Computer Vision: Summary and Anti-summary

Computer VisionCS 543 / ECE 549

University of Illinois

Derek Hoiem

05/04/2010

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 = P X

• 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)

? ?

MatchingRepresentation: 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

MatchingSearch: 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

MatchingRegistration: 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

B1B2

B3

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

CategorizationMatch 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 LabelsTraining

Images

Classifier Training

Image Features

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

FeatureExtraction

Interpretation

Action

Texture Color Optical Flow

Stereo Disparity

Grouping Surfaces Bits of objects

Sense of depth

Objects Agents and goals

Shapes and properties

Open paths Words

Walk, touch, contemplate, smile, evade, read on, pick up, …

Motion patterns

Anti-summary• Summary of things not covered

Term “anti-summary” from Murphy’s book “Big Book of Concepts”

Context

• Biederman’s Relations among Objects in a Well-Formed Scene (1981):

– Support

– Size

– Position

– Interposition

– Likelihood of Appearance

Hock, Romanski, Galie, & Williams 1978

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

Tennis serve Volleyball smash

http://vision.stanford.edu/documents/YaoFei-Fei_CVPR2010b.pdf

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