Homework 3

• Link to Lab 2 Image Processing

• “Soften” operation matrix
  • We do lose information in this process, as there's no way to definitively know the individual contributions of each of the neighboring values, as they're all identical in weight.

\[ \left[ {\begin{array}{ccc} 1/9 & 1/9 & 1/9
1/9 & 1/9 & 1/9
1/9 & 1/9 & 1/9
\end{array} } \right] \]

• Gaussian Matrix

\[ \left[ {\begin{array}{ccc} 1/16 & 1/16 & 1/16
1/16 & 1/2 & 1/16
1/16 & 1/16 & 1/16
\end{array} } \right] \]

\[ \theta_2 = \tan ^{-1}\left(\frac{\frac{50 pixels}{72 pixels}}{.5}\right) = 54.24^{\circ} \] \[ \theta_1 = \tan ^{-1}\left(\frac{\frac{30 pixels}{72 pixels}}{.5}\right) = 39.8^{\circ} \]

\[ L = 90^{\circ} - \theta_1 = 50.194^{\circ} \]

\[ R = 90^{\circ} - \theta_2 = 35.7556^{\circ} \]

\[ \tan(R) = \frac{d}{12.5 + r}; \tan(L) = \frac{d}{r} \]

\[ \tan(R)*(12.5 + r) = \tan(L)*r \Rightarrow r = \frac{12.5}{\tan(L) - \tan(R)} = 18.75 \]

\[ d = \tan(R)*(12.5 + r) = 22.5 \]