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Image Segmentation 圖像分割

Digital images 數碼影像​

  • Image representations 圖像表示
    • 2dimensional arrays of pixels 二維像素陣列
      • (x,y)
    • multi-dimensional arrays of pixels 多維像素陣列
      • (x,y,z)
      • (x,y,t)
      • (x,y,z,t)
      • (x,y,z,b 1 ,b 2 , ... , bN)

Characterising images as objects 圖像物件特徵​

  • Spatial resolution 空間解析度
    • Pixel size 像素大小
    • Pixels / inch 像素/英吋
  • Intensity resolution 亮度解析度
    • Bits per pixel 每像素位元數
  • Time resolution 時間解析度
    • Frames per second 幀/秒
  • Spectral resolution 色彩解析度
    • Number of bands 波段數 + bandwidth 帶寬

Characterising images as signals 圖像信號特徵​

  • Image statistics 圖像統計
    • Mean, standard deviation 平均值、標準差
    • Histogram: frequency distribution graph 直方圖：頻率分佈圖

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Characterising images as signals 圖像信號特徵​

  • Image noise 圖像雜訊
    • Signal-to-noise ratio (SNR) 信號雜訊比

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Characterising images as objects 圖像物件特徵​

  • This requires that image is partitioned into meaningful regions. 這需要將圖像劃分為有意義的區域。
  • The process of partitioning is known as segmentation 分割的過程稱為分割。

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Image Segmentation 圖像分割​

  • Partitioning an image into meaningful regions with respect to a particular application 針對特定應用程序將圖像劃分為有意義的區域
  • Simple segmentation is based on measurements taken from the image and might be based on brightness (grey-level), colour, texture, motion, etc. 簡單的分割是基於從圖像中取得的測量值，可能基於亮度（灰階），顏色，紋理，運動等。

Image segmentation techniques 圖像分割技術​

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Image Segmentation 圖像分割​

  • Image Segmentation can be classified as: 圖像分割可以分類為：
    • Non-automated 非自動化
      • Identifying regions by hand! 手動識別區域！
    • Semi-automated 半自動化
      • Thresholding 閾值
      • Region Growing 區域生長
      • Active Contour, etc ... 主動輪廓等...
  • Automated 自動化
    • Model based segmentation 基於模型的分割
      • Area of intensive research 高度研究

Non-automated segmentation 非自動化分割​

  • Given an image, select and define a region of interest by hand. 給定一個圖像，手動選擇和定義感興趣的區域。
    • Rough estimate of the region of interest. 感興趣區域的粗略估計。

Hand Segmentation? 手動分割？​

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Thresholding 閾值​

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  • Histogram-based segmentation (thresholding) 基於直方圖的分割（閾值）
    • Given an image, select a suitable threshold value to separate the image into two regions. 給定一個圖像，選擇一個適當的閾值來將圖像分割為兩個區域。

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Histogram of an image 圖像的直方圖​

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Thresholding 閾值​

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Thresholding challenges 閾值挑戰​

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Thresholding challenges 閾值挑戰​

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Thresholding challenges 閾值挑戰​

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Thresholding challenges 閾值挑戰​

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Thresholding challenges 閾值挑戰​

  • How do we determine the threshold? 我們如何確定閾值？
  • Many approaches possible 可能有很多方法
    • Interactive threshold 互動門檻
    • Adaptive threshold 自適應閾值
    • Variance minimisation method (Otsu's threshold selection algorithm) 方差最小化法（大津的閾值選擇算法）
      • In the simplest form, the algorithm returns a single intensity threshold that separate pixels into two classes, foreground and background. 在最簡單的形式中，該算法返回一個強度閾值，將像素分為兩個類別，前景和背景。
      • This threshold is determined by minimizing intra-class intensity variance, or equivalently, by maximizing inter-class variance. 這個閾值是通過最小化類內強度變異數來確定的，或者通過最大化類間變異數來確定。

Otsu's Threshold Selection Algorithm 大津的閾值選擇算法​

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Thresholding - Problems 閾值 - 問題​

  • Manual methods:
    • Time consuming
    • Operator error
    • Subjective
  • Different regions / image areas may need different levels of threshold 不同的區域/圖像區域可能需要不同的閾值水平
  • Noise

Smoothing & Thresholding 平滑和閾值​

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Mathematical morphology 數學形態學​

  • Morphology is concerned with study of form and shape. 形態學關注形式和形狀的研究。
  • Operations of mathematical morphology are defined in terms of interactions of two sets of points. One set (usually a large one) corresponds to an image; the other (usually much smaller) is called a structuring element. 數學形態學的操作是根據兩組點的互動來定義的。一組（通常是一個大的）對應於一個圖像；另一組（通常要小得多）稱為結構元素。
  • A structuring element can be thought of as a "brush" with which an image is "overpainted" in a number of specific ways, depending on the morphological operation. 結構元素可以被認為是一個"筆刷"，用於以多種特定方式"重新繪製"圖像，具體取決於形態學操作。
  • Examples of typical structuring elements (grey dots indicate "active" members of the structuring element set): 結構元素的典型示例（灰色點表示結構元素集的"活動"成員）： 20

Mathematical morphology 數學形態學​

  • Two principal operations of mathematical morphology are dilation and erosion. 數學形態學的兩個主要操作是膨脹和侵蝕。
  • Dilation (expansion) 膨脹（擴展）
    • adding a "layer" of pixels to the periphery of objects 在對象的外圍添加一個像素"層"
    • the object will grow larger, close objects will be merged, holes will be closed 這個對象將變大，接近的對象將被合併，洞將被關閉
  • Erosion (shrinking) 侵蝕（縮小）
    • removing a "layer" of pixels all round an object 一個對象周圍移除一個像素"層"
    • the object will get thinner, if it is already thin it will break into several sections 這個對象將變得更薄，如果它已經很薄，它將分成幾個部分

Mathematical morphology 數學形態學​

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Advanced segmentation methods 進階分割方法​

  • Active contours (snakes) 活動輪廓（蛇）
  • Watershed segmentation 水域分割
  • Level-set methods 等級集方法
  • Active shape model segmentation 活動形狀模型分割

Active (snake) contours 活動（蛇）輪廓​

E[(C)(p)]=α∫01Eint (C(p))dp+β∫01Eimg(C(p))dp+γ∫01Econ (C(p))dpE[(C)(p)]=\alpha \int_0^1 E_{\text {int }}(C(p)) d p+\beta \int_0^1 E_{i m g}(C(p)) d p+\gamma \int_0^1 E_{\text {con }}(C(p)) d p

  • The internal term stands for regularity/smoothness along the curve and has two components (resisting to stretching and bending) 輪廓內部項代表沿輪廓的規則性/平滑性，並具有兩個部分（抵抗拉伸和彎曲）
    • sensitivity to the amount of stretch in the snake and the amount of curvature in the snake 對蛇的拉伸量和蛇的曲率量的敏感性
  • The image term guides the active contour towards the desired image properties (strong gradients) 圖像項引導活動輪廓向所需的圖像屬性（強梯度）靠近
    • Energy in the image is some function of the features of the image, for example edges 圖像中的能量是圖像特徵的某種函數，例如邊緣
  • The external term can be used to account for use defined constraints, or prior knowledge on the structure to be recovered 外部項可用於考慮用戶定義的限制，或對要恢復的結構的先驗知識
    • allowes for user interaction to guide the snakes, not only in initial placement but also in their energy terms. 使用戶交互來引導蛇，不僅在初始放置中，而且在它們的能量項中。
  • The lowest potential of such a cost function refers to an equilibrium of these terms 最低潛力的成本函數指的是這些項的平衡

Active contours 活動輪廓​

E[(C)(p)]=α∫01Eint (C(p))dp+β∫01Eimg(C(p))dp+γ∫01Econ (C(p))dpE[(C)(p)]=\alpha \int_0^1 E_{\text {int }}(C(p)) d p+\beta \int_0^1 E_{i m g}(C(p)) d p+\gamma \int_0^1 E_{\text {con }}(C(p)) d p

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Watershed segmentation 水域分割​

  • Classify pixels into three classes: 分類像素為三類：
    • belonging to a local minimum 屬於局部最小值
    • catchment basin or watershed: pixels at which a drop of water would flow to that local minimum 捕捉盆地或水域：像素，水滴將流向該局部最小值
    • divide of watershed lines: pixels at which water would flow to two minima. 水域線的分割：像素，水將流向兩個最小值。

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Watershed segmentation 水域分割​

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