On the Stationary Solution of PDE based Curve Evolution

Wang Junyan, Chan Kap Luk and Wang Yadong

School of Electrical & Electronic Engineering

Nanyang Technological University, Singapore

{wa0009an,eklchan,yadongwang}@ntu.edu.sg

The problems with the videos are fixed.
 

 

Introduction

This page contains the experimental results appeared in paper On the Stationary Solution of PDE based Curve Evolution and additional results for this paper. Additional results on real medical image are now included. Comparisons with other existing methods, such as Geodesic Active Contour (GAC), GAC with balloon force, GAC with adaptive balloon force are shown.

The videos stored in zip files are downloadable from here. They show the curve evolution processes. We also provide the original images from which the regions of interests are extracted, the ground truth and the initialization (see the first frame in the video) for the curve evolution. We initialize the curve in the same way for different methods and for each region of interest of the image. The parameters are the same for all the images too.
 

The Results

Images

Videos by Our Method

Other Methods

Videos

Comments

Click here to see

Synthetic Image 1

 

click here to download the results by

EDF+GAC

click here to download the results by

GAC

click here to download the results by

GAC with balloon force

click here to download the results by

GAC with adaptive balloon force

Click here to see

 Synthetic Image 2

 

click here to download the results by

EDF+GAC

click here to download the results by

GAC

click here to download the results by

GAC with balloon force

click here to download the results by

GAC with adaptive balloon force

Click here to see

Real Image 1*

Click here to see

Ground Truth**

click here to download the results by

EDF+GAC

click here to download the results by

GAC

click here to download the results by

GAC with balloon force

click here to download the results by

GAC with adaptive balloon force

Click here to see

Real Image 2

Click here to see

 Ground Truth

click here to download the results by

EDF+GAC

click here to download the  results by

GAC

click here to download the results by

GAC with balloon force

 

click here to download the results by

GAC with adaptive balloon force

 

Conclusion

  • The curve evolution by GAC is easily trapped by Pseudo Stationary Positions, even when the scenario is quite clean.
  • Balloon force can help GAC to escape from Pseudo Stationary Positions and optimal solution as seen in the videos.
  • Adaptive balloon force can be effective in some simple applications. However, the curve evolution by GAC with the adaptive balloon force can still be trapped by Pseudo Stationary Positions.
  • Our method is the only one by which the curve converges to targeted boundary. Our method can steer the the curve out of the Pseudo Stationary Positions and converge to target boundary.