课程名称︰数位影像处理
课程性质︰资工系选修
课程教师︰洪一平
开课学院：电机资讯学院
开课系所︰资讯工程学系
考试日期（年月日）︰2015/11/23
考试时限（分钟）：120
试题 :
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)