1. Outline Neural networks - reviewed Texture modeling
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 par
Training data file – network training.par
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Visual Perception Modeling

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
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Visual Perception Modeling

4. Visual Perception Modeling
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,
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5. Visual Perception Modeling
Some Texture Examples
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6. Visual Perception Modeling
Non-texture Examples
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7. Visual Perception Modeling
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
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8. Deterministic textures
A set of primitives
A placement rule
Examples include
A tile of floor
Regular structures
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9. Visual Perception Modeling
Stochastic Textures
Stochastic textures
Do not have easily identifiable primitives
However, there are local statistics/local properties that are varying slowly or approximately periodic
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10. Visual Perception Modeling
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?
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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
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12. Psychophysical Texture Models
Texture discrimination
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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
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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
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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
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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
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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
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18. 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
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19. Visual Perception Modeling
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
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