What is the discrete step size after rgb2hsv conversion

Hi everyone,

For my internship I'm doing some image processing, just starting out and it is a surprisingly large and interesting field :-) Currently I'm thresholding HSV images, but my input images are in the RGB 24 bit color space.

I'm converting my 8 bit RGB colour channels to HSV channels with the matlab 'rgb2hsv' function. Quite an easy step, but I also need to know what the discrete step size of the different channels (i.e. H, S and V) are. Is there some way to calculate this? Is there a general formula that you can apply to an X-bit RGB image to obtain the discrete steps in the HSV colour space?

Thanks in advance for your comments!

Answer 1

[Image Analyst]

What do you mean by the step size? The spatial quantization of the hsv images is the same as your input images. The intensity quantization depends on the range of what you put in. Try this code and examine the output

rgbImage = imread('peppers.png');
hsvInt = rgb2hsv(rgbImage);
hsvDouble = rgb2hsv(double(rgbImage));
rgbScaled = im2double(rgbImage);
hsvScaled = rgb2hsv(rgbScaled);

whos hsvInt
hsvInt(200,200,3)

whos hsvDouble
hsvDouble(200,200,3)

whos hsvScaled
hsvScaled(200,200,3)

[Dabbler]

Hi Image Analyst,

Excuse me for asking this unclear question. First of all thanks for all the posts in this forum. You've already helped me a lot by all your answers across Matlab Central :-)

At first I was using the RGB colour space to threshold the red from an image, but this was not intuitive and thus I switched to the hsv colour space. The good thing about the RGB colour space was that I knew that my pixels were read as 3 channels with 256 possibilities per channel. The step size would be 1 in this case. Normalizing the image to the range [0,1] will create a step size of 1/255. Step size is obviously not the correct term, so maybe we should talk about the bit size of each pixel channel (i.e. R has 8 bits, G has 8 bits and B has 8 bits).

Is there a certain amount of bits that is available for each pixel channel in the HSV image? From your code snippet it leads me to believe that at least the Value channel is equal to an 8-bit channel. (It's weird to see that only the hsvDouble's value channel isn't normalized) The reason that I believe the amount of bits for the hue and saturation channels is changed is because the following code returns a 'false'.

clear all; close all; clc;
rgbImage = imread('peppers.png');
hsvImage = rgb2hsv(rgbImage);
newRgbImage = hsv2rgb(hsvImage);
binaryCheck = (rgbImage == newRgbImage);
disp(all(binaryCheck(:)));

Do you think this is because of the fact that there is a remapping of the data or something like an floating point error?

I hope the questions are clear this time :-D

[Image Analyst]

It's probably just roundoff or quantization error. See http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

hsv is a double image so it has 8 bytes of precision (53 bits for mantissa and the rest for exponent).

But the real question is what do you want to do once it's in that color space?

By the way, you know that "red" is at the 0 degree hue angle. So to get things that look reddish, you need to go both from 0-20 or so degrees, and from 340 to 360 degrees to make sure you get the reddish things on both sides of the "a" axis. It's not like that with any other color since it doesn't cross a boundary like that.

[Dabbler]

What I want to do after conversion is to threshold the image. To do this I created six thresholds: hueLowerBound, hueUpperBound, satLowerBound, satUpperBound, valLowerBound, valUpperBound. The lower bound for the hue is defined as the smallest amount of degrees from 0 to 340 and the hueUpperBound is defined as the smallest amount of degrees from 0 to 20 degrees.

I did some hand selections of the regions of interest by hand. In Matlab I want to optimize the thresholds by comparing them with this golden standard (the hand selection). The problem lies within the fact that optimizing these six parameters requires a huge amount of processing power, when done in a brute force grid search. One low resolution grid search with 11^6 possibilities took me about three hours ^_^ It took three of these runs during my previous weekend to get down to a mismatch of lower than 5%. The mismatch being defined as the overestimated pixels + the underestimated pixels.

After this initial grid search I was wondering how to bring down computing time and what the amount of significant digits should be. Implementing a search with the matlab fminsearch already brought my calculation time down to 60 seconds, with very similar results. (although this is offcourse a non-exhaustive search method).

Because I wanted to assess how well the fminsearch performed, I wanted to plot the parameter space. This way I could see in more detail, how sensitive / insensitive my parameters are. This is the point, where I realised that I didn't knew anything about the bits per pixel.

The fact that the rgb2hsv converts my discrete numbers to "infinite" numbers doesn't make it any easier. Offcourse I'm not going to evaluate the parameters up to a resolution of 53 bits. In this case I will get there through some trial and error.

Any tips are more than welcome. For example, do you think I can get better detection of my area by using a blob detection method?

This is what most of my histological slices look like: Image on Nature's Website. Except for the fact that my scaffold is dark black and my tissue is deep red.

[Image Analyst]

I don't know what you're doing when you do the optimization but if you're adjusting values, you don't have to change them in jumps of 0.0000000001, you can do larger jumps. Just see what a one gray level difference corresponds to. Find the hue for (128,128,128) and for (128,128,129) and see how much the hue is different, then just change your steps by that much.

Anyway, it really depends on what shape of the gamut do you want to carve out of the image. HSV will get you a cylindrical pie shaped sector. Delta E will get you a sphere. RGB will get you a rectangular block (in RGB space). It also depends on if you want to apply the same color classification to each image or if you want it to adapt thresholds depending on the image content.

Maybe you can try Brett's tool for exploring your data: http://www.mathworks.com/matlabcentral/fileexchange/38484-segmenttool-an-interactive-gui-for-segmenting-images