1 Introduction

LoFTR, cvpr21 先讲讲它的5 minutes introduction video非常合适。

Reading: [HZ] Chapter: 4 “Estimation – 2D projective transformation” Chapter: 11 “Computation of the fundamental matrix F” [FP] Chapter:10 “Grouping and model fitting

1.1 Fitting in Parametric Space

What is parametric space?

$f(x)=\Sigma{w_i*B_i(x)}$

Fitting, matching and recognition are interconnected problems

• Curve fitting (line, circle)
• Matching ⇒ Homographic transformations 单应性变换, Fundamental matrices, Shape models

Goals: Fitting as Search in Parametric Space

1. What model represents this set of data/features best?
   1. e.g. line or circle
2. How many model instances are there?
3. Which of model instances gets which data/feature?
   1. may be non local
4. Computational complexity is important
   1. It is infeasible to examine every possible set of parameters and every possible combination of features

1.2 Example: Line Fitting

Why fit lines?