Linear Combination In Color Model
- 1. Linear Combination In Color Model Prepared by: Md. Washim (2015-3-60-032) Sharmin Sultana Koly (2015-3-65-010) Sheikh Aminul Islam (2015-3-65-013)
- 2. Introduction The project was given as the review of the course “Linear Algebra and Complex Variable” to show the output of the course learning and utilizing. Our project is about to show the use of Linear combination to solve problems.
- 3. Linear Combination In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of u and v would be any expression of the form k1u + k2v, where u and v are constants).
- 4. Color Model A color model is a system for creating a full range of colors from a small set of primary colors. There are two types of color models: 1. Additive color models use light to display color. Example: RGB colors used in software UI designing. 2. Subtractive color models uses printing inks. Example: CMYK colors used in modern printers.
- 5. RGB (Used in Electronic Media)
- 6. CMYK (Used in Print Media)
- 7. RGB (Additive color model) In computer, RGB color is usually stored as a triplet of integer numbers in the range 0 to 255. (255,0,0) is Red (0, 255,0) is Green (0,0, 255) is Blue We can view those colors as the vectors in 3D space having those components. Any other color is obtained as a linear combination of these basic colors.
- 8. Linear Combination in RGB Let’s take these three colors as three vectors, r for Red g for Green b for Blue Then the Linear Combination w is, w = k1r + k2g + k3b Where k1, k2, k3 are three scalars.
- 9. Now, If we take components as, r = (255,0,0), g = (0,255,0), b = (0,0,255) For k1 = 0.6, k2 = 0 and k3 = 0.8 the Linear combination is, w = 0.6 (255, 0, 0) + 0 (0, 255, 0) + 0.8 (0, 0, 255) = (153, 0, 204) This linear combination of 3 colors form Purple color.
- 11. Linear Combination in CMYK Let’s take these four colors as four vectors: c for Cyan m for Magenta y for Yellow k for key (Black) Then the Linear Combination w is, w = n1c + n2m + n3y + n4k Where n1, n2, n3 and n4 are three scalars.
- 12. Now, If we take components as, c = (100, 0, 0, 0), m = (0, 100, 0, 0), y = (0, 0, 100, 0), k = (0, 0, 0, 100) For n1 = 0.5, n2 = 0.3, n3 = 0 and n4 = 0.05 the Linear combination is, w = 0.5 (100, 0, 0, 0) + 0.3 (0, 100, 0, 0) + 0 (0, 0, 100, 0) + 0.05 (0, 0, 0, 100) = (50, 30, 0, 5) This linear combination of 4 colors form Sky Blue color.
- 14. Conclusion From this course “Linear Algebra and Complex Variables” we have learnt a lot of things which are used in our real life in various ways. Doing this project, we could feel the reality of mathematics and hopefully we will use the other methods learnt from this course and try to solve harder problem in our real life.