07 how to transform rgb to cmy

07 how to transform RGB to CMY

Transforming RGB (Red, Green, Blue) color values to CMY (Cyan, Magenta, Yellow) color values is a common operation in color management, especially in printing and digital imaging. CMY is often used in color printing processes, while RGB is used in electronic displays.

### RGB to CMY Conversion Formula

The transformation between RGB and CMY is straightforward because CMY is essentially the complementary color model to RGB. Here’s how you can convert RGB values to CMY:

1. **Normalize RGB Values:**
   - Ensure that the RGB values are normalized to the range [0, 1] (if they are not already). For 8-bit images, RGB values are typically in the range [0, 255].
   - To normalize, divide each RGB value by 255.

   \[
   R_{norm} = \frac{R}{255}
   \]
   \[
   G_{norm} = \frac{G}{255}
   \]
   \[
   B_{norm} = \frac{B}{255}
   \]

2. **Convert RGB to CMY:**
   - Apply the following formula to convert normalized RGB values to CMY:

   \[
   C = 1 - R_{norm}
   \]
   \[
   M = 1 - G_{norm}
   \]
   \[
   Y = 1 - B_{norm}
   \]

3. **Convert Back to 8-Bit Values (Optional):**
   - If you need the CMY values in the range [0, 255], you can scale them back:

   \[
   C_{8bit} = C \times 255
   \]
   \[
   M_{8bit} = M \times 255
   \]
   \[
   Y_{8bit} = Y \times 255
   \]

### Example:

Let’s say you have an RGB color with the following values:

- **R = 100**
- **G = 150**
- **B = 200**

1. **Normalize RGB:**
   \[
   R_{norm} = \frac{100}{255} \approx 0.392
   \]
   \[
   G_{norm} = \frac{150}{255} \approx 0.588
   \]
   \[
   B_{norm} = \frac{200}{255} \approx 0.784
   \]

2. **Convert to CMY:**
   \[
   C = 1 - 0.392 \approx 0.608
   \]
   \[
   M = 1 - 0.588 \approx 0.412
   \]
   \[
   Y = 1 - 0.784 \approx 0.216
   \]

3. **Convert Back to 8-Bit Values:**
   \[
   C_{8bit} = 0.608 \times 255 \approx 155
   \]
   \[
   M_{8bit} = 0.412 \times 255 \approx 105
   \]
   \[
   Y_{8bit} = 0.216 \times 255 \approx 55
   \]

Thus, the CMY values corresponding to the RGB color (100, 150, 200) are approximately (155, 105, 55) in 8-bit color representation.

### Summary

To transform RGB to CMY:
1. Normalize the RGB values to the range [0, 1].
2. Apply the formulas to get CMY values.
3. Optionally, scale the CMY values back to the range [0, 255].

This transformation is useful in color printing and other applications where CMY color space is preferred or required.