em mrf
Download
Skip this Video
Download Presentation
基于 EM 的 MRF 彩色图像分割

Loading in 2 Seconds...

play fullscreen
1 / 54

基于 EM 的 MRF 彩色图像分割 - PowerPoint PPT Presentation


  • 176 Views
  • Uploaded on

基于 EM 的 MRF 彩色图像分割. 李求旭. 领域系统和势团 Markov Random Fields Markov-Gibbs 等价性 有用的 MRF 模型 多级 GRF 模型和 MML 模型 MAP-MRF 标记 观察模型. 一个简单的例子:图像纹理分割 MRF 参数估计 基于 EM 和 MRF 的彩色图像分割 图像特征的提取 聚类的个数的分析. 领域系统和势团. Sites 和 Labels

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 基于 EM 的 MRF 彩色图像分割' - charis


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2
领域系统和势团
  • Markov Random Fields
  • Markov-Gibbs 等价性
  • 有用的MRF模型
  • 多级GRF模型和MML 模型
  • MAP-MRF标记
  • 观察模型
slide3
一个简单的例子:图像纹理分割
  • MRF 参数估计
  • 基于EM和MRF的彩色图像分割
  • 图像特征的提取
  • 聚类的个数的分析
slide4
领域系统和势团
  • Sites 和 Labels
  • A labeling of the sites in S in terms of the labels in L: f = { }
  • Sites S= {1,…m}
cliques
Cliques
  • A cliquec for (S, N) is defined as a subset of sites in S .在c中所有的sites都是相邻的。
  • 对于(S,N)所有势团的集合是:
markov gibbs
Markov-Gibbs 等价性(证明省略)
  • An MRF is characterized by its local property (the Markovianity)
  • GRF is characterized by its global property (the Gibbs distribution).
  • The Hammersley-Clifford theorem establishes the equivalence of these two types of properties
slide12
The theorem states that F is an MRF on S with respect to N if and only if F is a GRF on S with respect to N
gibbs random field definition
Gibbs Random Field----definition
  • F is said to be a Gibbs Random Field on S with respect to N if and only if its configurations obey a Gibbs distribution:
slide15
有用的MRF模型
  • Auto-Models
  • auto-logistic model (Ising model)
  • auto-binomial model
  • auto-normal model(Gaussian MRF )
  • multi-level logistic (MLL) model (potts model)
  • Hierarchical GRF Model
mll grf
MLL 模型和多级GRF模型
  • There are M (>2) discrete labels in the label set ,L={1,2,…,M}.
slide17
在多级两层Gibbs模型中:
  • The higher level Gibbs distribution uses an isotropic random field (MLL)
  • A lower level Gibbs distribution describes the filling-in in each region
  • 在纹理分割中:

blob-like regions are modeled by a high level MRF which is an isotropic MLL

these regions are filled in by patterns generated according to MRFs at the lower level

map mrf
MAP-MRF标记
  • 1.贝叶斯估计:

估计 的贝叶斯风险被定义为:

2. d:观察的数据

C( , f)是费用函数

p(f | d)is the posterior distribution

slide19
费用函数:
  • 根据(1),贝叶斯风险为:
slide20
根据(2)贝叶斯风险为:
  • where k is the volume of the space containing all points f for which
slide21
因此:最小化风险就相当于最大化后验概率p(f|d).这就是我们所知的最大后验概率估计。因此:最小化风险就相当于最大化后验概率p(f|d).这就是我们所知的最大后验概率估计。
map mrf approach for solving computer vision problems
MAP-MRF approach for solving computer vision problems :
  • Pose a vision problem as one of labeling in categories LP1-LP4 and choose an appropriate MRF representation f.
  • Derive the posterior energy to define the MAP solution to a problem.
  • Find the MAP solution.
slide27
一个简单的例子:图像纹理分割
  • Texture segmentation is to segment an image into regions according to the textures of the regions
  • Texture segmentation, as other labeling problems, is usually performed in an optimization sense, such as MAP
slide29
MRF 参数估计
  • EM算法:一种迭代的标记-估计算法
em mrf1
基于EM和MRF的彩色图像分割
  • 对图像中的每个像素,计算一个d维的特征向量X, X可以包含各种不同的颜色表示,以及一序列滤波器的输出。
  • 我们将图像模型表示如下:图像中的每个像素均是由g个图像分割中的某一个的密度函数计算得到的。因此为产生一个像素,首先选择一个图像分割区域,然后通过该区域的密度函数生成所需的像素
slide32
我们希望确定以下参数:
  • 1.每一个分割(块)的参数
  • 2.混合权重
  • 3.各个像素来源于模型中的哪个分量(从而实现图像分割)
slide33
一个两难问题的提出:
  • 1 . 如果我们已经知道了各个像素分别来源于哪个分量,那么确定参数将会变得容易

2. 如果知道了参数, 那么对于每个像素,就能够确定最可能产生那个像素的分量(这样就确定了图像分割)

3.但问题是两者都不知道。

slide35
The expectation-maximization (EM) algorithm is a general technique for finding maximum likelihood (ML) estimates with incomplete data
  • In EM, the complete data is considered to consist of the two parts:
slide38
EM算法的主要思想是1.通过用期望值来替代丢失的(隐藏的)数据,为丢失的数据获取工作变量的集合2.接着将计算出的不完备数据的期望值代入到完备数据的似然函数中,用这个函数计算相对要简单一些3.然后最大化这个函数获得参数的值。EM算法的主要思想是1.通过用期望值来替代丢失的(隐藏的)数据,为丢失的数据获取工作变量的集合2.接着将计算出的不完备数据的期望值代入到完备数据的似然函数中,用这个函数计算相对要简单一些3.然后最大化这个函数获得参数的值。
  • 这时不完备数据的期望值可能已经改变了。
  • 通过交替执行期望阶段和最大化阶段,迭代直致收敛
slide39
EM算法的形式化描述
  • 1.使用不完备的数据以及参数的当前值来计算完备数据的期望值(E步)
  • 2.使用E步计算出的完备数据的期望值,最大化完备数据关于参数的对数似然函数(M步)。
  • 1,2步交替直到收敛。
slide40
可以证明,不完备数据的对数似然函数在每个阶段都是增长的,也就说参数序列收敛到不完备数据对数似然函数的某个局部最大值。可以证明,不完备数据的对数似然函数在每个阶段都是增长的,也就说参数序列收敛到不完备数据对数似然函数的某个局部最大值。
  • However, we cannot work directly with this complete-data log likelihood because it is a random function of the missing variables f. The idea of the EM algorithm is to use the expectation of the complete-data log likelihood which will formalize EM
slide41
The M-step performs maximum likelihood estimation as if there were no missing data as it had been filled in by the expectations
label process
Label process
  • The label process w is modeled as a MRF

with respect to a second order neighborhood system

image process
Image process
  • 多元高斯密度分布是一种典型的适合大多数分类问题的模型。其中,对于某个给定的类m,特征向量d是连续取值的。
slide47
EM算法
  • 假设存在r个像素,丢失(隐藏)的数据形成一个r×L的数组表示的指示变量Z.
  • 在每一行,除了一个像素,其他的值均为0,这个值表示每个像素的特征向量来源于哪个块(分割)
slide51
图像特征的提取
  • The brightness and texture features are extracted from the L* component and the color features are extracted from the a* and b* components.
slide52
two brightness features: brightness gradient and local energy content of the L* component; three color features: color gradient, local energy content of the a* and b* components;
  • three texture features: phase divergence, homogeneity and homogeneous intensity; and two position features(x,y) coordinates of the pixels
slide53
聚类的个数的分析
  • 基于直方图的聚类个数分析
ad