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) -- (8.8, -3.15); \draw[gray] (3.15, 2.5) -- (3.15, -8.8); \draw[very thick] (0, 0) rectangle (6.3, -6.3); \draw (1, 0) arc[radius=1, start angle=0, end angle=-30] node[midway, anchor=west]{$30^\circ$}; \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=sourth]{$(63, 0)$}; \fill (2.8, -3) circle(1pt) node[anchor=south]{$I'(28, 30) =\ ?$}; \end{tikzpicture} Fig 1(c): https://i.imgur.com/DoT5cAv.png \begin{tikzpicture} \draw[ thick, densely dotted, draw=black, fill=lightgray, cm={cos(30), -sin(30), sin(30), cos(30), (3.1, -3.1)} ] (-3.1, 3.1) rectangle (3.2, -3.2); \draw[gray] (-2.5, -3.1) -- (8.8, -3.1); \draw[gray] (3.1, 2.5) -- (3.1, -8.8); \draw[very thick] (0, 0) rectangle (6.3, -6.3); \draw (3.1, 0) node[anchor=south west]{$30^\circ$}; \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]{$I''(28, 30) =\ ?$}; \fill (3.1, -3.1) circle(1pt) node[anchor=north]{$(31, 31)$}; \end{tikzpicture} 2. (10 points) Following question is about aliasing. (a) (5 points) Describe the sampling theorem and explain why aliasing would occur if the chosen sampling rate is inappropriate. (b) (5 points) How to prevent aliasing problem when shrinking an image? 3. (10 points) Following question is about image processing. (a) (5 points) Explain the effect of reducing the sampling rate to one-fourth in the original Barbara image shown below. What causes these differences? https://i.imgur.com/cNOVHEQ.png https://photos.app.goo.gl/P6a9TJo2LD1pxPzH8 (b) (5 points) Considering the processed (resulting) image on the right, what would be the most likely (3 × 3) spatial filter applied to the input image on the left, specify its mask. https://i.imgur.com/1Z10QCs.png https://photos.app.goo.gl/eVpVZ1fprg4JUmXE7 4. (20 points) Assume you are given an image that suffers from the following problems related to image quality. 1. The image does not have enough contrast. Most areas in the image appear to be too bright. 2. The structures and boundaries in the image are blurred and thus it is hard to see the details of objects in the image. 3. There are random sparse black spots (pepper noise) that seem to be caused by some electronics noises. You are asked to propose a system that use techniques you have learned in this class to improve the overall image quality. Note that we don't want the result to be too artificial. Choose the method carefully. Please design a conceptual diagram for a quality enhancement system that ad- dresses all the problems mentioned above. Provide justifications for the use of each component and the specific order you adopt in combining different components. Try to provide as much information as needed. For example, if you use contrast stretching, specify the shape of the intensity mapping function. If you use sharpening filters, specify the specific type of filter you will use. 5. (10 points) Following question is about Nyquist Rate. (a) (5 points) What is the definition of Nyquist Rate? (b) (5 points) What is the Nyquist Rate of f(t) = cos(2πnt)? 6. (20 points) Laplacian operator uses the 2nd order derivative, $\nabla^2 f = \partial^2 f / \partial x^2$, to estimate the magnitude of the spatial vari- ation at a point. A popular method based on Laplacian for enhancing the image quality is called "high-frequency emphasis". It can be modeled by the follo- wing equation: \[g = f - \nabla^2 f\] (a) (5 points) Laplacin operator, $\nabla^2 f$ is often implemented in the spatial domain with the following mask: [1 -2 1] Note the origin corresponds to the center of the mask. Derive the corres- ponding spatial-domain mask that can be used to compute g. (b) (10 points) We can model the high-frequency emphasis process as a linear filter like the one shown below: https://i.imgur.com/EJJTEgW.png \begin{tikzpicture} \draw (0, 0) node[anchor=east]{$f$}; \draw[-stealth] (0, 0) -- (1, 0); \draw (1, -.5) rectangle (3, .5); \draw (2, 0) node{$h$}; \draw[-stealth] (3, 0) -- (4, 0); \draw (4, 0) node[anchor=west]{$g$}; \end{tikzpicture} Derive the Discrete Fourier Transform of the filter, h. (c) (5 points) Plot the spectrum and explain that indeed it is a good appro- ximation of the spectrum of the Laplacian operation in the frequency do- main. 7. (10 points) Consider the 3 images given below: https://i.imgur.com/olXG1Xa.png https://photos.app.goo.gl/uoGpTq5uvVSs5Si18 The left image is the original image, and the next two are processed images. Explain what type of filter has produced the effect in these two images. -- 有好多題直接就是複雜圖片，只剩直接截圖一途[rdrrC] -- 第01話 似乎在課堂上聽過的樣子 第02話 那真是太令人絕望了 第03話 已經沒什麼好期望了 第04話 被當、21都是存在的 第05話 怎麼可能會all pass 第06話 這考卷絕對有問題啊 第07話 你能面對真正的分數嗎 第08話 我，真是個笨蛋 第09話 這樣成績，教授絕不會讓我過的 第10話 再也不依靠考古題 第11話 最後留下的補考 第12話 我最愛的學分 --

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