ECE 181b Homework 2
Spring 2006
1
Image of Line in 3D
Question 1 Show Analytically that the image of a line in 3-D space is a line
in the image. Assume perspective projection.
10 points
Answer 1 The equation of a straight line in 3D is
x = mx z + bx
y = m
Image Recognition
Local or Global?
Tuesday, March 2, 2010
Project
Eigenfaces for Face Recognition
Bag of Features for Object Classication
Tuesday, March 2, 2010
Bag-of-features models
from Fei-Fei Li, Rob Fergus, and Antonio Torralba
Tuesday, March 2, 2
An Overview of Face Recognition Using
Eigenfaces
Acknowledgements: Original Slides from
Prof. Matthew Turk
- also notes from the web
-Eigenvalues and Eigenvectors
-PCA
-Eigenfaces
Eigenfaces
Monday, February 22, 2010
1
Outline
Why automated face recognit
Camera Models
Acknowledgements
Marc Pollefeys for some of the slides
Hartley and Zisserman: book figures from the web
Matthew Turk: for some of the slides
Spring 2006
Thursday, February 18, 2010
Camera Models
Single view geometry
A camera is a mapping bet
Epipolar Geometry
CS / ECE 181B
Chapter 9, Hartley & Zisserman
(available online free,
http:/www.robots.ox.ac.uk/~vgg/hzbook/hzbook1.html)
Spring 2006
Thursday, February 18, 2010
Stereo
Ack: M. Turk and M. Pollefeys
1
Seeing in 3D
Humans can perceive dep
Stereo matching
Stereo matching is the correspondence problem
For a point in Image #1, where is the corresponding point in
Image #2?
Thursday, February 18, 2010
Stereo matching
Stereo matching is the correspondence problem
For a point in Image #1, whe
Projective Transformations
Acknowledgements
Marc Pollefeys: for allowing the use of his excellent slides on this topic
http:/www.cs.unc.edu/~marc/mvg/
Richard Hartley and Andrew Zisserman, "Multiple View Geometry in Computer Vision"
Spring 2006
Friday, Fe
Projective geometry- 2D
Acknowledgements
Marc Pollefeys: for allowing the use of his excellent slides on this topic
http:/www.cs.unc.edu/~marc/mvg/
Richard Hartley and Andrew Zisserman, "Multiple View Geometry in Computer Vision"
Spring 2006
Wednesday, Fe
Week 4
CS/ECE 181B
SIFT
Scale Invariant Feature Transform
Lowe, David G. Distinctive Image Features from Scale Invariant Features, International
Journal of Computer Vision, Vol. 60, No. 2, 2004, pp. 91-110
Good software reference
http:/www.vlfeat.org/inde
Linear Filtering
CS / ECE 181B
Ack: Prof. Matthew Turk for the slides
Monday, January 11, 2010
Linear Filtering
CS / ECE 181B
Today
Convolution, Fourier Transforms and
Correlation
Ack: Prof. Matthew Turk for the slides
Monday, January 11, 2010
Area opera
Final Exam
ECE/CS 181b
June 12, 2008
Name:
This is a closed book/notes examination. Calculators
and other devices with memory are not allowed.
Instructions: All questions on this exam are weighted equally. To receive
full credit, answer the following ques
Introduction to Computer Vision
CS / ECE 181B
Prof. Matthew Turk
Adam Ibrahim
Today
Final exam review
Everything we covered is important, but here is a
reminder of the primary topics and principles of the
quarter
Final exam
Next Friday, noon-3pm in regul
Depth of Focus/Field
Blur is caused (primarily) by imaging points away from the
focal plane
Depending on sensor resolution, small amounts of blur may
not matter
All in focus
Partly in focus
1
1
Depth of focus/field
Depending on sensor resolution, small
Linear Algebra Primer
Dr. Juan Carlos Niebles
Stanford AI Lab
Prof. Fei-Fei Li
Stanford Vision Lab
Another, very in-depth linear algebra review from CS229 is available here:
hIp:/cs229.stanford.edu/secLon/cs229-linalg.p
Lecture 5:
Edge Detec.on
Dr. Juan Carlos Niebles
Stanford AI Lab
Professor Fei-Fei Li
Stanford Vision Lab
Fei-Fei Li
Lecture 5 - 1
10-Oct-16
What we will learn today
Edge detec.on
A simple edge detector
Canny edge detector
A model Mng method
CIE 1931 color matching functions
Compute tristimulus values (X, Y, Z) from the input light (power
spectrum)
Dot products between the input light and the three curves, as
weve already seen in the readings
Rather than regular R, G, and B curves, we use
Histogram Equalization / Edge
Detection / Image Pyramids
Histogram equalization
A method to improve contrast in an image, by stretching out
the intensity range
2
Histogram equalization
Examples of images that may need equalization:
Bright images
Dark im
Finding Patterns in an Image
Convolution and Correlation
Convolution
F is the image
H is the pattern or kernel
R is the output image
M 1N1
Rij H m n Fi m , j n
m 0 n 0
Correlation
Same as convolution without the flip
Correlation
Cross Correlation: Tw
The Hough Transform
For finding lines from edges
Example
Edge points
Strongest lines
How can we automatically find these two lines from the edge points?
2
Hough Transform
Two issues
Identity: there are so many edge points, which ones should be grouped
t
Segmentation and clustering
Segmentation is about labeling similar
pixels as belonging to the same group
or segment
Pixels that belong together = pixels that
cluster
Clustering can be done along many
dimensions (intensity, color, depth,
motion, texture
Vanishing points and horizon lines
Lines under perspective projection have
vanishing points, while planes have vanishing
lines.
We can learn some things about a scene by
looking at image lines and points.
Vanishing point
The vanishing point of a straig
Template matching
Goal: find
in image
An image patch representing
an eye
Main challenge: What is a
good similarity or distance
measure between two
image patches?
Correlation
Zero-mean correlation
Sum of Squared Differences
Normalized Cross Correlat
Mahalanobis distance
Given existing clusters,
what constitutes a good
measure for the distance of
a vector to these clusters ?
Is the Euclidean distance even appropriate ?
Picture modified from https:/web.stanford.edu/class/cs345a/slides/12-clustering.p
Representing 3D rotation Quaternions
Quaternion
q (qw , q x , q y , q z )
or
q 1
How many DOF?
q ( w, x, y, z )
Inverse:
q 1 ( qw , q x , q y , q z ) (qw , q x , q y , q z )
Quaternion from axis/angle (n , ) :
Rotation matrix from quaternion:
x 2 y 2
Image formation & processing
January 2010
Sunday, January 10, 2010
Image Formation
Geometry of image formation
(camera models and calibration)
where?
Radiometry of image formation
how bright?
2
Sunday, January 10, 2010
Digital images
Were interested
ECE 181b Homework 3
Image Rectication
April 20, 2006
The goal of this project is to explore some fundamental concepts of projective geometry
related to the problem of image rectication. We will rectify the image of one of the facades
of the Bren School of
Introduction to Computer Vision
CS / ECE 181B
Thursday, April 13, 2004
Image Formation
Course web site
http:/www.ece.ucsb.edu/~manj/cs181b
http:/www.ece.ucsb.edu/~manj/ece181b
Not a substitute for attending the class
Note that not all lecture are in P