Outline
• Neural networks - reviewed
– Back-propagation program
• Texture modeling
– Introduction
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
5/29/2016
Visual Perception Modeling
2
Back Propagation Program – cont.
• Homework #5
– Gain some first-hand experience with neural
networks
– Study how the parameters affect the performance
of neural networks
5/29/2016
Visual Perception Modeling
3
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, ......
5/29/2016
Visual Perception Modeling
4
Some Texture Examples
5/29/2016
Visual Perception Modeling
5
Non-texture Examples
5/29/2016
Visual Perception Modeling
6
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
5/29/2016
Visual Perception Modeling
7
Deterministic textures
• Deterministic textures
– A set of primitives
– A placement rule
– Examples include
• A tile of floor
• Regular structures
5/29/2016
Visual Perception Modeling
8
Stochastic Textures
• Stochastic textures
– Do not have easily identifiable
primitives
– However, there are local
statistics/local properties that
are varying slowly or
approximately periodic
5/29/2016
Visual Perception Modeling
9
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?
5/29/2016
Visual Perception Modeling
10
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
5/29/2016
Visual Perception Modeling
11
Psychophysical Texture Models
• Texture discrimination
5/29/2016
Visual Perception Modeling
12
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
5/29/2016
Visual Perception Modeling
13
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
Pd (i, j ) | {( r , s) : I (r , s)  i, I (r  dx, s  dy)  j} |
5/29/2016
Visual Perception Modeling
14
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
Pd  P d  Pd
– The co-occurrence matrix reveals certain
properties about spatial distribution of the gray
levels in the texture images
5/29/2016
Visual Perception Modeling
15
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
2
P
 d (i, j )
i
• Entropy
i
  Pd (i, j ) log Pd (i, j )
i
• Contrast
j
2
(
i

j
)
Pd (i, j )

i
5/29/2016
j
Visual Perception Modeling
16
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
5/29/2016
Visual Perception Modeling
17
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
N N
image
I (u, v) I (u  x, v  y )

 ( x, y )  u 1 v 1 N N
2
I
(
u
,
v
)

u 1 v 1
5/29/2016
Visual Perception Modeling
18
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
5/29/2016
Visual Perception Modeling
19