo despite a very strong angle difference.
Top of the ears – 8/42 – 19% Variance
Bottom of the ears – 7/42 – 16.6% Variance
And now 30 degrees angled downwards. This is more common than 30 degrees upward (which is unusual), but still fairly uncommon.
The differential here is about half the differential of the 60 degree downwards comparison, which is exactly what we would expect at 30 degrees.
Top of the ears – 14/105 – 13.3% Variance
Bottom of the ears – 14/105 – 13.3% Variance
So we can see what sort of variances we should expect with severe head tilt in undoctored photographs. Most photographs of people contains head tilts within 15 degrees up or down. This includes photographs where people tilt their heads to the side which we then correct using Photoshop. In that case, the head is more likely to be at a 0 degree angle.
I was unable to find stock photos of models tilting their heads at slighter degrees, like the ones you see above. I asked Mark to take a few photos of himself as an experiment. Below we see an image of Mark at a level position and then Mark angling his head up approximately 10 degrees.
Top of the ears – 19/290 – 6.5%
Bottom of the ears – 20/290 – 6.89%
So based on my experiment (admittedly imperfect), at an up or down tilt of 15 degrees or less, we should expect ear alignment variance to be somewhere between 0%-10%.
Last week we had a controversial twin post regarding Katy Perry. Many people pointed towards the angle of her head as an explanation for the difference in ear alignment. I still remain confident in Katy Perry being twins, and let me show you why.
In the images below, there is a difference in angle degree of approximately 10 degrees, although I believe all of us can agree that it is less than 15-20 degrees.
Top of the ears – 41/277 – 14.8% (!!!!!)
Bottom of the ears – 60/277 – 21.66% (!!!!)
Looking at the examples above, we should expect a variance of between 0%-10% and instead we get a variance of between 14.8%-21.66%! Those are 2.5x-3x higher a variance than we expect.
Let’s look at a few more twins from the archive.
Here we have an angle difference of around 10-15 degrees, so we should expect variance of under 10% in Robert De Niro.
Top of the ears – 40/238 – 16.8%
Bottom of the ears – 22/238 – 9.24%
We see that the top of the ear is way too high.
Now, the Rihanna twins with an angle of about 10 degrees. Mark had a similar angle difference and came in at 6%-7%.
Top of the ears – 30/270 – 11.11%
Bottom of the ears – 20/270 – 7.4% (note how her earring is pushing her bottom lobe upwards. I was conservative but it should be about 1% higher).
The top of Rihanna’s ear is about twice as high as it should be.
Now these aren’t open and shut cases. If you want to play devil’s advocate you can point to Photoshop editing, camera lenses, and contour makeup. That’s fair, and I will write posts in the future showing why most of those are not good reasons either, but for now, hopefully those of you who are most concerned by head angles will begin to see what is expected, and what is abnormal.
16 thoughts on “Hey, Their Heads Are At Different Angles!”
Great analysis. There’s just one thing I’m not 100% clear on. When you say, for example, that the percentage change in the top of Rihanna’s ears is 30/270, where are you getting the number 30 from? What I understand you to be doing is measuring the pixel distance between the line marking the top of her ears in one picture and the line measuring the top of the ears in the second picture, (where the pictures have been re-sized to have the pupils one inch apart). In Rihanna’s case, that difference is 30 pixels, which you then divide by the length of her face (in the picture with less tilt?). Did I understand correctly?
At the beginning of the post you wrote “I will measure the pixel distance of the top and bottom of the ears and divide that by their head size to get a percentage.” But that makes it sound like you’re measuring the pixel length of the ear, rather than the discrepancy in pixel height between the the tilted and untilted (or less tilted) pictures. It seems what you’re doing is measuring the pixel distance between the tops of the ears in each picture and the bottom of the ears in each picture. Or measuring the pixel distance between the tops and bottoms of the ears in each picture and dividing that by the head size. I also assume you take the head size with the least angle?
Yes, you understood correctly, and I could have been clearer in my post.
For the length of the face, I take the image that is most level and measure from the trachion/hairline to the bottom of the chin. If you do the same to a picture with a head tilt, the length will be smaller.
For the variance, I measure the distance between the top of the ear in one picture and the top of the ear in the other, then do the same for the bottom of the ears. I divide each number by the head size and get a percentage variance.
I stumbled on that formula because everybody’s head and ears are different sizes, and I needed a constant to reflect an expected change consistent with everyone.
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Great, just what about it did you like? Do you think it will help people find just the right fashion for whichever angle they want to bend their head at?
Thanks Straight, for this post and all the work behind it. I want the world to know I am much better looking in person than in my photo. This is what my wife tells me, anyway.
I am going to set up another menu on the right above here to grab this post and the one I did some time back on the way we do facial comparisons. That and any future posts on our technology can go there so that people can have a handy reference when they ahve questions about our work.
Maybe combine the posts into a single “FAQ about our methodology” link? You could also address the height question.
There’s a few other things that need to be addressed: contour makeup, camera lens, and Photoshop. I might also need to really dive into plastic surgery before and after. Lots of stuff to do that will be important for convincing people in the future once people become more open minded to this stuff.
By the way, I’m going to read your full paper tonight or tomorrow. We have the hurricane hitting soon so I won’t have much to do for a day or two.
Sure thing. No rush: it’s been over 120 years — a few extra days won’t matter. Here is a slightly updated version of the paper. Mainly just minor edits for clarity: https://goo.gl/egzVeF
Good luck weathering the storm!!
Also, Straight, when you have time, please look over my post “The Math of Facial Alignment” – I did it with my spotty CPA statistical background in mind, where we are dealing with the math of coincidence – say that the odds of one plane being successfully hijacked by people carrying box cutters is one in 600, then four times in one day, one in a kajillion. It’s not that the four events happened, but rather that they happened on one day. That is the “co” in “coincidence.”
With facial features, it is not that one or two align, as that would be expected. It is that many do. I used seven features, but could have added more.
I used ten as the baseline number – the odds that pupils are the same distance as one in ten. But what I do when I am performing this work is more precise than that, aligning them and making minute adjustments of 1/100 increase or decrease so that to my eyes, they are precisely at one inch. The variance in pupil distance would be key, and I have seen them from very close to very wide, but have no statistical data to back me. I would say they can vary by as much as two inches.
And on with the other features – a portrait artist will tell you that despite our perceptions the eyes are set about halfway between top of head and chin, but that might vary by an inch or more … distance, top of eye to top of lip – maybe between one and two inches.
So not having a database of variances in facial features, and using one in ten as the odds of any matching on two different people, I came up with 10 to the 7th, or one in 10,000,000 as the odds of two random people matching. I frankly think the odds are much, much higher. I was being conservative.
But do look that over and make additions and corrections as you see fit. I was told by a participant at the Mathis conference (not MM) that my numbers were whacko. I stand by them anyway.
One way would be to take, say, 100 photographs from a facial recognition stock image directory where they are all facing the same direction and angle and match each one up to someone else of the same gender and race.
Then you point out 6 or 7 alignment checkpoints (nose, upper lip, etc.) and in a spreadsheet keep track of how many checkpoints each matchup aligned with. I don’t know if it’s a big enough sample size, but it should be good enough to give us a ballpark.
I’ll sleep on it.
Ooooh, that’s a great idea. I like it!
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boy, the level of censorship here is radically high. no dissension or creative ideas allowed. how many people do you allow to comment? 10?
For those interested, there is a low-level spook attack going on here, that is, some trolls who work for pay and interact with other trolls are assigned the task of undermining work like ours. Below is an “inside baseball” look at what is banned here.
One IP address, a kid I think with a drinking problem.
Fictionslayer now comments, without censorship, that we are censoring. The objective is to plant the idea tha there is a lot of discussion that we are taking down. Not true.
Another spook. Never underestimate. This comment is the result of a phone or chat conversation.
We’d love to have more thoughtful, well-intentioned commentary and constructive criticism here. If you’d care to contribute anything remotely resembling that, we’re happy to have you. Unfortunately the powers that be are trying to gain full spectrum dominance over the internet and are spending untold sums showering the worldwide web with their JTRIG and COINTELPRO minions. So please, bug off. You are wasting your time here, as your methods are transparent. Plus I’m afraid you’ll give us cooties.