Machine Learning (2) Notes | EduRev

: Machine Learning (2) Notes | EduRev

 Page 1


Recap: Multiple Views and Motion 
• Epipolar geometry 
– Relates cameras in two positions 
– Fundamental matrix maps from a point in one image to a line (its 
epipolar line) in the other 
– Can solve for F given corresponding points (e.g., interest points) 
• Stereo depth estimation 
– Estimate disparity by finding corresponding points along scanlines 
– Depth is inverse to disparity 
• Motion Estimation 
– By assuming brightness constancy, truncated Taylor expansion leads to 
simple and fast patch matching across frames 
– Assume local motion is coherent 
– “Aperture problem” is resolved by coarse to fine approaches and 
iterative refinement 
 
? ? 0 ? ? ? ?
t
T
I v u I
Page 2


Recap: Multiple Views and Motion 
• Epipolar geometry 
– Relates cameras in two positions 
– Fundamental matrix maps from a point in one image to a line (its 
epipolar line) in the other 
– Can solve for F given corresponding points (e.g., interest points) 
• Stereo depth estimation 
– Estimate disparity by finding corresponding points along scanlines 
– Depth is inverse to disparity 
• Motion Estimation 
– By assuming brightness constancy, truncated Taylor expansion leads to 
simple and fast patch matching across frames 
– Assume local motion is coherent 
– “Aperture problem” is resolved by coarse to fine approaches and 
iterative refinement 
 
? ? 0 ? ? ? ?
t
T
I v u I
Machine Learning 
 
Computer Vision 
James Hays, Brown 
 
Slides:  Isabelle Guyon,  
Erik Sudderth,  
Mark Johnson, 
Derek Hoiem 
Photo: CMU Machine Learning  
Department protests G20 
Page 3


Recap: Multiple Views and Motion 
• Epipolar geometry 
– Relates cameras in two positions 
– Fundamental matrix maps from a point in one image to a line (its 
epipolar line) in the other 
– Can solve for F given corresponding points (e.g., interest points) 
• Stereo depth estimation 
– Estimate disparity by finding corresponding points along scanlines 
– Depth is inverse to disparity 
• Motion Estimation 
– By assuming brightness constancy, truncated Taylor expansion leads to 
simple and fast patch matching across frames 
– Assume local motion is coherent 
– “Aperture problem” is resolved by coarse to fine approaches and 
iterative refinement 
 
? ? 0 ? ? ? ?
t
T
I v u I
Machine Learning 
 
Computer Vision 
James Hays, Brown 
 
Slides:  Isabelle Guyon,  
Erik Sudderth,  
Mark Johnson, 
Derek Hoiem 
Photo: CMU Machine Learning  
Department protests G20 
   It is a rare criticism of elite American university 
students that they do not think big enough. But that is 
exactly the complaint from some of the largest 
technology companies and the federal government. 
   At the heart of this criticism is data. Researchers and 
workers in fields as diverse as bio-technology, 
astronomy and computer science will soon find 
themselves overwhelmed with information. 
   The next generation of computer scientists has to 
think in terms of what could be described as Internet 
scale. 
New York Times 
Training to Climb an Everest of Digital 
Data. 
By Ashlee Vance. 
Published: October 11, 2009 
 
Page 4


Recap: Multiple Views and Motion 
• Epipolar geometry 
– Relates cameras in two positions 
– Fundamental matrix maps from a point in one image to a line (its 
epipolar line) in the other 
– Can solve for F given corresponding points (e.g., interest points) 
• Stereo depth estimation 
– Estimate disparity by finding corresponding points along scanlines 
– Depth is inverse to disparity 
• Motion Estimation 
– By assuming brightness constancy, truncated Taylor expansion leads to 
simple and fast patch matching across frames 
– Assume local motion is coherent 
– “Aperture problem” is resolved by coarse to fine approaches and 
iterative refinement 
 
? ? 0 ? ? ? ?
t
T
I v u I
Machine Learning 
 
Computer Vision 
James Hays, Brown 
 
Slides:  Isabelle Guyon,  
Erik Sudderth,  
Mark Johnson, 
Derek Hoiem 
Photo: CMU Machine Learning  
Department protests G20 
   It is a rare criticism of elite American university 
students that they do not think big enough. But that is 
exactly the complaint from some of the largest 
technology companies and the federal government. 
   At the heart of this criticism is data. Researchers and 
workers in fields as diverse as bio-technology, 
astronomy and computer science will soon find 
themselves overwhelmed with information. 
   The next generation of computer scientists has to 
think in terms of what could be described as Internet 
scale. 
New York Times 
Training to Climb an Everest of Digital 
Data. 
By Ashlee Vance. 
Published: October 11, 2009 
 
Machine learning: Overview 
• Core of ML: Making predictions or decisions 
from Data. 
• This overview will not go in to depth about 
the statistical underpinnings of learning 
methods. We’re looking at ML as a tool. Take 
CS 142: Introduction to Machine Learning to 
learn more. 
 
Page 5


Recap: Multiple Views and Motion 
• Epipolar geometry 
– Relates cameras in two positions 
– Fundamental matrix maps from a point in one image to a line (its 
epipolar line) in the other 
– Can solve for F given corresponding points (e.g., interest points) 
• Stereo depth estimation 
– Estimate disparity by finding corresponding points along scanlines 
– Depth is inverse to disparity 
• Motion Estimation 
– By assuming brightness constancy, truncated Taylor expansion leads to 
simple and fast patch matching across frames 
– Assume local motion is coherent 
– “Aperture problem” is resolved by coarse to fine approaches and 
iterative refinement 
 
? ? 0 ? ? ? ?
t
T
I v u I
Machine Learning 
 
Computer Vision 
James Hays, Brown 
 
Slides:  Isabelle Guyon,  
Erik Sudderth,  
Mark Johnson, 
Derek Hoiem 
Photo: CMU Machine Learning  
Department protests G20 
   It is a rare criticism of elite American university 
students that they do not think big enough. But that is 
exactly the complaint from some of the largest 
technology companies and the federal government. 
   At the heart of this criticism is data. Researchers and 
workers in fields as diverse as bio-technology, 
astronomy and computer science will soon find 
themselves overwhelmed with information. 
   The next generation of computer scientists has to 
think in terms of what could be described as Internet 
scale. 
New York Times 
Training to Climb an Everest of Digital 
Data. 
By Ashlee Vance. 
Published: October 11, 2009 
 
Machine learning: Overview 
• Core of ML: Making predictions or decisions 
from Data. 
• This overview will not go in to depth about 
the statistical underpinnings of learning 
methods. We’re looking at ML as a tool. Take 
CS 142: Introduction to Machine Learning to 
learn more. 
 
Impact of Machine Learning 
 
• Machine Learning is arguably the greatest 
export from computing to other scientific 
fields. 
 
 
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