Computer Vision Chapter 9:Texture

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Computer Vision

Chapter 9 Texture

Presented by 王夏果 and 傅楸善教授 Cell phone: 0937384214 E-mail: [email protected]

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DC & CV Lab.

DC & CV Lab. CSIE NTU

Introduction

 What does texture mean? Formal approach

or precise definition of texture does not exist!

 Texture discrimination techniques are for the

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Definition of Texture

 Non-local property, characteristic of region

larger than its size

 Repeating patterns of local variations in

image intensity which are too fine to be distinguished as separated objects at the observed resolution

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Definition of Texture (cont.)

 For humans, texture is the abstraction of

certain statistical homogeneities from a portion of the visual field that contains a

quantity of information grossly in excess of the observer’s perceptual capacity

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Texture Analysis Issues

 Pattern recognition: given texture region,

determine the class the region belongs to

 Generative model: given textured region,

determine a description or model for it

 Texture segmentation: given image with

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Statistical Texture-Feature

Approaches

 Autocorrelation function

 Spectral power density function  Edgeness per unit area

 Spatial gray level co-occurrence probabilities  Graylevel run-length distributions

 Relative extrema distributions  Mathematical morphology

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Image Texture Analysis

 Give a generative model and the values of its

parameters, one can synthesize

homogeneous image texture samples associated with the model and the given value of its parameters.

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Image Texture Analysis (cont.)

 Verification: verify given image textures

sample consistent with model

 Estimation: estimate values of model

parameters based on observed sample examples of model-based techniques

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Some Model-Based Techniques

 Autoregressive, moving-average, time-series

models (extended to 2D)

 Markov random fields  Mosaic models

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Texel

 Texture element, basic textural unit of some

textural primitives qualitatively evaluated image texture properties

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Some Texture Features

 Fineness  Coarseness  Contrast  Directionality  Roughness  Regularity  Smoothness  Granulation

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Some Texture Features (cont.)

 Randomness  Lineation  Mottled  Irregular  Hummocky

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Texture and Scale

 For any textural surface, there exists a scale

at which, when the surface is examined, it ap pears smooth and textureless. (see from infini te distance)

 As resolution increases, the surfaces appears

as a fine texture and then a coarse one, and f or multiple-scale textural surface the cycle of smooth, fine, and coarse may repeat.

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Texture and Scale (cont.)

 Thus, texture cannot be analyzed without

frame of reference on scale or resolution.

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Characterizing Texture

 Characterize gray level primitive properties  Characterize spatial relationships between

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First-Order Gray-Level Statistics

 Statistics of single pixels

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Second-Order Gray-Level

Statistics

 The combined statistics of gray levels of pairs

of pixels in which each two pixels in a pair have a fixed relative position

 E.g. co-occurrence

 Gray level spatial dependence: characterize

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Co-Occurrence Matrix

 The gray level co-occurrence can be specifie

d in a matrix of relative frequencies Pij with w hich two neighboring pixels separated by dist ance d occur on the image, one with gray lev el i and the other with gray level j

 Symmetric matrix

 Function of angle and distance between pixel

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Co-Occurrence Matrix (cont.)

 Probability of horizontal, d pixels apart pixels

P(i, j, d, 0°) =

#{[(k, l), (m, n)] | k-m = 0, |l-n| = d, I(k, l) = i, I(m,n) = j}

 Probability of 45_°, d pixels apart pixels

P(i, j, d, 45°) =

#{[(k, l), (m, n)] | (k-m = d, l-n = -d) or (k-m = -d, l-n = d), I(k, l) = i, I(m,n) = j}

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Co-Occurrence Matrix (cont.)

P(i, j, d, 90°) =

#{[(k, l), (m, n)] | |k-m| = d, l-n = 0, I(k, l) = i, I(m,n) = j}

P(i, j, d, 135°) =

#{[(k, l), (m, n)] | (k-m = d, l-n = d) or (k-m = -d, l-n = -d), I(k, l) = i, I(m,n) = j}

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Co-Occurrence Matrix (cont.)

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Matrix with Highest Entropy

 When all entries in P_ijare equal

 Image where no preferred gray-level pairs exi

st features calculated from the co-occurrence matrix

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Generalized Gray Level Spatial

Dependence Models for Texture

 Simple generalization: consider more than

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Generalized Co-Occurrence

 Strong texture measures take into account

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Texture Primitive

 Connected set of pixels characterized by

attribute set

 Simplest primitive: pixel with gray level

attribute

 More complicated primitive: connected set of

pixels homogeneous in level, characterized by size, elongation, orientation, and average gray level

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Spatial Relationship

 We have a list of primitives, their center

coordinate, and their attributes after the primitives have been constructed.

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Autocorrelation Function

 Texture relates to the spatial size of the gray

level primitives on an image

 Gray level primitives of larger size are

indicative of coarser texture

 Gray level primitives of smaller size are

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Autocorrelation Function (cont.)

 Autocorrelation function describes the size of

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Autocorrelation Function (cont.)

 If the gray level on image is relatively large:

texture is coarse, autocorrelation drops off slowly with distance

 If the gray level on image is relatively small:

texture is fine, autocorrelation drops off quickly with distance

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Digital Transform Methods and

Texture

 In the digital transform method of texture anal

ysis, the digital image is typically divided into a set of non-overlapping small square subima ges

 The vectors is reexpressed in a new coordina

te system

 Fourier transform uses the complex sinusoid

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Texture Energy

 The image is first convolved with a variety of

kernels

 Then each convolved image is processed

with a nonlinear operator to determine the total textural energy in each pixel’s

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Texture Edgeness

 Autocorrelation function and digital transform

both reference texture to spatial frequency

 Texture Edgeness: conceive texture in terms

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Texture Edgeness (cont.)

 Use small neighborhood to detect microedge  Use large neighborhood to detect macroedge

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Vector Dispersion

 Divide the texture into mutually exclusive

neighborhoods

 A sloped plane fit to the gray levels is

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Relative Extrema Density

 Count the number of extrema per unit area fo

r a texture measure

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Relative Extrema Density (cont.)

 Relative minimum:

g(i) g(i+1) and g(i) g(i-1)≦ ≦

 Relative maximum:

g(i) g(i+1) and g(i) g(i-1)≧ ≧

 Pixels in a constant run: both minimum and m

aximum

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Mathematical Morphology

 Granularity of a binary image F:

#F: number of elements in F

: disk structuring element of diameter d

 G(d) measures the proportion of pixel parti

cipating in grains of size smaller than d

F

H

F

d

G

d

#

1 )

(







d H

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Mathematical Morphology (cont.)

 Scale-k volume of the blanket around a gray

level intensity surface I:

⊕k: k-fold dilation Θk: k-fold erosion



    ) , ( ) , )( ( ) , )( ( ) ( c r k k H r c I H r c I k V

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Autoregression Models

 Doing linear estimates of a pixel’s gray level

with the gray levels in the neighborhood

 For coarse texture, coefficient will be similar  For fine texture, coefficient will vary widely

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Autoregression Models

 Next gray value a_N+1 : linear combination of

synthesized data and noise value

 a_k : given starting sequence

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Autoregression Models (cont.)

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Autoregression Models (cont.)

 Easy to use the estimator in a node that synt

hesized textures from any initially given linear estimator

 Sufficient to capture everything in a texture

 But the textures it can characterize are likely t

o consist mostly of microtextures

 Microtexture: gray level primitives are small, s

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Discrete Markov Random Fields

 Assumption: the texture field is stochastic

and stationary and satisfies a conditional independence assumption

 When the distributions are Gaussian, each

pixel’s value is a combination of the value in its neighborhood plus a noise term

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Discrete Markov Random Fields

(cont.)

h: coefficients, computed from texture image with

least-square method

u: joint set of possible correlated Gaussian rando

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Random Mosaic Models

 Constructing steps:

1. Provide a mean of tessellating a plane into

cells

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Structural Approaches to Texture

Models

 Pure structural model: primitives in regular

repetitive spatial arrangements

 To describe the texture, describe the

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Texture Segmentation

 Each region has homogeneous texture, and

each pair of adjacent regions is differently textured

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Synthetic Texture Image

Generation

 Fractals: shapes that exhibit recursive

self-similarity

 Every fractal can be recursively subdivided

into smaller non-overlapping shapes, each of which is a scale-down version of the whole, either in a deterministic sense or in a

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Shape from Texture

 Use image texture gradients to estimate surfa

ce orientation of the observed 3D object

 Assumption: no depth changes and no textur

e changes in observed texture area, and no s ubtextures

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Shape from Texture (cont.)

 Unknown plane where texture observed

Ax + By + Cz + D = 0

where

 From perspective projection, 3D point

(x, y, z) with projection (u, v)

1

2 2 2

_

_B

_

_C

_

A

z x f u  z y f v 

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Shape from Texture (cont.)

Cf

Bv

Au

Df

z







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Summary

 Texture: in terms of primitives and spatial

relationships

 Qualitatively, shape from texture can work  Quantitatively, the techniques are generally