Outline

1
Outline

• Neural networks - reviewed
• Back-propagation program
• Texture modeling
• Introduction

2
Back Propagation Program

• Programs
• Backprop.c main program
• Propagation.c contains procedures for BP
• Para-util.h and type-def.h contain data
  structure definitions
• Located at
• liux/public_html/courses/research/programs/neural
  -networks
• Parameter files
• Control parameter file network-3-3-1.par
• Training data file network-3-3-1-training.par

3
Back Propagation Program cont.

• Homework 5
• Gain some first-hand experience with neural
  networks
• Study how the parameters affect the performance
  of neural networks

4
Texture Modeling

• Texture is a phenomenon
• Is widespread
• Easy to recognize
• Hard to define as many other perceptual phenomena
• Texture arises from different resources
• Views of large numbers of small objects
• Grass, brush, pebbles, hair, ......
• Surfaces with orderly patterns
• Cheetah skins, zebra stripes, ......

5
Some Texture Examples
6
Non-texture Examples
7
Texture Definition

• Image texture is defined as a function the
  spatial variation in pixel intensities
• Local statistics or local properties are
  constant, slowly varying, or approximately
  periodic

8
Deterministic textures

• Deterministic textures
• A set of primitives
• A placement rule
• Examples include
• A tile of floor
• Regular structures

9
Stochastic Textures

• Stochastic textures
• Do not have easily identifiable primitives
• However, there are local statistics/local
  properties that are varying slowly or
  approximately periodic

10
Texture Modeling

• Texture modeling is to find feature statistics
  that characterize perceptual appearance of
  textures
• There are two major computational issues
• What kinds of feature statistics shall we use?
• How to verify the sufficiency or goodness of
  chosen feature statistics?

11
Texture Modeling cont.

• The structures of images
• The structures in images are due to the
  inter-pixel relationships
• The key issue is how to characterize the
  relationships

12
Psychophysical Texture Models

• Texture discrimination

13
Psychophysical Texture Models cont.

• Julesz conjecture
• Two textures that have identical second-order
  statistics are not pre-attentively discriminable
• Second-order statistics
• First-order statistics are the histogram of the
  texture images
• Second-order statistics are defined as the
  likelihood of observing a pair of gray values
  occurring at the endpoints of a dipole

14
Co-occurrence Matrices

• Gray-level co-occurrence matrix
• One of the early texture models
• Was widely used
• Suppose that there are G different gray values in
  a texture image I
• For a given displacement vector (dx, dy), the
  entry (i, j) of the co-occurrence matrix Pd is

15
Co-occurrence Matrices cont.

• Properties
• Size of the co-occurrence matrix is G x G
• The co-occurrence matrix in general is not
  symmetric
• A symmetric version can be computed as
• The co-occurrence matrix reveals certain
  properties about spatial distribution of the gray
  levels in the texture images

16
Co-occurrence Matrices cont.

• Useful texture features
• Because the co-occurrence matrices can contain
  many entries, a number of features are proposed
  to calculate from co-occurrence matrices
• Energy
• Entropy
• Contrast

17
Co-occurrence Matrices cont.

• Generalization of co-occurrence
• k-gon statistics
• In general, we can define an arbitrary polygon
  with k vertices and collect statistics on those
  vertices
• A line segment defines the co-occurrence
• A triangle defines 3-gon statistics
• It captures the dependence among pixels

18
Autocorrelation Features

• Autocorrelation features
• Many textures have repetitive nature of texture
  elements
• The autocorrelation function can be used to
  assess the amount of regularity as well as the
  fineness/coarseness of the texture present in the
  image

19
Geometrical Models

• Geometrical models
• Applies to textures with texture elements
• Then one can compute the statistics of local
  elements or extract the placement rule that
  describes the texture
• Voronoi tessellation features
• Structural methods