Frontal Area - Optics Experts?

Kraig Willett wrote:
> I have been working on developing a method to photographically determine frontal area of cyclists.
> If you get a chance, take a look at it here (yes, its free). ;-)
>
> http://www.biketechreview.com/projects/frontalarea/kw.htm
>
> My question to this group (hopefully there are some optics experts out there that can point me in
> the right direction): Is it possible to compare the results from different setups (camera height,
> separation distance, focal length of camera, etc..) by using some "correction" formulas?
>
> My hunch is that it should be possible, but I haven't really had the motivation to work on this
> project lately, since it suits my "comparative" needs just fine (same setup each time with the
> same camera).
>
> Basically, I was just curious and figured you all might be able to help out - plus it gives us
> something a bit out of the ordinary to noodle around.

The focal-length/camera-to-subject-distance does make a real difference here. With a short focal
length, close working distance, the proportional size of your shoulders and arms is exaggerated,
while the size of your butt is minimized.

I would think that Ideally you'd want to use at least a 135 mm lens (or equivalent) for this to
minimize the perspective distortion. A 200 would be even better. For your indoor setup, the
available space may be the limiting factor.

The camera height should be about at the center of the frontal area, figure about the same as the
top of the saddle or a bit higher. Longer lenses will reduce errors relating to positioning too.

Might be practical to set up outdoors with the cyclist in the shade of a building, and a bright
background. If you can establish a clear silhouette effect, (underexpose the cyclist, set your
exposure for the background) you should be able to tinker with the contrast as needed using
Photoshop or some similar software tool. Make sure to use a lens hood.

Sheldon "Click" Brown +-------------------------------------+
| Only those who attempt the absurd | will achieve the impossible. | --Albert Einstein |
+-------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone
617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com

"Sheldon Brown" <[email protected]> wrote in message
news:[email protected]...
> The focal-length/camera-to-subject-distance does make a real difference here. With a short focal
> length, close working distance, the proportional size of your shoulders and arms is exaggerated,
> while the size of your butt is minimized.
>
> I would think that Ideally you'd want to use at least a 135 mm lens (or equivalent) for this to
> minimize the perspective distortion. A 200 would be even better. For your indoor setup, the
> available space may be the limiting factor.
>
> The camera height should be about at the center of the frontal area, figure about the same as the
> top of the saddle or a bit higher. Longer lenses will reduce errors relating to positioning too.
>
> Might be practical to set up outdoors with the cyclist in the shade of a building, and a bright
> background. If you can establish a clear silhouette effect, (underexpose the cyclist, set your
> exposure for the background) you should be able to tinker with the contrast as needed using
> Photoshop or some similar software tool. Make sure to use a lens hood.
>
> Sheldon "Click" Brown +-------------------------------------+
> | Only those who attempt the absurd | will achieve the impossible. | --Albert Einstein |
> +-------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone
> 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
> http://captainbike.com http://sheldonbrown.com
>

If you're really serious about this, investigate a topic called photogrammetry. I did some courses
in this in university and it's somewhat interesting. As Sheldon says, if you use a fixed focal
length lens you can get some rough guesses on distances on your prints, assuming your camera
position is the same and you have some point of reference in the frame to compute scale. One problem
that arises is that as you get away from the centre of the frame the image is distorted and the
distances become less accurate. In photogrammetry they generally use 2 cameras a fixed distance
apart and then digitize reference points. You can use this to build a more accurate 3-d model of
your subject. This is, however, quite labour-intensive from a computational standpoint unless you
purchase one of the off-the-shelf packages for doing this type of thing. I spent most of my days in
Analytical Photogrammetry with my mouth open catching flies...

Cheers,

Scott..

In article <[email protected]>,
Sheldon Brown <[email protected]> wrote:

> Kraig Willett wrote:
> > I have been working on developing a method to photographically determine frontal area of
> > cyclists. If you get a chance, take a look at it here (yes, its free). ;-)
> >
> > http://www.biketechreview.com/projects/frontalarea/kw.htm
> >
> > My question to this group (hopefully there are some optics experts out there that can point me
> > in the right direction): Is it possible to compare the results from different setups (camera
> > height, separation distance, focal length of camera, etc..) by using some "correction" formulas?

<snip> Interesting notion.

> The focal-length/camera-to-subject-distance does make a real difference here. With a short focal
> length, close working distance, the proportional size of your shoulders and arms is exaggerated,
> while the size of your butt is minimized.

As Sheldon says, focal length and distance to subject are going to be a big issue- a headache even-
and make it difficult to compare. The view camera folks would probably be the best resource for this
sort of thing, as they're more used to thinking about image size and more used to doing math. Ansel
Adams's book _The Camera_ would be where I'd start looking for this sort of information.

But apparent size and distance are mathematically related (height = distance times angle in radians,
the angle being that from the eye of the observer to the edges of the object).

I wonder about a cameraless option: a simple frame (e.g., an 8 x 10 inch rectangular opening cut out
of a board) set at a specific distance from the rider *and* a specific distance from the observer-
this allows for comparisons and simplifies the math. In the frame is a sheet of plastic or glass
with a rectangular grid- say 5 mm x 5 mm- marked on it. Find the apparent size as measured by the
reference marks. Then it's a simple calculation to compare the apparent size of the image with the
real size of the rider.

To make this as simple as possible, the rider and the observer have to be at specific distances from
the viewing frame, of course, and th eobserver is looking through one eye for the results to be
comparable. So this still isn't foolproof but it would be simpler and eliminate the issues about
focal length, different lenses and distortion, etc.

Hope this helps.

Kraig Willett wrote:
> I have been working on developing a method to photographically determine frontal area of cyclists.
> If you get a chance, take a look at it here (yes, its free). ;-)
>
> http://www.biketechreview.com/projects/frontalarea/kw.htm
>
> My question to this group (hopefully there are some optics experts out there that can point me in
> the right direction): Is it possible to compare the results from different setups (camera height,
> separation distance, focal length of camera, etc..) by using some "correction" formulas?
>
> My hunch is that it should be possible, but I haven't really had the motivation to work on this
> project lately, since it suits my "comparative" needs just fine (same setup each time with the
> same camera).
>
> Basically, I was just curious and figured you all might be able to help out - plus it gives us
> something a bit out of the ordinary to noodle around.
>
> --
> ==================
> Kraig Willett www.biketechreview.com
> ==================
>
>
Disclaimer: I am not an optics expert (IANAOE).

Sorry Ihave no magic correction formula, although this method could possibly be used to develop one.

I have shot many photos of building exteriors and pieced sections of them together for estimates and
presentations.

When doing this I usually use known factors like masonry coursing or window sizes and a graphics
program to undo the distortion caused by the camera location or lens.

I sometimes drop the "corrected" image into a 2D CAD program and use that with known linear
mesurements to work out surface areas for estimates.

Perhaps if you shot test shots of a panel marked off in a known grid using different distances,
camera heights and lenses you could determine the level of distortion and the amount of correction
necessary graphically for various combinations.

Fast, fairly rough estimates of distances for shots "in the field" can be determined by opening the
aperture of the lens to max and using the focal depth of field on an object as a guide.

When shooting a bicycle head on in action there would be some fixed measurements such as wheel size
that could then be related to a suitable grid model.

Marcus

Tim McNamara <[email protected]> wrote:
> Sheldon Brown <[email protected]> wrote:

> > The focal-length/camera-to-subject-distance does make a real difference here. With a short focal
> > length, close working distance, the proportional size of your shoulders and arms is exaggerated,
> > while the size of your butt is minimized.

> As Sheldon says, focal length and distance to subject are going to be a big issue- a headache
> even- and make it difficult to compare.

It's actually only the camera-subject distance which is significant. In the absence of lens
distortion, an ideal short and long lens both placed at (for example) 20 feet from the subject would
produce the same perspective. The wide angle lens just includes more around the subject. Wide angle
lens are said to have a more exaggerated perspective because one tends to stand closer while using
them. (BTW, most reasonable lenses should not have pincushion/barrel distortion that significantly
affects a rough area measurement. Zoom lenses do tend to have more distortion, though.)

Because the rider is a complex 3-D shape, it is probably too difficult to make a model that takes
what the camera saw and turns it into an exact frontal area measurement. The errors are going to be
related to the size and depth of the subject (basically hands to butt) divided by subject-camera
distance. I think if you can get the camera to subject distance about 4-5 times the depth of subject
the errors are minimal. So say about 5 meters. BTW, Kraig, if you use a length reference it has to
be at the center of the subject, not behind him, obviously.

> I wonder about a cameraless option: a simple frame (e.g., an 8 x 10 inch rectangular opening cut
> out of a board) set at a specific distance from the rider *and* a specific distance from the
> observer- this allows for comparisons and simplifies the math. In the frame is a sheet of plastic
> or glass with a rectangular grid- say 5 mm x 5 mm- marked on it. Find the apparent size as
> measured by the reference marks. Then it's a simple calculation to compare the apparent size of
> the image with the real size of the rider.

This is equivalent to a pinhole camera with the pinhole/lens at the location of the observer's eye
and the pinhole-film distance equal to the pinhole-frame distance. BTW, it is also a device which
Albrecht Durer used to measure perspective - there is an engraving of the artist looking through the
grid at a model.

Sheldon Brown <[email protected]> wrote:

>With a short focal length, close working distance, the proportional size of your shoulders and arms
>is exaggerated, while the size of your butt is minimized.

Hey, that sounds easier than the Atkins diet. If you can figure out how to get it into a pill,
you'll be a very rich man!

Mark Hickey Habanero Cycles http://www.habcycles.com Home of the $695 ti frame

I wrote:

>>>The focal-length/camera-to-subject-distance does make a real difference here. With a short focal
>>>length, close working distance, the proportional size of your shoulders and arms is exaggerated,
>>>while the size of your butt is minimized.

Benjamin Weiner wrote:

> It's actually only the camera-subject distance which is significant. In the absence of lens
> distortion, an ideal short and long lens both placed at (for example) 20 feet from the subject
> would produce the same perspective. The wide angle lens just includes more around the subject.
> Wide angle lens are said to have a more exaggerated perspective because one tends to stand closer
> while using them.

This is correct, but in practice, one will normally want to choose a working distance that provides
a near-full-frame image. If you use a short lens, this puts you into a close working distance where
the inverse square law will produce skewed results.

I made the long-lens recommendation for practical reasons, without wanting to get into unnecessary
technicalities. If you want, though, I'd be glad to explain the Scheimpflug principle, or circles of
confusion, or depth of field...

> (BTW, most reasonable lenses should not have pincushion/barrel distortion that significantly
> affects a rough area measurement. Zoom lenses do tend to have more distortion, though.)

Such distortions are generally insignificant with long lenses, though not uncommon with why dangles.

For this application, I'd think that using a fixed focal length would reduce errors. Fixed
length teles of very high quality are dirt cheap on the used market, since most folks go for
zooms these days.

Sheldon "Optics" Brown +----------------------------------------------------+
| A little inaccuracy sometimes saves tons of |
| explanation. --H.H.Munro ("Saki")(1870-1916) |
+----------------------------------------------------+ Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com

Thanks for the input guys.

FWIW, I am currently using a pretty cheap digital camera with a lens that is spec'd as f=38 to
228mm on a 35mm camera (is that the correct way to say what it is that I am using?). My separation
distance is 64" (ground contact point of front tire to camera lens) with the camera being 41"
above the ground plane. I include a known reference length in the shot in order to correlate
pixels to meters.

I threshold the image to b/w and then fill in any holes, and end by counting pixels - I have this
automated so it is extremely repeatable - but there are clearly things that I need to explore a bit
further. The first thing I will do is a seperation distance sweep holding everything else constant.

Thanks again for the thoughts, -kraig

On Tue, 8 Jul 2003, Kraig Willett wrote:

> FWIW, I am currently using a pretty cheap digital camera with a lens that is spec'd as f=38 to
> 228mm on a 35mm camera (is that the correct way to say what it is that I am using?). My separation
> distance is 64" (ground contact point of front tire to camera lens) with the camera being 41"
> above the ground plane. I include a known reference length in the shot in order to correlate
> pixels to meters.

When I've seen this done the distance from camera to subject was much longer, maybe 5-10x what you
used. But if you are consistent with the setup then your trends are probably useful.

Kraig Willett wrote:
> Thanks for the input guys.
>
> FWIW, I am currently using a pretty cheap digital camera with a lens that is spec'd as f=38 to
> 228mm on a 35mm camera (is that the correct way to say what it is that I am using?). My separation
> distance is 64" (ground contact point of front tire to camera lens) with the camera being 41"
> above the ground plane. I include a known reference length in the shot in order to correlate
> pixels to meters.

OK, lets figure the rider's shoulders are above the tire patch, 64 inches from the camera. Figure
the rider's hips are 18 inches farther away, 82 inches.

64 squared is 4096

82 squared is 6724.

4096 / 6724 = .61

Thus, the apparent cross sectional area for the riders hips will be only 61% of what it should be,
compared with the area of the shoulder region.

You really need a longer working distance.

Sheldon "Inverse Square Law" Brown
+----------------------------------------------------------------+
| Anyone who cannot cope with mathematics is not fully human. | At best he is a tolerable
| subhuman who has learned to wear | shoes, bathe, and not make messes in the house. | --Robert
| A. Heinlein |
+----------------------------------------------------------------+ Harris Cyclery, West Newton,
Massachusetts Phone 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts
shipped Worldwide http://captainbike.com http://sheldonbrown.com

So, the question for everyone here, Sheldon, is what is going to happen to frontal area when I do a
separation distance sweep?

Will it increase or decrease as my butt gets bigger and my arms smaller!

-kraig

Hmmm, my post from last night seems to have disappeared into the ether.

Seems to me that it would be much simpler to eliminate the camera and lens. What you want is a
silhouette of the rider, correct? How about this, borrowed from James J. Gibson's experiments into
perception of apparent size and distance from 50+ years ago, mixed with a bit of Ansel Adams's
method for teaching how to frame an image using a cutout matte board:

Cut out an 11 X 14 opening in a board. Cover the opening with clear material upon which a 5 mm x 5
mm grid has been ruled. Place what is now a viewing screen between the rider and the observer. You
should use the consistent distances between the screen and the rider, and the screen and the
observer. Backlight the rider against a contrasting background. The rider must be far enough away
for the entire silhouette to be visible on the viewing screen with some margin. Look at the image
through one eye and check the measurements on the grid.

The grid will allow you to identify the apparent image size. Since the relationship between distance
and apparent size is known, it's a simple equation to convert the apparent image size to the real
size. Height = distance x angle in radians, according to Kaufman (angle being the angle of a
triangle from the eye to the screen, with a base from the top to the bottom of the image of the
rider). Once you know h, D and angle from the observer to the screen, substituting the distance from
the observer to the rider will give you h. Once you know the area of the image on the screen, it's a
simple transformation to estimate frontal area of the rider.

On Mon, 07 Jul 2003 17:02:15 -0400, Sheldon Brown <[email protected]> wrote:

>For this application, I'd think that using a fixed focal length would reduce errors. Fixed
>length teles of very high quality are dirt cheap on the used market, since most folks go for
>zooms these days.

Well.. really only the older low-quality stuff. Try buying a 300/2.8 L-series sometime, or a 600/4,
let alone a 1200/5.6 for that matter. Okay, so the last one is a bit of a cheat as they are only
made to special order for between 80 and 120 thousand bucks depending on how much the salesperson
likes you and how much room there is in the production schedule, but what the hell. The more
sensible pro-level primes are still between 33 and 66 percent of RRP depending on condition,
averaging 50%.

Jasper

I wrote:

>>For this application, I'd think that using a fixed focal length would reduce errors. Fixed
>>length teles of very high quality are dirt cheap on the used market, since most folks go for
>>zooms these days.

Jasper Janssen wrote:

> Well.. really only the older low-quality stuff. Try buying a 300/2.8 L-series sometime, or a
> 600/4, let alone a 1200/5.6 for that matter. Okay, so the last one is a bit of a cheat as they are
> only made to special order for between 80 and 120 thousand bucks depending on how much the
> salesperson likes you and how much room there is in the production schedule, but what the hell.
> The more sensible pro-level primes are still between 33 and 66 percent of RRP depending on
> condition, averaging 50%.

I wasn't talking about exotica like that, that wouldn't exist if they didn't play baseball in Japan.
I was talking about garden variety 135 or 200 mm lenses of moderate aperture, which are common as
dirt on the used market, and high quality ones too.

F'rinstance, a quick look at eBay "completed items" searching for "nikkor 135 f2.8" shows 4 of them
sold last month for prices between US$69 and US$125.

This application doesn't call for anything even that fancy--even a simple t-mount preset lens would
be perfectly adequate. The woods are full of them.

Sheldon "Be Realistic" Brown +-----------------------------------------+
| Well, the truth is usually just | an excuse for a lack of imagination... | --Garak, DS-9 |
+-----------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone
617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com

On Tue, 08 Jul 2003 23:47:16 -0400, Sheldon Brown <[email protected]> wrote:

I wrote:
>> schedule, but what the hell. The more sensible pro-level primes are still between 33 and 66
>> percent of RRP depending on condition, averaging 50%.
>
>I wasn't talking about exotica like that, that wouldn't exist if they didn't play baseball in
>Japan. I was talking about garden variety 135 or 200 mm lenses of moderate aperture, which are
>common as dirt on the used market, and high quality ones too.

True, the more garden-variety numbers are easy to get. Plus those kinds of lenses were very well
understood by optical science even at the time, and made from very conventional designs. There's an
800 or 1000 refractor for.. I'm not sure, either Pentax 67/645 with adapter to M42 or someone
else's, that's about a metre long and one of the better performers in its focal length class. Just
very heavy and big compared to the modern designs that essentially integrate 2+x times
teleconverters.

>F'rinstance, a quick look at eBay "completed items" searching for "nikkor 135 f2.8" shows 4 of them
>sold last month for prices between US$69 and US$125.
>
>This application doesn't call for anything even that fancy--even a simple t-mount preset lens would
>be perfectly adequate. The woods are full of them.

I've got a whole bunch of various Takumars here, they work pretty well. The Super Multi Coated
models are the ones to get, they even feature aperture interlock to bodies that support it, and the
multi coated really helps for daylight shooting. Failing that, Super Takumars (Autos but with a
single coating) or from before that Auto Takumars (aperture on/off control from body).

Which one is T-mount? F-mount: Nikon, FD: Canon pre-AF, K-mount: Pentax bayonet, OM: Olympus,
M42/P-mount: screw-on, are the names I know.

Jasper

I asserted:

>>This application doesn't call for anything even that fancy--even a simple t-mount preset lens
>>would be perfectly adequate. The woods are full of them.

Jasper Janssen asked:

> Which one is T-mount? F-mount: Nikon, FD: Canon pre-AF, K-mount: Pentax bayonet, OM: Olympus,
> M42/P-mount: screw-on, are the names I know.

A "T" mount is a simple intermediate screw mount. A T mount lens doesn't fit directly on any camera,
but uses an adaptor module. Adaptor modules exist for all of the mounts you list and pretty much all
other SLR mounts.

They were formerly quite common on aftermarket telephoto lenses, generally with manual diapraghm
operation, though later T mounts did suppor diaphragm operation. As lens mounts started transmitting
more information between the lens and the camera body, they went out of style, but there are
skillions of the old lenses out there dirt cheap, often with quite respectable optics.

T mounts are also commonly used for microscope adaptors, slide copiers and other specialized
applications.

Sheldon "Former Camera Repairman" Brown +----------------------------------------+
| Millions of people say I exaggerate. | --Marty Gasman |
+----------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone
617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com