集合理論.

Presentation on theme: "集合理論."— Presentation transcript:

1 集合理論

2 Translation (平移)of set A by point z=(z1,z2)
Reflection (反射)of set B

3 基本的邏輯運算 logical operations
AND, OR, and NOT

4 黑 1 白 0

5 膨脹 Dilation

6 膨脹 應用: 橋接縫隙 結果: 直接產生二元影像 (以平滑濾波產生者為灰階影像) 結構元素

7 侵蝕 Erosion

8 使用型態學腐蝕及膨脹運算移除影像中的細節
腐蝕Erosion A structuring element of size 13*13 pixels 膨脹Dilation

9 斷開Opening - 先侵蝕再擴張

10 閉合 Closing - 先擴張再侵蝕

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12 斷開運算Opening operation
A。B is a subset (subimage) of A. If C is a subset of D, then C。B is a subset of D。B. (A。B)。B=A。B. 閉合運算Closing operation A is a subset (subimage) of A•B . If C is a subset of D, then C•B is a subset of D•B. (A•B)•B=A•B.

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14 形態交離轉換 * * B1 found a match(“hit”) in A and B2 found a match in AC
(Morphological Hit-or-Miss Transformation) * * B1 found a match(“hit”) in A and B2 found a match in AC

15 邊界抽取 Boundary extraction

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17 區域填充 Region Filling Non-boundary point – 0 Seed -- 1 p

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19 連通成分的抽取 Extraction of Connected Components

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21 凸形封包 Convex Hull * 凸形區 Convex
The straight line segment joining any two points in A lies entirely within A Convex Hull(凸形封包) H of any set S The smallest convex set containing S 凸形區缺額 (Convex deficiency) H-S “×” means “don’t care” * 缺點 成長超過確保凸形所需的最小尺寸

22 使用沿著垂直、水平、對角向的原始點集合的最大尺寸來限制成長

23 細線化Thinning *

24 厚化 Thickening * 

25 骨架(skeletons) 由右圖推論 (a)點z屬於A的骨架S(A)，(D)z為包含於A中且中心為z的最大圓盤
(b) (D)z在兩個不同點接觸A邊界

26 骨架 Skeletons 此最後結果並不保證線段連通性

27 剪除 用於細線化或骨架演算法的後處理，用於清除多餘的寄生部分 A * X1 X2 X3 X4

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33 ㄧ維函數的 膨脹 表示式 觀念上, “ f 被 b 滑動”與“ b 被 f 滑動”結果相同

34 灰階影像的型態學處理 灰階膨脹 Gray-scale Dilation ㄧ般效果(結構元素均為正值) 結果影像較為明亮
黑暗細節不是減少就是消除 (取決於它們的值及形狀與結構元素的相關程度)

35 ㄧ維函數的 侵蝕 表示式

36 灰階侵蝕 Gray-scale Erosion
ㄧ般效果(結構元素均為正值) 影像較暗 明亮的細節被減少 (取決於細節周邊的灰階値和結構元素的形狀及振幅)

37 斷開Opening 閉合 Closing

38 斷開的效應 Opening 閉合的效應 Closing 小而明亮的細節(相對於結構元素的尺寸) 被除去 其餘的灰階和較大的亮度區域不被干擾
小而暗的細節被去除 保留不大受干擾的亮區

39 平滑化(smothing) Opening followed by Closing

40 型態梯度 Morphological gradient
-- 邊界影像

41 頂-帽轉換 Top-hat transformation
使用帶有平頂的圓筒狀或平行管狀的結構元素 強化帶有陰影的細節

42 紋理分割 Textural Segmentation
Step 1: Closing with larger structuring elements (The size larger then that of the small blobs) The small blobs are removed and left-hand side of the image get brighter. Step 2: Opening with larger structuring elements (The size larger then the seperation between the large blobs) The light pitches between large blobs are and right-hand side of image get darker. Step 3: A simple thresholding

43 粗糙度量測 Granulometry Three passes of opening with structuring elements in different size are applied. The difference between original image and its opening reveals the size distribution (area) of objects