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by Aditya

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Background

My digital pictures can be read into a computer program like Matlab or R as a m x n x 3 matrix where m x n is the number of pixels observed by each of the three (red, green, and blue) sensors, and each cell in the matrix has a number from 1-255 that reflects the brightness observed by the sensor.

I would like to use this information to obtain an objective measure of greenness in a photograph, because I want to attempt to correlate greenness to plant growth (imagine one picture per day of a corn field).

Previous work in this direction has had some success by calculating an index of green either as

  • green % = green/(blue + red) or
  • green divergence = 2*green - red - blue

from webcam images for each of the m x n pixels, but there was no control over the aperture or incident radiation (solar angle).

note that I am not looking for an 'absolute' measure of greenness, the scale and distribution of the number does not matter - it just has to provide a consistent relative measure of greenness.

Question

Can I use my SLR to get a robust measure of greenness that is invariant with any or all of the following:

  • cloud cover?
  • time of day?
  • day of year? (this is the only requirement)
  • proportion of sky / ground in the background?

Current Status

I have come up with the following ideas, but I am not sure which would be necessary, or which ones would have no effect on the ratio of green/(red + blue)

  1. take a picture of a white piece plastic, and use this image to normalize the other values
  2. Fix aperture
  3. Fix shutter speed
  4. set the white balance using a white piece of paper
  5. Take all photos from the same angle
  6. Take all photos at solar noon
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1  
You might consider artificial lighting, it'd make the procedure simpler. A flash should do adequately, just make sure it's the in the same location, and power. –  PearsonArtPhoto Mar 17 '11 at 5:35
    
@Pearsonarphoto - interesting idea, I was thinking about taking the photos during the day, but perhaps it makes more sense to do them at night with no moon. –  David Mar 17 '11 at 5:47
1  
If you're following Pearsonartphoto's advice, you'll want to set your shutter, aperture, and ISO manually - set your shutter to your flash's sync speed (generally 1/200 to 1/320), and set your aperture and ISO as low as they can go without running out of flash power. This will get your ambient as dark as possible - a full moon should be no problem (mid-day sun, on the other hand...) For this situation, on-axis flash would be best, since it will cast the fewest shadows. –  Evan Krall Mar 17 '11 at 6:37
2  
@Evan I disagree about on-axis flash. Reason being this: photo.stackexchange.com/questions/9531/… —Ways too much direct reflection. Except when using polarizers, as I described there -- but then one needs to make sure that gear stays the same and that white balance is done correctly. Polarizers change white balance. –  Simon A. Eugster Mar 17 '11 at 17:09
2  
Chlorophyll is brightest in the near infrared: yale.edu/ceo/Documentation/rsvegfaq.html There are standard measures of plant "greenness" based on this, such as NDVI. Thus, if you possibly can, get a camera that can record the NIR band. –  whuber Mar 18 '11 at 4:47

3 Answers 3

up vote 12 down vote accepted

If you can process the RAW files, you'll have a bayer pixel array comprised of RGRGRG and GBGBGB rows (or possibly RGBGRGBG rows.) You could ignore all the R and B pixels, sum up the G pixels, take the square root (since there are twice as many green pixels as there are red or blue), and divide by half the number of G pixels. That should give you the proper weighted average for "green" in your photo. You could then take the average of red and blue, and compute your green percentage from all three averages.

To be more accurate, you might want to factor in the proper weighting for red, green, and blue sensor pixels, since CMOS sensors have different sensitivities to each wavelength of light. The weights would depend on the sensor, generally. That would be the simple approach.

To account for color cast due to time of day, various types of artificial lighting, etc. then it might be more appropriate to preprocess each photo in a tool like Lightroom to correct white balance first, then perform your computation on standard RGB pixel images. Unlike processing RAW sensor data, you would want to weight your calculation based on pixel "green purity", rather than average the green component overall. The more pure green a pixel is, the higher its weight vs. pixels that are more red or blue. Normalizing white balance before processing should eliminate any need to complicate an otherwise fairly simple computation with tangents designed to account for umpteen factors like cloud cover, time of day, season, etc.

You might still want to account for large areas of non-incident pixels, such as sky. I can't really help you much in that area without knowing more about exactly what you are trying to achieve. Greenness of a "photograph" overall would probably be best served by computing the ratio of green to red and blue, which would include "sky" pixels.

As for your procedure, it should go without saying that if you take the pictures with the same camera settings, under the same illuminant (same intensity and color temperature), metered against a common baseline such as an 18% gray card, will obviously go a long way towards normalizing your results. With digital, any discrepancies can be corrected with RAW processing software and a basic white balance picker tool, so be sure to shoot in RAW.


To provide some more insight into calculating "greenness" of your photos. There are obviously the simple ways, such as calculating the weight of green bayer pixels vs. blue and red, or calculating green purity in relation to red/blue purity of RGB pixels. You might have more luck if you convert to a more appropriate color space, such as HSV (Hue/Saturation/Value, sometimes called HSB, replacing Value with Brightness), and compute your green amount using a curve in HUE space. (NOTE: HSL is a different type of color space, and would probably not be ideal to compute how much "green" is in a photo, so I would use HSV. You can learn more about these color spaces here.) Pure green (regardless of saturation or value) falls at a hue angle of 120°, and fall off from there as you move towards red (at 0°) or towards blue (at 240°). Between 240° and 360°, there would be zero amount of green in a pixel, regardless of saturation or value.

Hue Plot - Green Purity in Hue Degrees
Fig 1. Hue Plot - Green Purity in Hue Degrees

You can adjust the actual weighting curve to meet your specific needs, however a simple curve could be similar to the following:

range = 240
period = range * 2 = 240 * 2 = 480
scale = 360/period = 0.75
pureGreen = sin(scale * 120)

The value for pureGreen should be 1.0. A formula for computing greenness could then be done as follows:

             sin(scale * hue)   } 0 > hue > 240
greenness = 
             0                  } 240 <= hue <= 360 || hue == 0

The hue is the degree of color from your HSV color value. The radius is the half of period in which green is present to some degree. The scale adjusts the sin curve to our period, such that sin(scale * hue) peaks (returns 1.0) exactly where you would have pure green (ignoring that greens intensity). Since the amount of greenness is only valid in the first half of our period, the greenness calculation is only valid when hue is greater than 0° and less than 240°, and its zero for any other hue.

You can adjust the weighting by adjusting the period, the range within which you define green might be present (i.e. rather than from 0 to 240, you might set a constraint like 40 > hue > 200 instead), and define anything outside of that range to have a greenness of 0. It should be noted that this will be mathematically accurate, however it may not be entirely perceptually accurate. You can of course tweak the formula to adjust the point of pure green more towards yellow (which might produce more perceptually accurate results), increase the amplitude of the curve to plateau and expand the band of pure green to a range of hue, rather than a single hue value, etc. For total human perceptual accuracy, a more complex algorithm processed in CIE XYZ and CIE L*a*b* space might be required. (NOTE: The complexity of working in XYZ and Lab space increases dramatically beyond what I've described here.)

To compute the greenness of a photo, you could compute the greenness of each pixel, then produce an average. You could then take the algorithm from there, and tweak it for your specific needs.

You can find algorithms for color conversions at EasyRGB, such as the one for RGB to HSV:

var_R = ( R / 255 )                     // Red percentage
var_G = ( G / 255 )                     // Green percentage
var_B = ( B / 255 )                     // Blue percentage

var_Min = min( var_R, var_G, var_B )    //Min. value of RGB
var_Max = max( var_R, var_G, var_B )    //Max. value of RGB
del_Max = var_Max - var_Min             //Delta RGB value 

V = var_Max                             //Value (or Brightness)

if ( del_Max == 0 )                     //This is a gray, no chroma...
{
   H = 0                                //Hue (0 - 1.0 means 0° - 360°)
   S = 0                                //Saturation
}
else                                    //Chromatic data...
{
   S = del_Max / var_Max

   del_R = ( ( ( var_Max - var_R ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_G = ( ( ( var_Max - var_G ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_B = ( ( ( var_Max - var_B ) / 6 ) + ( del_Max / 2 ) ) / del_Max

   if      ( var_R == var_Max ) H = del_B - del_G
   else if ( var_G == var_Max ) H = ( 1 / 3 ) + del_R - del_B
   else if ( var_B == var_Max ) H = ( 2 / 3 ) + del_G - del_R

   if ( H < 0 ) H += 1
   if ( H > 1 ) H -= 1
}
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1  
+1 to the raw processing technique. The dcraw source would be a good starting point cybercom.net/~dcoffin/dcraw/dcraw.c –  mattdm Mar 17 '11 at 17:50
1  
Raw Processing would make calculating green level easier, however it would make dealing with color cast considerably more complex. –  jrista Mar 17 '11 at 18:23

GLOBE project?

Do not use a white piece of paper. These contain optical brighteners which convert some UV into blue light, causing incorrect exposure. This is why commercial graycards (as suggested by jrista) exist.

Taking all photos from exactly the same place is certainly the correct approach. Regarding shutter speed and aperture, these should not matter. Shutter speed does not change colour at all, aperture blurs the image, but I think this effect disappears anyway when you sum up all pixel values. I would rather try to get a constant exposure.

Regarding the difference between clouded and not clouded, you may just want to run some tests. If the true amount of green does not change quickly (i.e. from today to tomorrow), then it should not do so either when examining the pictures. Perhaps an empirical approach might help there (e.g. if you find out that the greenness is always 10 % higher when it is clouded, you could compensate for that).

share|improve this answer
    
its not a GLOBE project, but it could be turned in to one; thanks for pointing out that site. –  David Mar 17 '11 at 20:05
    
Maybe of interest for you too: I'm currently writing a program to analyse videos, e.g. from webcams, and output statistics (green share etc.). Should be finished in the coming weeks. phenocam.granjow.net –  Simon A. Eugster Feb 1 '12 at 17:09
    
that sounds useful. Have you been collaborating with any scientists? –  David Feb 1 '12 at 17:23
    
Not too much yet since the evaluation methods will be the last part (and can also be changed/added easily). But it is a project from ETH Zürich and will also be used there. (To be precise, initially it will be used by high-school students for their Globe project.) –  Simon A. Eugster Feb 5 '12 at 19:41
  1. I would suggest shooting 'RAW', and converting to 16-bit TIFF using the camera's auto white balance but no gamma correction (i.e. color balanced but linear output). 16-bit will enable better calculation of ratios and indices in deep shadows and highlights (i.e. no clipping). DCRAW can do this but your camera would come with its own software that's probably easier to use.

  2. If you want indices then RGB is really the only useful color space. You've already mentioned the 'green divergence' index (also called Excess Green Index) - this and the closely related Green Leaf Algorithm work pretty well. If you want to perform color-based pixel classification (i.e. veg versus non-veg) then I would look closely at L*a*b* color space rather than HSV/HSI. There is actually a pretty good demo on the Mathworks website that illustrates L*a*b* analysis. Classification could conceivably be combined with spectral analysis to answer the questions a) how many green pixels are there and b) how green are they? This might be more useful than just a greeness index, which would also be influenced by background spectral quality (soil, litter, etc.), which could also change over time. You mentioned a corn crop so I assume that you're pointing the camera down, not up?

  3. If you had two cameras then you could combine downward looking images (measuring greeness) with upward looking images that measure vegetation cover. Upward images would not be suitable for spectral analysis and pixel classification would be based on contrast between sky/non-sky, probably using only the blue channel of the RGB image.

  4. If you are collecting a (daily?) timeseries then you can divide the downward images into 'cloudy day' images and 'sunny day' images and check for bias. You could play with color balance during raw processing to correct for bias, if present, or just rescale one series to match the other (keep it simple) assuming that sunny and cloudy days are interspersed.

Have fun.

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A colour tile with red, green and blue tiles might be even better than a grey card if you go that path. –  fisheye May 4 '11 at 13:10

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