Lecture Slides on Learning Low-Level Vision | ECE 598, Papers of Electrical and Electronics Engineering

Material Type: Paper; Professor: Jones; Class: Electrical Machine Design; Subject: Electrical and Computer Engr; University: University of Illinois - Urbana-Champaign; Term: Unknown 2000;

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ECE598FL Readings on
Computer Vision
Learning Low-Level
Vision
Presented by: Juan Carlos Niebles
Based on:
Learning Low-Level Vision; by Freeman, Pasztor,
Charmichael, IJCV, 2000.
Comparison of Graph Cuts with Believe Propagation
for Stereo, using Identical MRF Parameters; by
Tappen, Freeman, ICCV, 2003.
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Download Lecture Slides on Learning Low-Level Vision | ECE 598 and more Papers Electrical and Electronics Engineering in PDF only on Docsity!

ECE598FL Readings on

Computer Vision

Learning Low-LevelVision Presented by: Juan Carlos Niebles Based on: Learning Low-Level Vision; by Freeman, Pasztor,Charmichael,

IJCV

, 2000.

Comparison of Graph Cuts with Believe Propagationfor Stereo, using Identical MRF Parameters; byTappen, Freeman,

ICCV

, 2003.

ECE598 Readings onComputer Vision

Contents 

Learning Low-Level Vision

Theory Behind the Method

Super-Resolution in detail

Other Problems Approached

Sources

ECE598 Readings onComputer Vision

Super-Resolution Example

^

The problem is how to obtaindetails of the represented

scene

from a finite resolution

image

^

Enlarging an 32x32 pixel areafrom the original picture, into a256x256 image (8X zoom): (a): Original Image(b) and (c): Interpolation by pixel replication

ECE598 Readings onComputer Vision

Super-Resolution Example

(b) and (c): Interpolation by pixel replication(d) and (e): Cubic-spline interpolation(f) and (g): After sharpening the interpolated

image in (d) and (e).

(h) and (i): Training-based Super-

Resolution Algorithm.

ECE598 Readings onComputer Vision

Markov Networks ^

A.k.a. Markov Random Fields (MRF)

^

An MRF for RVs

x

xN

, is an undirected graph on the

set of the RVs, along with one potential function for eachmaximal clique,

g

(xk

Ck

^

Ck

is the set of indices of the RVs in the

k

th^

maximal

clique. Clique= fully connected subgraph.Maximal Clique=A clique that cannot be made larger with still beinga clique.

The Joint Distribution is given by:

( )

(^

)

∏=

K k

C k^

k x g

Z

P^

1 1 x

ECE598 Readings onComputer Vision

Slide taken from: Bayesian Learning of Directed and Undirected Graphical Models; by ZoubinGhahramani. 2003.

( )

(^

)

∏=

K k

C k^

k x g

Z

P^

1 1 x

ECE598 Readings onComputer Vision

Inference Equations

No theoreticalsupport, butexperimentalresults are good.

TreeNetwork

Some theoreticaljustifications.

MarkovNetworkwithoutloops

Useful in nets withloops?

MAP Estimate for nets without loops

[^

]^

(^

)^

(^

)

(^

)∏

=^

k

k j

j j

x

j

jl

l j

j j

k j

x k j

M

y x

x

M y x x x M

j k

max arg

max MAP

(^

)^

(^

)

(^

) (

∏ )∏

=^ =

≠^ k

k j

j j j

x

j

jl

l j

k k j k

x k j

M x y P x P x M x y P x x P M

j k

max arg

ˆ

max MAP

ECE598 Readings onComputer Vision

Representation ^

Images and Scenes are arrays of vector valued pixelsindicating color image intensities. They are divided intopatches.

^

Dimensionality is reduced using PCA.

^

At each node, a set of 10 or 20“scene candidates” is collectedfrom the training data whichhave image data closelymatching the observation, orlocal evidence, at that node.

ECE598 Readings onComputer Vision

Contents 

Low Level Vision: Issues to solve

Theory Behind the Method

Super-Resolution in detail

Other Problems Approached

Sources

ECE598 Readings onComputer Vision

Super-Resolution problem 

The input

image

is a low-resolution image.

The

scene

to be estimated is a high-

resolution version of the same image.

Applications could include enlargement ofdigital or film pictures, upconversion ofvideo from NTCS format to HDTV, imagecompression.

ECE598 Readings onComputer Vision

Assumptions 1.

Highest resolution frequency band (

H

) is

conditionally independent of the lowerfrequency bands (

L ), given the mid-frequency

band (

M

):

Statistical relationships between image bandsare independent of image contrast, apart froma multiplicative scaling.

(^

)^

(^

) M H P L M H P |

, |^

=

ECE598 Readings onComputer Vision

Training Set after Assumptions

ECE598 Readings onComputer Vision

Learning and Inference ^

Gaussian mixtures are fitted to the joint probabilities P (

xk

,^ x

)^ j

,^ P

( y

,^ k

xk

) , and

P(x

) , using the training data set j

(40,000 image/scene pair).

^

Given a new

image

, the 10 closest training samples to

each input patch are selected.

^

The inference equations areevaluated at 10 scene candidatepoints.

(^

)^

(^

)

(^

) (

∏ )∏

=^ =

≠^ k

k j

j j j

x

j

jl

l j

k k j k

x k j

M x y P x P x M x y P x x P M

j k

max arg

ˆ

max MAP

ECE598 Readings onComputer Vision

The tiger experiment

^

Training set: 80 images(animals and urban) a.^

Nearest neighborsolution b.^

st 1 Iteration c.^

nd 2 Iteration d.^

rd 3 Iteration e.^

Input data f.^

Desired output