Depar tment o f E lect r ica l and E lect ron ic Engineer ing ,

The Univers i ty o f Hong Kong,

Pokfu lam Road,

Hong Kong

Three-dimensional curve reconstruction from multiple images

Outline

IntroductionProblem formulationCurve reconstructionExperimental resultsConclusions

Introduction

Unlike most existing methods, our approach does not require any other additional information of the image features or calibration of cameras.

Since this is a point-based curve reconstruction approach , the problem of missing and/or partially occluded curves is readily handled using methods that are already established for occluded points.

Outline

IntroductionProblem formulationCurve reconstructionExperimental resultsConclusions

Problem Formulation

Problem Formulation

The 2D reprojection error measured can be defined as

Outline

IntroductionProblem formulationCurve reconstructionExperimental resultsConclusions

Curve Reconstruction

Curve Reconstruction

Introducing (5) into (3)

Curve Reconstruction

To avoid the non-linearity in the function,we can introducing the inverse depth =

Curve Reconstruction

We may incorporate constraint 7(b) into the cost function (7) by means of a penalty term with a penalty factor γ.

Curve Reconstruction

We use a three-step process to obtain a good initial guess for iterative algorithm.

(1) 2D representative point selection.(2) initial point correspondences

establishment1. Affine-invariant points detection2. Affine-invariant segments matching3. Matching section extension4. Similarity score computation

(3) initial 3D reconstruction

Curve Reconstruction

Point-based curve reconstruction algorithm

Curve Reconstruction

Outline

IntroductionProblem formulationCurve reconstructionExperimental resultsConclusions

Experimental Result

Synthetic Images

Experimental Result

Tissue Box

Jar

Experimental Result

Mug

Dell Box

Outline

IntroductionProblem formulationCurve reconstructionExperimental resultsConclusions

Conclusions

In this paper, we propose a new approach for reconstructing 3D curves from a sequence of images taken by uncalibrated cameras.

It is capable of constructing both planar curves and non-planar curves, and it readily handles cases where not all curves are visible or some curves are partially occluded.