Model Fitting - Introduction to Computer Version - Lecture Sli, Lecture notes of Computer Science

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Model Fitting

Computer Vision

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Fitting: find the parameters of a model that

best fit the data

Alignment: find the parameters of the

transformation that best align matched points

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H

Example: Estimating an homographic

transformation

Slide from Silvio SavareseDocsity.com

Example: Estimating “fundamental matrix”

that corresponds two views

Slide from Silvio SavareseDocsity.com

Example: fitting a 3D object model

Slide from Silvio SavareseDocsity.com

Critical issues: noisy data

Slide from Silvio SavareseDocsity.com

H

Critical issues: outliers

Slide from Silvio SavareseDocsity.com

Critical issues: missing data (occlusions)

Slide from Silvio SavareseDocsity.com

Fitting and Alignment: Methods

• Global optimization / Search for parameters
  • Least squares fit
  • Robust least squares
  • Iterative closest point (ICP)
• Hypothesize and test
  • Generalized Hough transform
  • RANSAC

Slide from Derek HoiemDocsity.com

Simple example: Fitting a line

Slide from Derek HoiemDocsity.com

Least squares: Robustness to noise

Least squares fit to the red points:

Slides from Svetlana LazebnikDocsity.com

Least squares: Robustness to noise

Least squares fit with an outlier:

Problem: squared error heavily penalizes outliersDocsity.com

Robust least squares (to deal with outliers)

General approach: minimize

ui ( xi , θ ) – residual of ith^ point w.r.t. model parameters θ ρ – robust function with scale parameter σ

u (^) i xi, ; i

The robust function ρ

• Favors a configuration with small residuals
• Constant penalty for large residuals

n i 1

2 u (yi mxi b)

Slide from S. SavareseDocsity.com

Choosing the scale: Just right

The effect of the outlier is minimized

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