Computer Vision Exercise

子航xzh發表於2023-01-18

計算機視覺練習題

Local feature

Harris Corner

Harris

  • Solution

    \[\begin{array}{l}\text { (1) } I_{x}=\left[\begin{array}{ccc}8 & 10 & 12 \\16 & 14 & 12 \\18 & 10 & 10\end{array}\right] \quad I_{y}=\left[\begin{array}{ccc}8 & 14 & 16 \\16 & 14 & 16 \\10 & 10 & 4\end{array}\right] \\ \sum_{(x, y )\in W} I_{x}^{2}=8^{2}+10^{2}+12^{2}+16^{2}+14^{2}+12^{2}+18^{2}+10^{2}+10^{2}=1428 \\\sum_{(x, y)\in W} I_{y}^{2}=8^{2}+14^{2}+16^{2}+16^{2}+14^{2}+16^{2}+10^{2}+10^{2}+4^{2}=1440 \\\sum_{(x, y)\in W} I_{x} I_{y}=8 \times 8+10 \times 4+12 \times 16+16^{2}+14^{2}+12 \times 16+18 \times 10+10^{2}+10 \times 4=1360 \\M=\left[\begin{array}{ll}1428 & 1360 \\1360 & 1440\end{array}\right] \\\text { (2) } \left.R=\operatorname{det} M-\alpha \text { (trace }(M)^{2}\right)=\lambda_{1} \lambda_{2}-\alpha\left(\lambda_{1}+\lambda_{2}\right)^{2} \\\lambda_{1} =74 \\\lambda_{2} = 2794 \\R=206756-0.05 \times(2868)^{2} \\=-204515.2<0 \text { 是邊界 } \\\end{array} \]

Model fitting

RANSAC

RANSAC

  • Solution

    解：

    (1) 這裡設一共取樣\(N\)次，每次選\(s\)個點，這個\(s\)可以表示模型複雜度。

    \[\begin{array}{l}{\left[1-(1-0.2)^{s}\right]^{N}=1-0.9} \\N= \frac{\log0.1}{\log(1-0.8^{s})}, s=2\end{array} \]

    (2)一共需要3個點，因為圓有圓心\((x_0,y_0)\)和半徑\(R\)，至少需要三個點。（構成一個內接三角形）

霍夫變換-極座標空間

Hough

  • Solution

    (1) : \(\rho=x_{0} \cos \theta+y_{0} \sin \theta\)

    (2) : \(H\) 的最大值為8， \(\theta\)為\(\frac{\pi}{2}\)。

    \[\left. \begin{array}{l}\rho=\cos \theta \\\rho=2 \cos \theta \\\rho=3 \cos \theta \\\rho=4 \cos \theta \\\rho=5 \cos \theta \\\rho=7 \cos \theta \\\rho=8 \cos \theta \\\rho=9 \cos \theta \end{array} \right\} +3 \sin \theta \]

簡答

Introduce two real-life computer vision systems, including key problems faced and solution philosophy

  • Answer

    1. Face recognition access control (人臉識別門禁)

      Key problems

      • Intra-class variance(類內差異)：不同的人，不同的裝扮，
      • View variance
      • scale discrepancy
      • Motion
      • Different lightning
      • multi object

      Solution philosophy

      1. 廣泛收集資料集，先進行預訓練
      2. 壓縮模型引數量，加快推理速度

    2. Defect detection

      Key problems

      • 小樣本
      • 不同材料的反光度不同

      Solution philosophy

      • 硬體更新，三維建模
      • 加快推理速度
      • 可以多考慮傳統模型，而不是資料驅動的模型

Now, you are an expert in computer vision and in charge of designing a regular attendance check system (e.g., a course for one term). Assuming that there is a fixed camera in front of the lecture room with 20 rows amounting to 200 seats, you should design a system to fulfill two objectives quickly for every lecture:

  • obtain the number of the attendance;
  • find out the people who are absent exactly.

Please briefly describe your pipeline for implementing this task, the difficulties in this task and your solutions. (8 marks)

  • Answer

    難點：光照，資料量少，多尺度

    解決：預訓練模型

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