電腦視覺 Computer and Robot Vision I Chapter2: 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 2.1 Introduction Introduction 3

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 2.1 Introduction 4

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 2.1 Introduction 5

Computer and Robot Vision I 2.2 Thresholding Introduction 6

 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 2.2 Thresholding 7

Introduction  Mathematical Formulation  : row and column  : gray-level intensity image  : intensity threshold  : binary intensity image Thresholding

Introduction Thresholding How to select an appropriate threshold ?

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 Thresholding Image

Histogram  Definition of Histogram  Histogram Probability Thresholding number of elements m spans each gray level value e.g

Histogram  Examples Thresholding

Histogram Thresholding

Histogram Thresholding T=110T=130T=150T=170

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 Thresholding

Within-Group Variance  Definition: weighted sum of group variances  : probability for the group with values  : variance for the group with values Thresholding

Within-Group Variance  Objective Formulation  Find a threshold which minimizes Thresholding

Within-Group Variance  Implementation Issue  Step1: For t=0,…,255  Step2: Compute,,, and  Step3: Compute  Step4: If is less than the value in the previous iteration Thresholding All variables should be re-compute at each iteration.

Within-Group Variance  Implementation Issue  Speed-Up Formulation Thresholding

Within-Group Variance  Implementation Issue  Speed-Up Formulation Thresholding

Within-Group Variance  Implementation Issue  Speed-Up Formulation Thresholding

Within-Group Variance  Implementation Issue  Speed-Up Formulation Thresholding

Within-Group Variance  Implementation Issue  Speed-Up Formulation Thresholding constant minimizemaximize

Within-Group Variance  Implementation Issue  Speed-Up Formulation We have recursive form to compute optimal threshold Thresholding

Within-Group Variance  Example Thresholding

Kullback Information Distance  Assumption  The observations come from a weighted mixture of two Gaussians distributions. Gaussian Distribution of Background Gaussian Distribution of Object Thresholding

Kullback Information Distance Thresholding Background Gaussian Distribution Object Gaussian Distribution

Kullback Information Distance  Objective Formulation T  Determine a threshold T that results in two Gaussian distributions which minimize Kullback divergence P(I) :P(I) : observed histogram distribution f(I) Tf(I) : a mixture of Gaussian distributions determined by T Thresholding

Kullback Information Distance  Objective Formulation  Known Parameter: Observed Histogram  Unknown Parameter: Two Gaussian Distributions Thresholding

Kullback Information Distance  Solution Derivation Thresholding Constant

Kullback Information Distance  Solution Derivation  Assumption: The modes are well separated Thresholding

Kullback Information Distance  Solution Derivation Thresholding

Kullback Information Distance  Implementation Issue  Step1: For t=0,…,255  Step2: Compute,,, and  Step3: Compute  Step4: If is less than the value in the previous iteration Thresholding

Kullback Information Distance  Example Thresholding

Kullback Information Distance Thresholding Within Group Variance (Otsu) Kullback Information (Kittler-Illingworth)

Computer and Robot Vision I 2.3 Connected Component Labeling Introduction 36

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 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 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 Connected Component Labeling

Connected Component Operators  Neighborhood Types Connected Component Labeling 4-connected 8-connected Original ImageConnected Components

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 Connected Component Labeling

Connected Component Algorithms  Common Features Connected Component Labeling 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

Algorithm1: Iterative Algorithm  Algorithm Steps  Step1 (Initialization): Assign an unique label to each pixel.  Step2 (Iteration) : Perform a sequence of top- down and bottom-up label propagation Connected Component Labeling Use no auxiliary storage Computational Expensive

Algorithm2: 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 Connected Component Labeling

Algorithm2: Classic Algorithm  Example: Connected Component Labeling {2=4} {3=5} {1=5}

Algorithm2: Classic Algorithm  Example:  Resolve Function Connected Component Labeling {2=4}{3=5}{1=5}{2=4}{1=3=5} Computational Efficiency Need a lot of space to store equivalence

Computer and Robot Vision I 2.4 Signature Segmentation and Analysis Introduction 47

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 Signature Segmentation and Analysis

Introduction  General Signatures  Vertical Projection  Horizontal Projection  Diagonal Projection 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 Signature Segmentation and Analysis

Signature Segmentation Signature Segmentation and Analysis

Signature Segmentation Signature Segmentation and Analysis

Signature Segmentation Signature Segmentation and Analysis OCR: Optical Character Recognition MICR: Magnetic Ink Character Recognition

The End Computer and Robot Vision I