東京大学 情報理工学系研究科 創造情報学専攻 2007年8月実施 筆記試験 第3問

标签：

• Tokyo-University
• Hough-Transform-for-Line-Detection

Author

itsuitsuki

Description

Consider a method to find equations of two straight boundary lines of the two-colored regions like Fig. 1. Suppose the points in Fig. 2 are derived through processing the image of Fig. 1 and answer the following questions.

(1) The line $L_0$ that passes the point $(x_0, y_0)$ as in Fig. 3 is described as $y=a_0x+b_0.$ The point $P_0(a_0, b_0)$ of the $a$-$b$ parameter coordinates (Fig. 4) shows the line $L_0$. Explain what the parameters of $a_0, b_0$ mean in the $x$-$y$ coordinates.

(2) Rotate the line $L_0$ in Fig. 3 at the point $(x_0, y_0)$. Illustrate the trajectory of the point $P_0$ in the $a$-$b$ coordinates.

(3) Consider the three points $(x_i, y_i), 1 \le i \le 3$ on a line as in Fig. 5. Let $L_i$ be a line that passes $(x_i, y_i), 1 \le i \le 3$. Rotate each line $L_i$ at $(x_i, y_i)$. Illustrate the corresponding trajectories of the point $P_i$ in the $a$-$b$ coordinates.

(4) Considering the methods described above, explain how to get the equations of the two straight boundary lines from the points of Fig. 2.