symoon11 / level-set-method-shape-reconstruction

Shape Reconstruction via Level Set Method

About the Project

This project is for implementing shape reconstruction program via level set method. It is based on a paper written by H. Zhao(2000).

Algorithm

Goal: Shape Reconstruction from an unorganized data set.

key Idea: Want to find a function on an image whose zero level set is nearly the same as what we want to reconstruct.

To do this, we define a functional that measures how well a function reconstruct a shape. Let $S$ be an unorganized data set and $\Gamma$ be a zero level set of a function. Given a point $x$ on $\Gamma$, define $dist(x,S)$ and $E(\Gamma)=\big[\int_{\Gamma}d^p(x)ds \big]^{1/p}$. Then $E$ is non-negative and if $\Gamma$ is close to $S$, $E$ is close to 0. It means that $E$ is an appropriate functional for shape reconstruction.

To minimize this functional, we use Level Set Method. If you want more detalis, see the paper.

How to run

There is one main file named 'shape_reconstruction' and 4 sample data for input. You can change the input in the main file. You also can change a hyper-parameter p.

Result

Here are some sample results.

Case 1. circle(before)

Case 1. circle(after)

You can see the red curve converges to the data points.

Acknowledgement

This project is collaborated with Kwanghyun Choi(Seoul National University).

Reference

[1] H. Zhao, et al. Implicit and Nonparametric Shape Reconstruction from Unorganized Data Using a Variational Level Set Method. Computer Vision and Image Understanding 80, 295–314 (2000).