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Pythonで画像処理をやってみよう!第6回 - Scale-space 第3回 -

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Python で画像処理をやってみよう!第4回 - Scale-space - 第35回 MPS ミーティング資料

Let's learn image processing with Python part 4. "Scale space"

The 35nd Morning Project Samurai (MPS) meeting document.

Published in: Software
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Pythonで画像処理をやってみよう!第6回 - Scale-space 第3回 -

  1. 1. 2015/9/19 MPS定例ミーティング Python で画像認識をやってみよう! 
 第6回 
 - Scale-space 第3回 - 金子純也 Morning Project Samurai 代表
  2. 2. 目次 • Morning Project Samurai • 前回の復習 • Coarse-to-fine Tracking • Interval Tree
  3. 3. Be Active, Be Creative!! MPS 第33回 (2015/8/22) MPS 定例ミーティング (c) Junya Kaneko
  4. 4. 目次 • Morning Project Samurai • 前回の復習 • Coarse-to-fine Tracking • Interval Tree
  5. 5. 基本アイデア 適切なスケールが事前にわからないなら。。。 元画像から色々なスケールの画像を 作っちゃえばいいじゃない!!
  6. 6. 元画像 ちょっと 小さい画像 さらに 小さい画像 (画像の出典: [1]) (画像の出典: [1]) (画像の出典: [1])
  7. 7. 元画像 ちょっと 小さい画像 さらに 小さい画像 (画像の出典: [1]) (画像の出典: [1]) (画像の出典: [1]) 新たな 構造は 付与 されない
  8. 8. Gaussian Convolution (Gaussian とのたたみ込み) もう、余裕ケロ
  9. 9.  の意味 * 元信号 重み
  10. 10. 絵で考えてみる
  11. 11. 絵で考えてみる
  12. 12. 絵で考えてみる
  13. 13. 絵で考えてみる
  14. 14. 絵で考えてみる
  15. 15. F(x0) は、元信号が x=x0 のとき最大となる
 重みを用いて元信号全体を平均化したもの 新たな信号 F(x) は x=x0 において元信号の
 全ての情報を含んでいるが、元信号の x=x0 直近の情報を強く反映している
  16. 16. σが大きくなるほど F(x) は元信号が一様にブレンドされた値の系列になる *
  17. 17. σ = 0.025 σ = 0.05 元信号
  18. 18. σが大きくなるほど F(x) は元信号が一様にブレンドされた値の系列になる 元信号中の細い特徴が無くなっていく 例: 市街地道路の写真 側道の植木の葉や枝といった情報はなくなり、
 植木があるという情報のみが残る
  19. 19. 目次 • Morning Project Samurai • 前回の復習 • Coarse-to-fine Tracking • Interval Tree
  20. 20. Coarse-to-fine Tracking 詳細を取り除いた信号 (画像) 中の特徴と 詳細な信号 (画像) 中の特徴と対応づける
  21. 21. Coarse-to-fine Tracking 詳細を取り除いた信号 (画像) 中の特徴と 詳細な信号 (画像) 中の特徴と対応づける 特徴って何 ?
  22. 22. Q. 特徴を考えてみよう!
  23. 23. A. みんなの回答
  24. 24. 信号の変曲点 を特徴として考える !
 
 (Fxx = 0, Fxxx != 0) 注: F の x による微分を Fx と表す
  25. 25. 異なるスケール間で 変曲点の対応関係を追跡可能にする 信号の変曲点 を特徴として考える !
  26. 26. 特徴に関する2つの仮定 • 仮定1: Identity assumption
 Scale-space で同じ Fxx = 0 の等高線上にある
 変曲点は、1つの共通のイベントによって発生 • 仮定2: Localization assumption
 イベントの真の発生箇所は、σ を 0 にした時の x
  27. 27. Scale-space F(x, σ) を作り、幾つかのσについて
 変曲点を求め、その等高線を書いてみよう! 積分、微分の求め方は覚えてるケロ? 変曲点はどうやって求めればいいケロ? 等高線はどうやって書けばいいケロ?
  28. 28. コンピュータが変曲点を トラッキング可能にする 必要あり!
  29. 29. 目次 • Morning Project Samurai • 前回の復習 • Coarse-to-fine Tracking • Interval Tree
  30. 30. σが小さくにつれて区間が単調に細分化!
  31. 31. σが小さくにつれて区間が単調に細分化! 木構造で、表現できそう !
  32. 32. 木構造
  33. 33. Interval Tree 区間 区間 区間 区間 区間 区間 区間 区間 区間 σ 0
  34. 34. Interval Tree を作ってみよう! 区間 区間 区間 区間 区間 区間 区間 区間 区間 σ 0

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