Does the im2gray function give greater 'weight' to red than green and blue?

I have the following colour coded echo strength image where the red indicates high levels of reflection, then yellow, then green:

I want to compare the actual image centroid with the weighted centroid and have done so using the following code:

clc

clear all

% import the Image %

imdata = imread("RCS_Example3.bmp");

% Display the image %

imshow(imdata)

% Convert to grayscale - Grayscale Images are 2D arrays because only

% need one value of intensity for each pixel %

RCSGray = im2gray(imdata);

imshow(RCSGray);

title("RCS Gray Scale");

BW = RCSGray > 0;

imshow(BW)

title('Binary Image')

s = regionprops(BW,RCSGray,{'Centroid','WeightedCentroid'});

imshow(RCSGray)

title('Weighted (red) and Unweighted (blue) Centroids');

hold on

numObj = numel(s);

for k = 1 : numObj

plot(s(k).WeightedCentroid(1), s(k).WeightedCentroid(2), 'r*')

plot(s(k).Centroid(1), s(k).Centroid(2), 'bo')

end

hold off

This produces the following figure (red star = weighted centroid, blue circle = actual centroid):

when converted to grayscale its hard to tell if the 'intensity' of the red spots on the original image is high and I want to know if the red spots are contributing a higher weighted value as they represent points of highest intensity reflection.

If this is correct, is there a way to work out how far apart the weighted and unweighted centroids are?

Thanks

[Stephen23]

"Does the im2gray function give greater 'weight' to red than green and blue?"

No. The exact weights given to each channel are given in the IM2GRAY documentation here:

https://www.mathworks.com/help/matlab/ref/im2gray.html#mw_0668b600-0226-4640-9ffc-8698ce324f94

Converting to grayscale is unlikely to help you with this task.

[Bruno Luong]

@Stephen23: Hmm I"m consude, the doc state

"The im2gray function converts RGB values to grayscale values by forming a weighted sum of the R, G, and B components:

0.2989 * R + 0.5870 * G + 0.1140 * B

These are the same weights used by the rgb2ntsc (Image Processing Toolbox) function to compute the Y component.

The coefficients used to calculate grayscale values in the im2gray function are identical to those used to calculate luminance (E'y) in Rec.ITU-R BT.601-7 after rounding to three decimal places.

Rec.ITU-R BT.601-7 calculates E'y using the following formula:

0.299 * R + 0.587 * G + 0.114 * B"

To me it doesn't look like RGB have same weight.

[Stephen23]

"To me it doesn't look like RGB have same weight."

Which is why I wrote "No" at the start of my comment, and absolutely nothing in my comment states that weights are the same.

It is unclear what the confusion is, because you did not explain what the problem is.

[Bruno Luong]

@Stephen23 I'm sorry, I missread your comment, when you state "No" I interpret like you negate OP's claim.

[Bruno Luong]

@Isaak If you want to see the effect of red color on centroid position, why not replace in your code the calculation

RCSGray = im2gray(imdata)

with

RCSGray = double(imdata(:,:,1)) % "RCSGray" as Read chanel

[Isaak]

Thanks for your comments @Stephen23 @Bruno Luong. Please see my response below to @Image Analyst for a bit more detail on what I am trying to achieve

[Stephen23]

@Isaak: the task is not clearly defined. Although you can use RGB2IND (as Image Analyst shows) to "undo" the pseudo-coloring, doing so requires knowing the colormap distribution, otherwise we simply do not know the scale of values that those colors represent. Are they a logarithmic scale, or evenly spaced, or unevenly spaced? We simply don't know.

For example, consider are the red pixels equally distant from green as green is from yellow? How far apart are light gray and dark gray values? What color is zero? The centroids will be essentially meaningless until this color scale is specified.

You might find this information in the documentation for the product/tool that generates that image, or perhaps online.

[Isaak]

Thanks @Stephen23 I think I understand what you're getting at. I'll need to go away and see if I can find the color map/ what scale the colours are assigned to from the software.

Cheers,

Isaak

Answer 1

[Image Analyst]

"I have the following colour coded echo strength image where the red indicates high levels of reflection, then yellow, then green"

What about gray and teal/aqua?

If you can, it's definitely best to get the original image values, not a pseudocolored image. Can you do that? If you can, it's easy. But WHY do you want the weighted centroid of this image when it looks like there are parts of the image that are clearly different and (perhaps) should not just be lumped in with the pixels of the entire image? I agree with Stephen that converting that to gray scale will not get you what you asked for (plus I'm not even sure what you're asking for is the proper thing to measure). What you would have to do, if you can't get the original image, is to use the colormap that was applied to this image to "undo" the pseudocoloring and get you back to the original values. It's what I do in the attached thermal image demo. What is your image of? It looks like maybe it's some kind of simulated inverse synthetic aperture radar image of a ship..

[Isaak]

The image is an output of a radar cross section calculator. It essentially simulates the intensity of radar reflection from particular geometry on the outline of a ship. Obviously flat surfaces (normal to the approach angle), cylinders, spheres etc have a high degree of reflection indicated by the red patches i.e. the incident wave is bouncing directly back at the reciever. The pure shape centroid is obviously directly in the middle of the image. What I am trying to understand is how much does the presence of red (high intensity), yellow (mid intensity), green (low intensity) cause the weighted centroid to deviate from the true shape/image centroid, with higher 'weight' given to the red spots and so on..

the teal colour just represents the environment and can be neglected. As for the grey oultine, that will obviously have some reflection intensity value but much lower than that of the hot spots (red-yellow-green). the patches beneath the ships outline represent reflection off the water surface.

As this is an output from software, I don't think it will be possible to extract the original image as suggested.

Is there a way of assigning my own weighted values to colours so that matlab processes the r,g,b accordingly?

Thanks

[Bruno Luong]

"Is there a way of assigning my own weighted values to colours so that matlab processes the r,g,b accordingl"

What's the proble? Just compute formula you like, instead of RGB2Gray formula

0.2989 * R + 0.5870 * G + 0.1140 * B 

You can compure

MyReddyGray = 0.7 * R + 0.2 * G + 0.1 * B 

Or even use solely red channel as I posted in the comment above, which correspoponds to the extreme weight setting

MyReddyGray = 1 * R + 0 * G + 0 * B 

It is just odd that instead of working directly on radar intensity you pass through RGB then wan to fix the weight so that it works again. Why do things simple when once can do in the complicated manner?

[Stephen23]

"Is there a way of assigning my own weighted values to colours so that matlab processes the r,g,b accordingly"

Yes, you would need to first specify the colormap (in order to correctly define the sequence and its distribution), then use RGB2IND (or DITHER or something similar) to "undo" the pseudo-coloring. This is what Image Analyst already showed you in their answer.

Simply multiplying the R,G,B, channels with some scalar values will not work.

[DGM]

If the software provides you with a colorbar, you may be able to use that to get a rough estimate of the colormap. At that point, IA's demo would work. If you have to take a screenshot, save it as PNG, not JPG, as capturing the ends of the colorbar is important for scaling, and JPG will skew them.

If there's a chance that the mapping is nonlinear, then you'd have to figure out what it is.