lab.tex 1.8 KB

1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677
  1. \chapter{Transformation L*a*b}
  2. \label{appendices_lab_transformation}
  3. L*a*b est otbenu en utilisant la transformation XYZ de la matrice d'image (espace CIZ XYZ). Les équations (\ref{eq:Lab_L}), (\ref{eq:Lab_a}), (\ref{eq:Lab_b}) détaillent la manière dont chaque canal est calculé.
  4. \begin{equation}
  5. L = 116 f_y - 16
  6. \label{eq:Lab_L}
  7. \end{equation}
  8. \begin{equation}
  9. a = 500(f_x - f_y)
  10. \label{eq:Lab_a}
  11. \end{equation}
  12. \begin{equation}
  13. b = 200(f_y - f_z)
  14. \label{eq:Lab_b}
  15. \end{equation}
  16. \vspace{1mm}
  17. \begin{equation}
  18. f_x = \left\{
  19. \begin{array}{lr}
  20. \sqrt[3]{x_r} & \text{if } x_r > \epsilon \\
  21. {{\kappa x_r + 16} \over {116}} & \text{otherwise}
  22. \end{array}
  23. \right.
  24. \label{eq:Lab_fx}
  25. \end{equation}
  26. \begin{equation}
  27. f_y = \left\{
  28. \begin{array}{lr}
  29. \sqrt[3]{y_r} & \text{if } y_r > \epsilon \\
  30. {{\kappa y_r + 16} \over {116}} & \text{otherwise}
  31. \end{array}
  32. \right.
  33. \label{Lab_fy}
  34. \end{equation}
  35. \begin{equation}
  36. f_z = \left\{
  37. \begin{array}{lr}
  38. \sqrt[3]{z_r} & \text{if } z_r > \epsilon \\
  39. {{\kappa z_r + 16} \over {116}} & \text{otherwise}
  40. \end{array}
  41. \right.
  42. \label{Lab_fz}
  43. \end{equation}
  44. % default display
  45. \hspace{18mm} $x_r = {{X} \over {X_r}}$,\hspace{2mm} $y_r = {{Y} \over {Y_r}}$, \hspace{2mm} $z_r = {{Z} \over {Z_r}}$
  46. \begin{equation}
  47. \epsilon = \left\{
  48. \begin{array}{lr}
  49. {0.008856} & \text{Actual CIE standard} \\
  50. {216 / 24389} & \text{Intent of the CIE standard}
  51. \end{array}
  52. \right.
  53. \label{Lab_espsilon}
  54. \end{equation}
  55. \begin{equation}
  56. \kappa = \left\{
  57. \begin{array}{lr}
  58. {903.3} & \text{Actual CIE standard} \\
  59. {24389 / 27} & \text{Intent of the CIE standard}
  60. \end{array}
  61. \right.
  62. \label{Lab_kappa}
  63. \end{equation}