Color Image Processing¶
Important: Please read the installation page for details about how to install the toolboxes. $\newcommand{\dotp}[2]{\langle #1, #2 \rangle}$ $\newcommand{\enscond}[2]{\lbrace #1, #2 \rbrace}$ $\newcommand{\pd}[2]{ \frac{ \partial #1}{\partial #2} }$ $\newcommand{\umin}[1]{\underset{#1}{\min}\;}$ $\newcommand{\umax}[1]{\underset{#1}{\max}\;}$ $\newcommand{\umin}[1]{\underset{#1}{\min}\;}$ $\newcommand{\uargmin}[1]{\underset{#1}{argmin}\;}$ $\newcommand{\norm}[1]{\|#1\|}$ $\newcommand{\abs}[1]{\left|#1\right|}$ $\newcommand{\choice}[1]{ \left\{ \begin{array}{l} #1 \end{array} \right. }$ $\newcommand{\pa}[1]{\left(#1\right)}$ $\newcommand{\diag}[1]{{diag}\left( #1 \right)}$ $\newcommand{\qandq}{\quad\text{and}\quad}$ $\newcommand{\qwhereq}{\quad\text{where}\quad}$ $\newcommand{\qifq}{ \quad \text{if} \quad }$ $\newcommand{\qarrq}{ \quad \Longrightarrow \quad }$ $\newcommand{\ZZ}{\mathbb{Z}}$ $\newcommand{\CC}{\mathbb{C}}$ $\newcommand{\RR}{\mathbb{R}}$ $\newcommand{\EE}{\mathbb{E}}$ $\newcommand{\Zz}{\mathcal{Z}}$ $\newcommand{\Ww}{\mathcal{W}}$ $\newcommand{\Vv}{\mathcal{V}}$ $\newcommand{\Nn}{\mathcal{N}}$ $\newcommand{\NN}{\mathcal{N}}$ $\newcommand{\Hh}{\mathcal{H}}$ $\newcommand{\Bb}{\mathcal{B}}$ $\newcommand{\Ee}{\mathcal{E}}$ $\newcommand{\Cc}{\mathcal{C}}$ $\newcommand{\Gg}{\mathcal{G}}$ $\newcommand{\Ss}{\mathcal{S}}$ $\newcommand{\Pp}{\mathcal{P}}$ $\newcommand{\Ff}{\mathcal{F}}$ $\newcommand{\Xx}{\mathcal{X}}$ $\newcommand{\Mm}{\mathcal{M}}$ $\newcommand{\Ii}{\mathcal{I}}$ $\newcommand{\Dd}{\mathcal{D}}$ $\newcommand{\Ll}{\mathcal{L}}$ $\newcommand{\Tt}{\mathcal{T}}$ $\newcommand{\si}{\sigma}$ $\newcommand{\al}{\alpha}$ $\newcommand{\la}{\lambda}$ $\newcommand{\ga}{\gamma}$ $\newcommand{\Ga}{\Gamma}$ $\newcommand{\La}{\Lambda}$ $\newcommand{\si}{\sigma}$ $\newcommand{\Si}{\Sigma}$ $\newcommand{\be}{\beta}$ $\newcommand{\de}{\delta}$ $\newcommand{\De}{\Delta}$ $\newcommand{\phi}{\varphi}$ $\newcommand{\th}{\theta}$ $\newcommand{\om}{\omega}$ $\newcommand{\Om}{\Omega}$
This numerical tour explores color image processing.
addpath('toolbox_signal')
addpath('toolbox_general')
addpath('solutions/multidim_1_color')
RGB Color Space¶
A color image $f \in \RR^{N \times 3}$ is made of three independent images, one for each channel red, green and blue (RGB color space).
Size $N= n \times n$ of the image.
n = 256;
N = n*n;
Loading an image $f \in \RR^{N \times 3}$.
name = 'hibiscus';
f = rescale( load_image(name,n) );
One can display on screen a color image in RGB space using the rule of additive color mixing.
Display the image $f$ and the three channels that compose the colors.
R = cat(3, f(:,:,1), zeros(n), zeros(n));
G = cat(3, zeros(n), f(:,:,2), zeros(n));
B = cat(3, zeros(n), zeros(n), f(:,:,3));
clf;
imageplot({f R G B}, ...
{ 'f' 'R (Red)' 'G (green)' 'B (blue)'}, 2, 2);
It is possible to obtain a grayscale image from a color image by linear averaging of the channels, to obtain the luminance channel $$ L = \frac{R+G+B}{3} $$
clf;
imageplot({f mean(f,3)}, {'f' 'L'});
CMY Color Space¶
Another popular representation for color images uses as basis colors the cyan, magenta and yellow (CMY color space). They are computed as $$ C=1-R, \quad f=1-G, \quad Y=1-B. $$
One can display on screen a color image in CMY space using the rule of substractive color mixing.
Show the C, f, Y channels.
f1 = cat(3, f(:,:,1), f(:,:,2)*0+1, f(:,:,3)*0+1);
f2 = cat(3, f(:,:,1)*0+1, f(:,:,2) , f(:,:,3)*0+1);
f3 = cat(3, f(:,:,1)*0+1, f(:,:,2)*0+1, f(:,:,3));
clf;
imageplot({f f1 f2 f3}, ...
{ 'f' 'C' 'f' 'Y'}, 2, 2);