Fitting: find the parameters of a model that best fit the data

Alignment: find the parameters of the transformation that best align matched points

– Design a suitable goodness of fit measure

• Similarity should reflect application goals
• Encode robustness to outliers and noise

– Design an optimization method

• Avoid local optima
• Find best parameters quickly

Methods:

1. Global optimization / Search for parameters → sensitive to outliers(bad match, extra point), doesn’t allow to get multiple good fits

– Least squares fit

Line Equation yi = mxi + b → Find (m, b) to minimize

– Robust least squares: nonlinear optimization problem

– Other parameter search methods

1. Hypothesize and test

– Generalized Hough transform

Hough Transform: Outline

1. Create a grid of parameter values