課程名稱︰數位影像處理
課程性質︰資工系選修
課程教師︰洪一平
開課學院：電機資訊學院
開課系所︰資訊工程學系
考試日期（年月日）︰2015/11/23
考試時限（分鐘）：120
試題 :
Note:
1. This exam contains 4 pages and 7 problems. Check to see if any pages are mis-
sing. Enter your name and student ID on the top of this page.
2. You may not use your books, notes, or any calculator on this exam.
3. You are required to show your work on each problem on this exam.
4. You have to turn in answer sheet and question sheet.
Good Luck!
1. (20 points) We have a 64 × 64 image, as shown in Figure 1(a), where the
pixel value of (x, y) is represented by I(x, y).
(a) (10 points) Rotate the image 30 degrees clockwise about the point (x, y)
= (0, 0), as shown in Figure 1(b). What is the intensity value of (28,
30) after rotation using bilinear interpolation? Express your answer by
I.
(b) (10 points) Rotate the image 30 degrees clockwise about the point (x, y)
= (31, 31), as shown in Figure 1(c). What is the intensity value of (28,
30) after rotation using bilinear interpolation? Express your answer by
I. (√3 = 1.732)
Fig 1(a): https://i.imgur.com/I097ajz.png
\begin{tikzpicture}
\draw[very thick, draw=black, fill=lightgray]
(0, 0) rectangle (6.3, -6.3);
\draw (0, 0) node[anchor=south]{$(0, 0)$};
\draw (0, -6.3) node[anchor=north]{$(0, 63)$};
\draw (6.3, -6.3) node[anchor=north]{$(63, 63)$};
\draw (6.3, 0) node[anchor=south]{$(63, 0)$};
\fill (2.8, -3) circle(1pt) node[anchor=south west]{$I(x, y)$};
\end{tikzpicture}
Fig 1(b): https://i.imgur.com/W0wCyFx.png
\begin{tikzpicture}
\draw[thick, densely dotted, draw=black, fill=lightgray, rotate=-30]
(0, 0) rectangle (6.3, -6.3);
\draw[gray] (-2.5, -3.15)