05/04/2010
Computer Vision: Summary and
Anti-summary
Computer Vision
CS 543 / ECE 549
University of Illinois
Derek Hoiem
Today’s class
• Administrative stuff
– HW 4 due
– Posters next Tues + reports due
– Feedback and Evaluation (end of class)
• Review of important concepts
• Anti-summary: important concepts that were not
covered
• Wide open problems
Review
•
•
•
•
Geometry
Matching
Grouping
Categorization
Geometry (on board)
• Projection matrix P = K [R t] relates 2d point x
and 3d point X in homogeneous coordinates:
x=PX
• Parallel lines in 3D converge at the vanishing
point in the image
– A 3D plane has a vanishing line in the image
• In two views, points that correspond to the
same 3D point are related by the fundamental
matrix: x’T F x = 0
Matching
• Does this patch match that patch?
– In two simultaneous views? (stereo)
– In two successive frames? (tracking, flow, SFM)
– In two pictures of the same object? (recognition)
?
?
Matching
Representation: be invariant/robust to expected
deformations but nothing else
• Change in viewpoint
– Rotation invariance: rotate and/or affine warp patch according to
dominant orientations
• Change in lighting or camera gain
– Average intensity invariance: oriented gradient-based matching
– Contrast invariance: normalize gradients by magnitude
• Small translations
– Translation robustness: histograms over small regions
But can one representation do all of this?
• SIFT: local normalized histograms of
oriented gradients provides robustness to
in-plane orientation, lighting, contrast, translation
• HOG: like SIFT but does not rotate to dominant orientation
Matching
Search: efficiently localize matching patches
• Interest points: find repeatable, distinctive points
– Long-range matching: e.g., wide baseline stereo, panoramas,
object instance recognition
– Harris: points with strong gradients in orthogonal directions
(e.g., corners) are precisely repeatable in x-y
– Difference of Gaussian: points with peak response in Laplacian
image pyramid are somewhat repeatable in x-y-scale
• Local search
– Short range matching: e.g., tracking, optical flow
– Gradient descent on patch SSD, often with image pyramid
• Windowed search
– Long-range matching: e.g., recognition, stereo w/ scanline
Matching
Registration: match sets of points that satisfy deformation
constraints
• Geometric transformation (e.g., affine)
– Least squares fit (SVD), if all matches can be trusted
– Hough transform: each potential match votes for a range of
parameters
• Works well if there are very few parameters (3-4)
– RANSAC: repeatedly sample potential matches, compute parameters,
and check for inliers
• Works well if fraction of inliers is high and few parameters (4-8)
• Other cases
– One-to-one correspondence (Hungarian algorithm)
– Small local deformation of ordered points
A1
A2
A3
Grouping
• Clustering: group items (patches, pixels, lines, etc.) that have similar
appearance
– Discretize continuous values; typically, represent points within cluster
by center
– Improve efficiency: e.g., cluster interest points before recognition
– Enable counting: histograms of interest points, color, texture
• Segmentation: group pixels into regions of coherent color, texture,
motion, and/or label
– Mean-shift clustering
– Watershed
– Graph-based segmentation: e.g., MRF and graph cuts
• EM, mixture models: probabilistically group items that are likely to
be drawn from the same distribution, while estimating the
distributions’ parameters
Categorization
Match objects, parts, or scenes that may vary in
appearance
• Categories are typically defined by human and may be related
by function, cost, or other non-visual attributes
• Naïve matching or clustering approach will usually fail
– Elements within category often do not have obvious visual similarities
– Possible deformations are not easily defined
• Typically involves example-based machine learning approach
Training
Labels
Training
Images
Image
Features
Classifier
Training
Trained
Classifier
Categorization
Representation: ideally should be compact,
comprehensive, direct
• Histograms of quantized interest points (SIFT, HOG),
color, texture
– Typical for image or region categorization
– Degree of spatial invariance is controllable by using spatial
pyramids
• HOG features at specified position
– Often used for finding parts or objects
Object Categorization
Sliding Window Detector
• May work well for rigid objects
• Combines window-based matching search
with feature-based classifier
Object or
Background?
Object Categorization
Parts-based model
• Defined by models of part appearance,
geometry or spatial layout, and search
algorithm
• May work better for articulated objects
Vision as part of an intelligent system
3D Scene
Feature
Extraction
Texture
Grouping
Surfaces
Interpretation
Action
Objects
Color
Bits of
objects
Agents
and goals
Optical
Flow
Stereo
Disparity
Sense of
depth
Motion
patterns
Shapes and
properties
Open
paths
Words
Walk, touch, contemplate, smile, evade, read on, pick up, …
Anti-summary
• Summary of things not covered
Term “anti-summary” from Murphy’s book “Big Book of Concepts”
Context
Hock, Romanski, Galie, & Williams 1978
• Biederman’s Relations among Objects in a Well-Formed Scene
(1981):
– Support
– Position
– Size
– Interposition
– Likelihood of Appearance
Machine learning
• Probabilistic approaches
– Logistic regression
– Bayesian network (special case: tree-shaped
graph)
• Support vector machines
• Energy-based approaches
– Conditional random fields (special case: lattice)
– Graph cuts and belief propagation (BP-TRW)
Further reading:
• Learning from Data: Concepts, Theory, and Methods by Cherkassky and Muliel (2007): I have not
read this, but reviews say it is good for SVM and statistical learning)
• Machine Learning by Tom Mitchell (1997): Good but somewhat outdated introduction to learning
• Heckerman’s tutorial on learning with Bayesian Networks (1995)
3D Object Models
• Aspect graphs (see Forsyth and Ponce)
• Model 3D spatial configuration of parts
– E.g., see recent work by Silvio Savarese and others
Action recognition
• Common method: compute SIFT + optical flow
on image, classify
• Starting to move beyond this
http://vision.stanford.edu/documents/YaoFei-Fei_CVPR2010b.pdf
Tennis serve
Volleyball smash
Geometry
• Beyond pinhole cameras
– Special cameras, radial distortion
• Geometry from 3 or more views
– Trifocal tensors
Much of this covered in Forsyth and Ponce or Hartley and Zisserman
Other sensors
• Infrared, LIDAR, structured light
http://bighugelabs.com/onblack.php?id=527329336
Physics-based vision
• Models of atmospheric effects, reflection,
partial transparency
– Depth from fog
– Removing rain from photos
– Rendering
– See Shree Nayar’s projects:
http://www.cs.columbia.edu/CAVE/projects/pbv.php
Wide-open problems
Computer vision is potentially worth billions per
year, but there are major challenges to overcome
first.
Major $$$
• Driver assistance (MobileEye received >$100M in
funding from Goldman Sachs)
• Entertainment (MS Natal and others)
• Robot workers
Wide-open problems
• How do you represent actions and activities?
– Probably involves motion, pose, objects, and goals
– Compositional
Wide-open problems
• How to build vision systems that manage the
visual world’s complexity?
– Potentially thousands of categories but it depends
how you think about it
Wide-open problems
• How should we adjust vision systems to solve
particular tasks?
– How do we know what is important?
Wide-open problems
• Can we build a “core” vision system that can
easily be extended to perform new tasks or
even learn on its own?
– What kind of representations might allow this?
– What should be built in and what should be
learned?
See you next week!
• Projects on Tuesday
– Pizza provided
– Posters: 24” wide x 32” tall
• Online feedback forms
Wide-open problems
• How do you represent actions and activities?
– Usually involve motion and objects
– Compositional
– Probably involves motion fields + pose estimation + object recognition + goal
reasoning
• How to build vision systems that manage the visual world’s complexity?
– Potentially thousands of categories but it depends how you think about it
• How should we adjust vision systems to solve particular tasks?
– How do we know what is important?
• Can we build a “core” vision system that can easily be extended to
perform new tasks or even learn on its own?
– What should be built in and what should be learned?
– What kind of representations might allow this?
Anti-summary outline
•
Context
– (well-formed scene)
•
•
Physics-based vision
Machine learning
– Probabilistic approaches
•
•
Logistic regression
Bayesian network (special case: tree-shaped graph)
– Support vector machines
– Energy-based approaches
•
•
•
Conditional random fields (special case: lattice)
Graph cuts and belief propagation (BP-TRW)
Action recognition
– Current methods: bag of SIFT + optical flow
•
Geometry
– Beyond perspective projection (non-pinhole cameras, radial distortion)
– Tri-focal tensors
•
Object recognition
– Aspect graphs (how does an object’s appearance change as you move around it?)
– 3D object models
•
Other sensors: laser range finders, infrared, structured light
The Vision Process
• Scene  two eyes  extract low-level
representation: {color, edges/bars/blobs,
motion, stereo}  interpretation: {3D
surfaces, physical properties, distance, objects
of interest, reading, reasoning about agents,
adjusting actions}
Summary outline
• Geometry
– Single-view (projection matrix)
– Multiview (epipolar geometry)
– Vanishing points + SFM + stereo
• Matching
– Image filtering
– Interest points
– RANSAC and Hough
• Tracking
– Repeated detection + simple motion model (e.g., doesn’t move
far, constant velocity)
• Categorization
– HOG + histograms
– Matching and modeling