電腦視覺 Computer and Robot Vision I

電腦視覺Computer and Robot Vision I • Chapter2:Binary Machine Vision: • Thresholding and Segmentation • Instructor: Shih-Shinh Huang

Contents Introduction Thresholding Connected Components Labeling Signature Segmentation and Analysis

Computer and Robot Vision I Introduction • 2.1 Introduction

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

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

Computer and Robot Vision I Introduction • 2.2Thresholding

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

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

2.2 Thresholding Introduction How to select an appropriate threshold ?

2.2Thresholding Introduction Image Image • 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.

2.2 Thresholding Histogram number of elements m spans each gray level value e.g. 0 - 255 Definition of Histogram Histogram Probability

2.2 Thresholding Histogram Examples

2.2 Thresholding Histogram

2.2 Thresholding Histogram T=110 T=130 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.

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

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

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

2.2 Thresholding Within-Group Variance • Implementation Issue • Speed-Up Formulation

2.2 Thresholding Within-Group Variance constant minimize maximize • Implementation Issue • Speed-Up Formulation

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

2.2 Thresholding Within-Group Variance Example

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

2.2 Thresholding Kullback Information Distance Background Gaussian Distribution Object Gaussian Distribution

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

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

2.2 Thresholding Kullback Information Distance Constant Solution Derivation

2.2 Thresholding Kullback Information Distance • Solution Derivation • Assumption: The modes are well separated.

2.2 Thresholding Kullback Information Distance Solution Derivation

2.2 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

2.2 Thresholding Kullback Information Distance Example

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

Computer and Robot Vision I Introduction • 2.3 Connected Component Labeling

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

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

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

2.3 Connected Component Labeling Connected Component Operators 4-connected Original Image Connected Components 8-connected Neighborhood Types

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.

2.3 Connected Component Labeling Connected Component Algorithms • 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 Common Features

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

2.3 Connected Component Labeling 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.

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

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

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

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.

2.4 Signature Segmentation and Analysis Introduction • General Signatures • Vertical Projection • Horizontal Projection • Diagonal Projection

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.

電腦視覺 Computer and Robot Vision I