Robert Collins
CSE486, Penn State
Lecture 15
Robust Estimation : RANSAC
Robert Collins
CSE486, Penn State
RECALL: Parameter Estimation:
Lets say we have found point matches between two images, and
we think they are related by some parametric transformatio
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
CSE/EE 486: Computer Vision I
Fall 2007 Course Overview
Textbook
required
Introductory Techniques for 3-D Computer Vision
by E. Trucco and A. Verri, Prentice Hall, 1998.
Robert Collins
CS
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
I have put some Matlab image tutorials on Angel.
Please take a look if you are unfamiliar with Matlab
or the image toolbox.
Lecture 3:
Linear Operators
Robert Collins
CSE486, Penn State
A
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Summary about Convolution
Computing a linear operator in neighborhoods centered at each
pixel. Can be thought of as sliding a kernel of fixed coefficients
over the image, and doing a weig
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Stereo Vision
Inferring depth from images taken at the same
time by two or more cameras.
Lecture 08:
Introduction to Stereo
Reading: T&V Section 7.1
Scene Point
y
Image Point
p = (x,y,f)
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Motivation: Matchng Problem
Vision tasks such as stereo and motion estimation require
finding corresponding features across two or more views.
Lecture 06:
Harris Corner Detector
Reading:
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Visualizing Images
Recall two ways of visualizing an image
Intensity pattern
2d array of numbers
Lecture 2:
Intensity Surfaces
and Gradients
We see it at this level
Robert Collins
CSE486,
Robert Collins
CSE486
Robert Collins
CSE486
Recall
Cascaded Gaussians
Lecture 10:
Pyramids and Scale Space
Robert Collins
CSE486
Example: Cascaded Convolutions
Robert Collins
CSE486
G*(G*f) = (G*G)*f [associativity]
Robert Collins
CSE486
Aside: Binomial
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Recall: Derivative of Gaussian Filter
Ix=dI(x,y)/dx
Gx
I(x,y)
Lecture 7:
Correspondence Matching
convolve
Gy
Reading: T&V Section 7.2
Iy=dI(x,y)/dy
convolve
Robert Collins
CSE486, Penn St
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Recall: Simple Stereo System
Z
Y
left
y
camera
located at
(0,0,0)
Lecture 09:
Stereo Algorithms
(X,Y,Z)
z
( ,
z
)
y
x
Tx
( ,
)
right
camera
located at
(Tx,0,0)
x
Image coords of point (X,
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Recall: Imaging Geometry
W
Object of Interest
in World Coordinate
System (U,V,W)
Lecture 13:
Camera Projection II
Robert Collins
CSE486, Penn State
Y
Z is optic axis
Image plane located
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Imaging Geometry
W
Object of Interest
in World Coordinate
System (U,V,W)
Lecture 12:
Camera Projection
Robert Collins
CSE486, Penn State
Y
Z is optic axis
Image plane located f units
ou
Robert Collins CSE486, Penn State
Robert Collins CSE486, Penn State
RECALL: Parameter Estimation:
Lecture 15 Robust Estimation : RANSAC
Let's say we have found point matches between two images, and we think they are related by some parametric transformati
Robert Collins
CSE486
Robert Collins
CSE486
Laplacian of Gaussian (LoG) Filter
- useful for finding edges
- also useful for finding blobs!
Lecture 11:
LoG and DoG Filters
Robert Collins
CSE486
approximation using Difference of Gaussian (DoG)
Recall: First
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Summary: Transformations
Euclidean
Lecture 14
Parameter Estimation
similarity
Readings T&V Sec 5.1 - 5.3
affine
projective
Robert Collins
CSE486, Penn State
Parameter Estimation
We will t
Robert Collins
CSE486
Lecture 11:
LoG and DoG Filters
Robert Collins
CSE486
Todays Topics
Laplacian of Gaussian (LoG) Filter
- useful for finding edges
- also useful for finding blobs!
approximation using Difference of Gaussian (DoG)
Robert Collins
CSE486
Robert Collins
CSE486, Penn State
Lecture 3:
Linear Operators
Robert Collins
CSE486, Penn State
Administrivia
I have put some Matlab image tutorials on Angel.
Please take a look if you are unfamiliar with Matlab
or the image toolbox.
I have posted Homewor
Robert Collins
CSE486, Penn State
Lecture 7:
Correspondence Matching
Reading: T&V Section 7.2
Robert Collins
CSE486, Penn State
Recall: Derivative of Gaussian Filter
Ix=dI(x,y)/dx
Gx
I(x,y)
convolve
Gy
Iy=dI(x,y)/dy
convolve
Robert Collins
CSE486, Penn St
Robert Collins
CSE486, Penn State
Lecture 09:
Stereo Algorithms
Robert Collins
CSE486, Penn State
Recall: Simple Stereo System
Z
Y
left
y
camera
located at
(0,0,0)
z
(
,
x
Image coords of point (X,Y,Z)
Left Camera:
Camps, PSU
z
)
Tx
Right Camera:
(X,Y,Z)
Robert Collins
CSE486, Penn State
Lecture 16:
Planar Homographies
Robert Collins
CSE486, Penn State
Motivation:
Points on Planar Surface
y
x
Robert Collins
CSE486, Penn State
Review : Forward Projection
World
Coords
Camera
Coords
Film
Coords
U
V
W
X
Y
Z
x
Robert Collins
CSE486, Penn State
Lecture 14
Parameter Estimation
Readings T&V Sec 5.1 - 5.3
Robert Collins
CSE486, Penn State
Summary: Transformations
Euclidean
similarity
affine
projective
Robert Collins
CSE486, Penn State
Parameter Estimation
We will t
Robert Collins
CSE486, Penn State
Lecture 06:
Harris Corner Detector
Reading: T&V Section 4.3
Robert Collins
CSE486, Penn State
Motivation: Matchng Problem
Vision tasks such as stereo and motion estimation require
finding corresponding features across two
Robert Collins
CSE486, Penn State
Lecture 08:
Introduction to Stereo
Reading: T&V Section 7.1
Robert Collins
CSE486, Penn State
Stereo Vision
Inferring depth from images taken at the same
time by two or more cameras.
Robert Collins
CSE486, Penn State
Basi
Robert Collins CSE486
Lecture 10: Pyramids and Scale Space
Robert Collins CSE486
Recall
Repeated convolution by a smaller Gaussian to simulate effects of a larger one.
Cascaded Gaussians G*(G*f) = (G*G)*f [associativity]
Robert Collins CSE486
Example: C
Robert Collins
CSE486, Penn State
Lecture 5:
Gradients and Edge Detection
Reading: T&V Section 4.1 and 4.2
Robert Collins
CSE486, Penn State
What Are Edges?
Simple answer: discontinuities in intensity.
Robert Collins
CSE486, Penn State
Boundaries of objec
Robert Collins
CSE486, Penn State
Lecture 17:
Mosaicing and Stabilization
Robert Collins
CSE486, Penn State
Recall: Planar Projection
Internal
params
Perspective
projection
u
Pixel coords
v
y
Homography
x
Rotation + Translation
Point on plane
Robert Colli
Robert Collins
CSE486, Penn State
Robert Collins
CSE486, Penn State
Lecture 18:
Generalized Stereo
Key idea: Any two images showing an overlapping
view of the world can be treated as a stereo pair.
Generalized Stereo:
Epipolar Geometry
. we just have to f
Robert Collins
CSE486, Penn State
Lecture 2:
Intensity Surfaces
and Gradients
Robert Collins
CSE486, Penn State
Visualizing Images
Recall two ways of visualizing an image
Intensity pattern
We see it at this level
2d array of numbers
Computer works at this
Robert Collins
CSE486, Penn State
Lecture 4:
Smoothing
Related text is T&V Section 2.3.3 and Chapter 3
Robert Collins
CSE486, Penn State
Summary about Convolution
Computing a linear operator in neighborhoods centered at each
pixel. Can be thought of as sl
Robert Collins
CSE486, Penn State
Lecture 12:
Camera Projection
Reading: T&V Section 2.4
Robert Collins
CSE486, Penn State
Imaging Geometry
W
Object of Interest
in World Coordinate
System (U,V,W)
U
V
Robert Collins
CSE486, Penn State
Imaging Geometry
Came