Photo Measuring with Bart Bouricius

General discussions of measurement techniques and the results of testing of techniques and equipment.

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#11)  Re: Photo Measuring with Bart Bouricius

Postby edfrank » Thu Mar 14, 2013 9:48 am

Bob, Bart,

I am just wondering about the interpolation.  If the tree were vertical with the upper measured value for the trunk directly over the base, then the height would be sinA x hypotenuse = tanA x horizontal distance to the trunk.  If the section from the top to the bottom as shown on the photograph were broken down into equal length segments, each segment would have the the same number of degrees of angle but would be of different lengths.  But then you could go back and use the tangent function to determine the height of each of those points, and thus determine the segment length between each of the interpolated lengths.   If the tree were slanted from vertical but still straight, then this process would give you the base length of a similar triangle with a length of trunk = hypotenuse = arctan (angle from base to uppermost measurement).  So the length of the trunk segments could be calculated if the tree were straight and either the upper and lower measured sections were directly over each other, or if the section was tilted and you were looking  in the same plane as the tilt angle.  A 10 degree slant in the tree would only affect the calculated length by 1.5% so minor irregularities on the trunk will not make that much difference. So segment length could be calculated if you treat interpolated points as angles and work from there.

Ed
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#12)  Re: Photo Measuring with Bart Bouricius

Postby edfrank » Thu Mar 14, 2013 9:58 am

The basic point being if you can calculate the height of a particular cross-section then you can calculate the distance as  [(height)2 + (horizontal distance)2] 1/2 and thus determine the width at the interpolated point.  The diameter of a cylinder isn't going to change no matter what the viewing angle, so the angle to the width measurement point only matters in regard to length.

In the field the angles to the measurement points could be directly measured with a clinometer, but I am trying to present a possible work-around for measurements based on a photo.

Ed
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#13)  Re: Photo Measuring with Bart Bouricius

Postby dbhguru » Thu Mar 14, 2013 1:47 pm

Ed, Bart, Larry, Doug, Will, et al.

  The attached Excel workbook just confirms what you already recognized, Ed. We can take multiple close up images from the same location and a reference object in any one of the images applies to the others. In the attachment, you'll notice three images of different parts of an oak named Pokey. I chose a spot in the dining room where I could see the tree to be measured. From there, I split a section of the tree up in three photos, keeping the same focal length throughout. Absolutely no change of camera settings. I also shot distances and reticle values to points in the three separate images. The reference object is the diameter at the location of the round marker near the base.

  As you can see, I got extremely close measurements via the reticle and the photo process. My next step is to develop a clean spreadsheet template for this process and good user instructions. The method really does work on circular objects. With reference object of known dimension, laser rangefinder, clinometer, and digital camera, we can model trunks for volume. Throw in a compass to get horizontal angles and the process can be extended to limbs at all angles.

Bob
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PhotoMeasurementPokey.xlsx
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#14)  Re: Photo Measuring with Bart Bouricius

Postby Don » Fri Mar 15, 2013 7:21 pm

Over a century of photogrammetry suggests that as you go in any direction from the center of the photo, increasing distortion due to the curvature of the lens the "optical factor", as Ed refers to it, changes. That is the case even in a flat field such as photographing a paragraph such as these looking straight down at the paper on a table, when using a camera with a specialized 'flat-field lens".

Add topography (whether it's aerial photography or land-based panoramic photography), and the amount of distortion increases with the background distance.

When the subject is a tree, it does present a flat field from it's base to it's top, but still experiences a variable "optical factor" as you "scroll" up and down from the center of the photo. To say nothing of issues such as variable distances between the base (baseline) and the top (hypotenuse), from the typical camera perspective.

I should think that the rule of thumb that photogrammetrists use may help here, which is to use the inner third of the image to experience the least distortion.  For example, I think I recall Randy Brown (you still around, Randy?" using a camera with very high resolution, and a quality wide angle lens.  This allows continued good image resolution, and keeps the distortion down (to the extent that the entire tree is framed in that inner third of the image's extent).

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#15)  Re: Photo Measuring with Bart Bouricius

Postby edfrank » Fri Mar 15, 2013 7:56 pm

Don

My use of optical factor really refers to the scale to distance ratio for the particular focal length.  It is the term used by the manufacturers for the reticle/monocular.  The distortion is a something to be aware of.  Using multiple images will help in this regard as the diameters to be measured can be centered in each individual photo rather than up and down the entire frame.  We really should look at photographing something like a brick wall with a regular grid pattern to see the potential effects of this distortion on the measurements.

Ed
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#16)  Re: Photo Measuring with Bart Bouricius

Postby dbhguru » Fri Mar 15, 2013 9:32 pm

Don, Ed,


     Keeping the target centered and small is the current order of the day. I plan to experiment more and will use a flat vertical surface to experiment with. There is another consideration for the method I'm using with Excel for a vertically oriented object seen at a high or low angle. I'll give an example. Suppose we're photographing a 160-foot tall tree from a baseline of 100 feet. The last 10 feet of trunk us tends an angle of 1.7 degrees, I.e. the field of view is 1.7 degrees for the segment from 150 to 160 feet. Now the angle for the first 10 feet (assuming our eye is at base level) is 5.7 degrees. Stated another way, an angle of say 1 degree covers more trunk farther up the tree. The implications in photographic images rule out measuring height directly from a photograph by any simple process. A pixel higher up the trunk becomes worth more, but how much more?

    Tomorrow, Monica and I head to Plattsburgh, NY for a couple days. I hope to extend the photo analysis beyond what I've done thus far, but the road has suddenly gotten rough. However, for the simple measurements done and passed along in the series of spreadsheets, we've got us a new technique.

Bob
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#17)  Re: Photo Measuring with Bart Bouricius

Postby edfrank » Fri Mar 15, 2013 10:00 pm

Bob,

You can measure height if you are willing to accept a tangent height and the error problems it entails.  You know the distance to the target and the size of the target.  From that you can calculate the angle that the length of the measuring stick represents.  From this you can measure the height of the tree in terms of the number of times that angle is expressed from top to bottom.  Thus you know the angle to the top of the tree,and at basically any point up and down the tree.  By using the tangent function you can calculate the height based upon the original horizontal distance to the tree.

You could also measure the distance to the top of the tree with the laser rangefinder and just make everything easier.  The angle to the top could be measured on the photo as outlined above, or more easily measured by a clinometer in the field.

Ed
"I love science and it pains me to think that so many are terrified of the subject or feel that choosing science means you cannot also choose compassion, or the arts, or be awe by nature. Science is not meant to cure us of mystery, but to reinvent and revigorate it." by Robert M. Sapolsky
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#18)  Re: Photo Measuring with Bart Bouricius

Postby dbhguru » Sat Mar 16, 2013 8:54 am

Ed,

   We have taking measurements in the field and using them in abstract mathematical models down pretty well. How well, we can then apply some, or all, of the field measurements to a photograph is a different proposition. I'm satisfied that we're okay in measuring narrow widths or heights at known distances on the photos using proportionality. But when we expand the area to be measured on the photograph and use an overlaid object like an Excel line shape compared to another overlaid shape line of known distance and actual size, we encounter a different set of challenges. I'll attempt to illustrate these challenges on a series of spreadsheets over the next week. Maybe we can settle on the combination of measurements and objects needed to bump this methodology up to the next level.

   I really appreciate you, Don, and others joining me on the project to develop photo measuring as a productive tool for us. I usually make these posts, recognizing that they have a limited appeal because I'm working on the fringes. On occasion, a new technique holds real promise. I believe, as do you, that the photo measuring has a place in our repertoire. Again, thanks.

Bob
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