Perception for Robots - University Of Maryland · Perception for Robots I. BASICS Thanks to Peter...
Transcript of Perception for Robots - University Of Maryland · Perception for Robots I. BASICS Thanks to Peter...
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Perception for Robots
I.
BASICS
Thanks to Peter Corke for the use of some slides
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What is a robot
• For the purposes of this class a robot is a goal oriented machine that can sense, reason and act.
sensing
reasoning acting
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BASIC QUESTIONS
• Where am I
• Where are you
• What are you
• How do I get there
• How to achieve a task
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Where am I
• Why not use GPS?
GPS is not perfect and has severe limitations is environments where robots are needed:
--- cities, mines, industrial sites, underwater,
deep forest.
It only tells where I am
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Urban Canyon Problem
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Industrial sites, mines
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Underwater, deep forest
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Humans and animals have a number of senses
• Sight
• Hearing
• Touch
• Smell
• Taste
• Balance
• Echolocation: bats, electric fields: sharks, compass: birds
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Vision
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Hearing
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Echolocation of bats
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Electric field sensing
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Magnetic field sensing
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Vision: most powerful sense
• Essential for survival: finding food, avoiding being food, finding mates
• Long range sensing: beyond our fingertip (vision is our way to touch the world)
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Evolution of the eye½ billion years
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Climbing mount improbable10 different designs
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A plethora of eyes
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Complex Eyes
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Compound eyes
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Human Eyes
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Two kinds of eyes at the top:Camera type or planar
Spherical
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Many cameras in the market
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Catadioptric – panoramic images
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How does Vision work?
• Ancient Greeks: Extramission Theory
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Descartes got it right
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Many theories over the centuries
• The Gestaltists
• Von Helmholz: Unconscious inference
• David Marr: A reconstruction process that tells us where is what.
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Theories influenced by the zeitgeist
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Animal perception is active
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Measuring eye movements
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Robots with Vision
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PR2 Humanoid
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Perception for Robots3 major problems
• Reconstruction
• Reorganization
• Recognition
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Reconstruction
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Reorganization: segmentation
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Reorganization: flow
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Recognition
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Images and Videos Contain
• Lines (contours, edges)
• Intensity and Color
• Texture
• movement
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Lines
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Color, Texture
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Motion
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Contents of the Class
• Image Processing: Images, Light and Color, Filtering, Noise, Convolution, Edge detection, contour finding, texture analysis, segmentation and grouping.
• 3D Geometry: Stereo, Multiple View Geometry, Epipolar Geometry, Projective Geometry
• Motion: Optical Flow, Egomotion, Motion Segmentation, Tracking
• Navigation: Map making, SLAM
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Break
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A theoretical model of an eye
• Pick a point in space and the light rays passing through
O
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Then cut the rays with a plane
• This gives an image
O
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Pinhole cameras
• Abstract camera
model - box with a
small hole in it
• Pinhole cameras
work in practice
(Forsyth & Ponce)
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If we change the plane, we get an new image
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How are these images related?(what remains invariant?)
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Conics
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Projection of circle
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Vanishing points
• Vanishing point
– projection of a point at infinity
image plane
cameracenter
ground plane
vanishing point
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Vanishing points (2D)image plane
cameracenter
line on ground plane
vanishing point
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Vanishing points
• Properties
– Any two parallel lines have the same vanishing point v
– The ray from C through v is parallel to the lines
– An image may have more than one vanishing point
image plane
cameracenter
C
line on ground plane
vanishing point V
line on ground plane
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Parallelism (angles) not invariant
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Cross ratio = only invariant
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Back to our question: how are the 2 images related to each other
Can we find a map, a function mapping x’ to x?
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Fundamental Theorem: If we know how 4 points map to each other in the two planes, then we know how all points map. (if aA, bB, cC,dD, then we can
map any point)
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Proof
a
b
d
cA
B
D
C
p P
s
S
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(0,0,0)
The projective plane• Why do we need homogeneous coordinates?
– represent points at infinity, homographies, perspective projection, multi-view relationships
• What is the geometric intuition?– a point in the image is a ray in projective space
(sx,sy,s)
• Each point (x,y) on the plane is represented by a ray (sx,sy,s)
– all points on the ray are equivalent: (x, y, 1) (sx, sy, s)
image plane
(x,y,1)
y
xz
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Projective lines• What does a line in the image correspond
to in projective space?
• A line is a plane of rays through origin
– all rays (x,y,z) satisfying: ax + by + cz = 0
z
y
x
cba0 :notationvectorin
• A line is also represented as a homogeneous 3-vector l
l p
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l
Point and line duality– A line l is a homogeneous 3-vector
– It is to every point (ray) p on the line: l p=0
p1p2
What is the intersection of two lines l1 and l2 ?
• p is to l1 and l2 p = l1 l2
Points and lines are dual in projective space
• given any formula, can switch the meanings of points and
lines to get another formula
l1
l2
p
What is the line l spanned by rays p1 and p2 ?
• l is to p1 and p2 l = p1 p2
• l is the plane normal
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Ideal points and lines
• Ideal point (“point at infinity”)– p (x, y, 0) – parallel to image plane
– It has infinite image coordinates
(sx,sy,0)y
x
z image plane
Ideal line
• l (a, b, 0) – parallel to image plane
(a,b,0)
y
x
z image plane
• Corresponds to a line in the image (finite coordinates)
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Fundamental Theorem(homography or collineation)
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Projective vs Affine
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Rectification