Announcements

	Final
		Monday 10:30-12:20, in this room
		Closed book/notes
		Comprehensive (through today)
		Review today
	Project 3 artifacts
	Evals
		at end of class

Modeling Texture

	What is texture?
	How can we model it?

Markov Chains

	Markov Chain
		a sequence of random variables
		is the state of the model at time t
		Markov assumption:  each state is dependent only on the previous one
			dependency given by a conditional probability:
		The above is actually a first-order Markov chain
		An N’th-order Markov chain:

Markov Chain Example:  Text

	“A dog is a man’s best friend. It’s a dog eat dog world out there.”

Text synthesis

	Create plausible looking poetry, love letters, term papers, etc.
	Most basic algorithm
		Build probability histogram
			find all blocks of N consecutive words/letters in training documents
			compute probability of occurance
		Given words
			compute          by sampling from
	Example on board...

[Scientific American, June 1989, Dewdney]

	“I Spent an Interesting Evening Recently with a Grain of Salt”
	- Mark V. Shaney
	(computer-generated contributor to UseNet News group called net.singles)

Modeling Texture

	What is texture?
		An image obeying some statistical properties
		Similar structures repeated over and over again
		Often has some degree of randomness

Markov Random Field

Texture Synthesis [Efros & Leung, ICCV 99]

	Can apply 2D version of text synthesis

Synthesizing One Pixel

		What is                                                                           ?
		Find all the windows in the image that match the neighborhood
			consider only pixels in the neighborhood that are already filled in
		To synthesize x
			pick one matching window at random
			assign x to be the center pixel of that window

Really Synthesizing One Pixel

Growing Texture

Window Size Controls Regularity

More Synthesis Results

More Results

Failure Cases

Image-Based Text Synthesis

Applications of Texture Modeling

	Super-resolution
		Freeman & Pasztor, 1999
		Baker & Kanade, 2000
	Image/video compression
	Video Textures
		Wei & Levoy, 2000
		Schodl et al., 2000
	Texture recognition, segmentation
		DeBonet
	Restoration
		removing scratches, holes, filtering
		Zhu et al.
	Art/entertainment