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 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 Visual Perception Modeling

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, ...... Visual Perception Modeling

5. Some Texture Examples Visual Perception Modeling

6. Non-texture Examples Visual Perception Modeling

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 Visual Perception Modeling

8. Deterministic textures • Deterministic textures • A set of primitives • A placement rule • Examples include • A tile of floor • Regular structures Visual Perception Modeling

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 Visual Perception Modeling

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? Visual Perception Modeling

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 Visual Perception Modeling

12. Psychophysical Texture Models • Texture discrimination Visual Perception Modeling

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 Visual Perception Modeling

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 Visual Perception Modeling

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 Visual Perception Modeling

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 Visual Perception Modeling

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 Visual Perception Modeling

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 Visual Perception Modeling

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 Visual Perception Modeling