Computer and Robot Vision I Chapter 2 Binary
電腦視覺 Computer and Robot Vision I Chapter 2: Binary Machine Vision: Thresholding and Segmentation Instructor: Shih-Shinh Huang 1
Contents § Introduction § Thresholding § Connected Components Labeling § Signature Segmentation and Analysis 2
Computer and Robot Vision I Introduction 2. 1 Introduction 3
2. 1 Introduction Binary Machine Vision § Binary Image § Binary Value 1: Part of Object § Binary Value 0: Background Pixel § Definition of Binary Machine Vision § Generation and analysis of such a binary image 4
2. 1 Introduction Binary Machine Vision § Thresholding § It is the first step of binary machine vision § It is a labeling operation § Connected Components / Signature Analysis § They are multilevel vision grouping techniques. § They make a transformation from image pixels to more complex units. • Regions • Segments 5
Computer and Robot Vision I Introduction 2. 2 Thresholding 6
2. 2 Thresholding Introduction § What is Thresholding ? § It is a labeling operation. § It assigns a binary value to each pixel. • Binary Value 1: pixels have higher intensity values • Binary Value 0: pixels have higher intensity values 7
2. 2 Thresholding Introduction § Mathematical Formulation § : row and column § : gray-level intensity image § : intensity threshold § : binary intensity image 8
2. 2 Thresholding Introduction How to select an appropriate threshold ? 9
2. 2 Thresholding Introduction § Approaches § Global Thresholding: use a global value to make the pixel distinction in the image. § Local Thresholding: use spatial varying threshold to label the local pixels. Image 10
2. 2 Thresholding Histogram § Definition of Histogram number of elements m spans each gray level value e. g. 0 - 255 § Histogram Probability 11
2. 2 Thresholding Histogram § Examples 12
2. 2 Thresholding Histogram 13
2. 2 Thresholding Histogram T=110 T=130 14 T=150 T=170
2. 2 Thresholding Within-Group Variance § Observations § A group is a set of pixels with intensity homogeneity. § Homogeneity is measured by the use of variance • High homogeneity group has low variance • Low homogeneity group has high variance § Objective § Select a dividing score such that the weighted sum of the within-group variances is minimized. 15
2. 2 Thresholding Within-Group Variance § Definition: weighted sum of group variances § : probability for the group with values § : variance for the group with values 16
2. 2 Thresholding Within-Group Variance § Objective Formulation § Find a threshold which minimizes 17
2. 2 Thresholding Within-Group Variance § Implementation Issue § Step 1: For t=0, …, 255 § Step 2: Compute , , , and § Step 3: Compute § Step 4: If is less than the value in the previous iteration All variables should be re-compute at each iteration. 18
2. 2 Thresholding Within-Group Variance § Implementation Issue § Speed-Up Formulation 19
2. 2 Thresholding Within-Group Variance § Implementation Issue § Speed-Up Formulation 20
2. 2 Thresholding Within-Group Variance § Implementation Issue § Speed-Up Formulation 21
2. 2 Thresholding Within-Group Variance § Implementation Issue § Speed-Up Formulation 22
2. 2 Thresholding Within-Group Variance § Implementation Issue § Speed-Up Formulation constant minimize maximize 23
2. 2 Thresholding Within-Group Variance § Implementation Issue § Speed-Up Formulation • We have recursive form to compute optimal threshold. 24
2. 2 Thresholding Within-Group Variance § Example 25
2. 2 Thresholding Kullback Information Distance § Assumption § The observations come from a weighted mixture of two Gaussians distributions. • Gaussian Distribution of Background • Gaussian Distribution of Object 26
2. 2 Thresholding Kullback Information Distance Background Gaussian Distribution Object Gaussian Distribution 27
2. 2 Thresholding Kullback Information Distance § Objective Formulation § Determine a threshold T that results in two Gaussian distributions which minimize Kullback divergence • P(I) : observed histogram distribution • f(I) : a mixture of Gaussian distributions determined by T 28
2. 2 Thresholding Kullback Information Distance § Objective Formulation § Known Parameter: Observed Histogram § Unknown Parameter: Two Gaussian Distributions 29
2. 2 Thresholding Kullback Information Distance § Solution Derivation Constant 30
2. 2 Thresholding Kullback Information Distance § Solution Derivation § Assumption: The modes are well separated. 31
2. 2 Thresholding Kullback Information Distance § Solution Derivation 32
2. 2 Thresholding Kullback Information Distance § Implementation Issue § Step 1: For t=0, …, 255 § Step 2: Compute , , , and § Step 3: Compute § Step 4: If is less than the value in the previous iteration 33
2. 2 Thresholding Kullback Information Distance § Example 34
2. 2 Thresholding Kullback Information Distance Within Group Variance (Otsu) Kullback Information (Kittler-Illingworth) 35
Computer and Robot Vision I Introduction 2. 3 Connected Component Labeling 36
2. 3 Connected Component Labeling Introduction § Description § Connected Components labeling is a grouping operation. § It performs the unit change from pixel to region or segment. § All pixels are given the same identifier • Have value binary 1 • Connect to each other 37
2. 3 Connected Component Labeling Introduction § Terminology § label: unique name or index of the region § connected components labeling: a grouping operation § pixel property: position, gray level or brightness level § region property: shape, bounding box, position, intensity statistics 38
2. 3 Connected Component Labeling Connected Component Operators § Definition of Connected Component § Two pixels and belong to the same connected component if there is a sequence of 1 -pixels , where • • • are neighbor 39
2. 3 Connected Component Labeling Connected Component Operators § Neighborhood Types 4 -connected Original Image 8 -connected 40 Connected Components
2. 3 Connected Component Labeling Connected Component Algorithms § Common Features § Process a row of image at a time § Assign a new labels to the first pixel of each component. § Propagate the label of a pixel to its neighbors to the right or below it. 41
2. 3 Connected Component Labeling Connected Component Algorithms § Common Features • What label should be assigned to A • How does the algorithm keep track of the equivalence of two labels • How does the algorithm use the equivalence information to complete the processing 42
2. 3 Connected Component Labeling Algorithm 1: Iterative Algorithm § Algorithm Steps § Step 1 (Initialization): Assign an unique label to each pixel. § Step 2 (Iteration) : Perform a sequence of topdown and bottom-up label propagation. • Use no auxiliary storage • Computational Expensive 43
2. 3 Connected Component Labeling Algorithm 2: Classic Algorithm § Two-Pass Algorithm § Pass 1: • Perform label assignment and label propagation • Construct the equivalence relations between labels when two different labels propagate to the same pixel. • Apply resolve function to find the transitive closure of all equivalence relations. § Pass 2: • Perform label translation. 44
2. 3 Connected Component Labeling Algorithm 2: Classic Algorithm § Example: {2=4} {3=5} {1=5} 45
2. 3 Connected Component Labeling Algorithm 2: Classic Algorithm § Example: § Resolve Function {2=4} {3=5} {1=5} {2=4} {1=3=5} • Computational Efficiency • Need a lot of space to store equivalence 46
Computer and Robot Vision I Introduction 2. 4 Signature Segmentation and Analysis 47
2. 4 Signature Segmentation and Analysis Introduction § Description § Signature analysis perform unit change from the pixel to the segment. § It was firstly used in character recognition § Definition of Signature § The signature, which is a projection, is the histogram of the non-zero pixels of the masked image. 48
2. 4 Signature Segmentation and Analysis Introduction § General Signatures § Vertical Projection § Horizontal Projection § Diagonal Projection 49
2. 4 Signature Segmentation and Analysis Signature Segmentation § Steps § Thresholding: generate the binary image. § Projection Computation: compute the vertical, horizontal, or diagonal projections. § Projection Segmentation: divide the image into several segments or regions according to the signatures. 50
2. 4 Signature Segmentation and Analysis Signature Segmentation 51
2. 4 Signature Segmentation and Analysis Signature Segmentation 52
2. 4 Signature Segmentation and Analysis Signature Segmentation OCR: Optical Character Recognition MICR: Magnetic Ink Character Recognition 53
Computer and Robot Vision I The End
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