Camera Calibration
Machine Vision (CIS 580)
Lens configuration (internal parameter)
x
X
1 = L K [R t ] 1
Spatial relationship between sensor and pinhole
(internal parameter)
Camera body configuration
(extrinsic parameter)
Why Do We Calibrate?
To
CIS 580 Spring 2013 - Lecture 5
January 30, 2013
Notes and gures by Matthieu Lecce.
2D Fourier Transform
Review:
f ( x, y)
F ( x , y )
1
2
f ( x, y)e j x x+y y dxdy
F ( x , y )e. d x dy
Results from last lecture:
Shift
Ane transformation:
x
f A
CIS 580 Spring 2013 - Lecture 6
Filters for detection
February 4, 2013
Notes and gures by Matthieu Lecce.
In this section, we are interested in building lters to detect patterns in a
signal. By pattern we mean a portion of the signal with a distinctive be
CIS 580 Spring 2013 - Lecture 7
February 6, 2013
Notes and gures by Matthieu Lecce.
Note on steerability of derivative lters
A filter is steerable when its response in any orientation can be
computed as a linear combination of the responses from a few lte
CIS 580 Spring 2013 - Lecture 9
February 13, 2013
Notes and gures by Matthieu Lecce.
Scale Space and Scale Invariant features
Last time, we introduced the diusion equation
L
= 1
t 2D 2
2L
with boundary
conditions L( x, y, t = 0) = I ( x, y), and said that
CIS 580 Spring 2013 - Lecture 12
February 25, 2013
Notes and gures by Matthieu Lecce.
Summary of the course so far
We used the Fourier transform to analyze a signal/image in terms of its
frequencies. We used the frequency domain to design proper lters th
CIS 580 Spring 2013 - Lecture 16
March 20, 2013
Notes and gures by Matthieu Lecce.
Review: Projective plane P2
P2 is the set of all projective equivalence classes, with projective equivalence dened as:
0
x x
x
x
x x
y y i 0 y = y fo
CIS 580 Spring 2013 - Lecture 18
March 27, 2013
Notes and gures by Matthieu Lecce &
Menglong Zhu.
Single-view geometry
Recover focal length from 2 vanishing points
Lets relate the projections of the vanishing points to the extrinsic and intrinsic camera p
CIS 580 Spring 2013 - Lecture 22
April 10, 2013
Notes and gures by Matthieu Lecce.
Reconstruction from two calibrated views
Structure from motion, epipolar geometry
We want to estimate the transformation between two camera and the 3D
positions of a set of
CIS 580, Machine Perception, Spring 2015
Project 1
Due: 2015.03.16. 11:59AM
Instructions. Submit your complete code to turnin. Note that this is an individual assignment.
In this project, you will estimate intrinsic parameters, i.e., focal length scale fa
Project 2: Structure from Motion
CIS 580, Machine Perception, Spring 2015
Preliminary report due: 2015.04.27. 11:59AM
Final Due: 2015.05.06. 11:59AM
This project aims to reconstruct a 3D point cloud and camera poses of 6 images as shown in Figure 1.
Your
CIS 580, Machine Perception, Spring 2013: Assignment 1
Due: Wednesday, January 23rd, 10:30am (use turnin)
Solutions (hand calculations, plots) have to be submitted electronically as a single pdf le using the turnin command below. No Word documents are acc
CIS 580, Machine Perception, Spring 2013: Assignment 2
Due: Wednesday, February 6th, 10:30am (before class) (use turnin)
Solutions (hand calculations, plots) have to be submitted electronically as a single pdf le using the turnin command below. No Word do
CIS 580, Machine Perception, Spring 2013: Assignment 3
Due: Fri Feb 2nd, 5:00 pm (use turnin)
Solutions (hand calculations, plots) have to be submitted electronically as a single pdf le using the turnin command below. No Word documents are accepted. Pleas
CIS 580 Spring 2013 - Lecture 4
January 28, 2012
Notes and gures by Matthieu Lecce.
Review from last lecture:
A discrete signal still has a continuous Fourier:
L1
h[n]e jn
h[n]
n=0
2s
L
2k
=
H [k ]
L
=
DFT
Remember the eect of derivation in Fourier dom
CIS 580 Spring 2012 - Lecture 3
January 25, 2012
Notes and gures by Matthieu Lecce.
Review from last lecture:
Sampling (or time-sampling) is a multiplication with the comb function
X(t) = (t nT ) (innite trail of Dirac functions).
n=
2n
n= ( T )
It corr
CIS 580 Spring 2013 - Lecture 2
January 16, 2013
Notes and gures by Matthieu Lecce.
Updated by Nicu Stiurca
Last lectures main result: linear shift-invariant (LSI) systems can be represented as a convolution.
The Fourier Transform
Quick reminder on comple
Single View Geometry
Camera model &
Orientation +
Position estimation
Jianbo Shi
What am I?
University of Pennsylvania
GRASP
1
Camera projection model
The overall goal is to compute 3D geometry of the scene
from just 2D images. We will first study 3D->2D
Linear Algebra Simplified
Readings
http:/szeliski.org/Book/drafts/SzeliskiBook_20100903_draft.pdf
-2.1.5 for camera geometry,
-2.1.3, 2.1.4 for rotation representation
Inner (dot) Product
v
w
& y1 #
$ !
T
v w = ( x1 , x2 , x3 )$ y2 ! = x1 y1 + x2 . y2 + x
Projec've Gemeotry
Jianbo Shi
Some slides taken from Steve Seitz
Measuring eld of view, by hand
Measuring focal point (nodal point), by hand
A Ligh'ng Reproduc'on Approach to Live-Ac'on Composi'ng, P. Debevec 2002
Lens Distor+on
Field Curvature
Joseph Petzval, a 19th century Hungarian
mathema+cian and physicist, Petzval eld
curvature describes an op+cal aberra+on
where the sharpest focus of the lens is on a
curved surface in t
Single View Metrology
Slides taken from Steve Seitz, A. Efros
Applica=ons of projec=ve geometry
Vermeers Music Lesson
Criminisi et al., Single View Metrology, ICCV 1999
Other methods
Horry et al., Tour Into the Pict
Camera model
world coordinates
ZW
image plane
coordinates
ZC
YC
XW
u
v
YW
optical axis
XC
camera coordinates
world coordinate system coordinates (Xw , Yw , Zw ),
camera coordinate system coordinates (Xc, Yc, Zc).
image homogeneous coordinates (u, v). The
Notes on Elementary Spectral Graph Theory
Applications to Graph Clustering
Jean Gallier
Department of Computer and Information Science
University of Pennsylvania
Philadelphia, PA 19104, USA
e-mail: jean@cis.upenn.edu
c Jean Gallier
February 17, 2013
2
Con
Rotation
Rotation
Rotation = axis + angle
Anders Adermark @ flickr
30 minutes shutter time. How cool isn't this? You see the stars
above the north axis of our globe being fixed, and then the circles
gets wider and wider the further you get from them.
Axi
Binocular Stereo
Philippos Mordohai
University of North Carolina at Chapel Hill
September 21, 2006
Outline
Introduction
Cost functions
Challenges
Cost aggregation
Optimization
Binocular stereo algorithms
2
Stereo Vision
Match something
Feature-based alg
CIS 580
Camera
Jianbo Shi
camera
Moments: sele
Reid Wiseman and Alexander Gerst
with a Nikon D2X and a Nikkor
10.5mm sheye lens,
DATE:1920
Side view of
photographers
posing together for a
photograph on the
roof of Marceau's
Studio, while Joseph
Machine Perception CIS 580 Spring 2012
Grading Policy: Homeworks 50%, Midterm 20%, Final 30%
Homeworks on paper and using Matlab.
Midterm is on paper.
Final is a project including paper calculations and Matlab.
Resources:
Szeliskis book
http:/research.mic
CIS 580 Spring 2012 - Lecture 16
March 14, 2012
Notes and gures by Matthieu Lecce.
Review: Projective plane P2
P2 is the set of all projective equivalence classes, with projective equivalence dened as:
0
x x
x
x
x x
y y i 0 y = y fo
CIS 580 Spring 2012 - Lecture 1
January 14, 2013
Notes and gures by Matthieu Lecce.
Updated by Nicu Stiurca.
Linear Shift-Invariant (LSI) Systems
Consider a continuous signal f : R R, t f (t ) and a lter f (t )
g(t ) = T cfw_ f (t ):
Figure 1: A lter rep