Fast and Accurate Redistancing for Level Set Methods

K. Krissian, C.-F. Westin
EUROCAST, Las Palmas de Gran Canaria, Spain
Computer Aided Systems Theory (EUROCAST'03)
Pages 48-51
February 24-28, 2003

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Abstract

Although the Level Set Method has only recently been introduced as an image processing tool, it has already proved useful in delineating contours and in segmenting objects. However, since this method represents contours with images, processing time may increase considerably. To offset this problem, it is common to create a narrow band of the image points lying within a given distance to the contour, and then process the contour evolution inside this narrow band. The use of the narrow band and numerical considerations require computing the distance to the evolving contour every few iterations. In (Russo, 2000) the authors identify the problem of preserving the exact position of the interface and propose to solve a new Partial Differential Equation for this purpose. In (Sethian, 1999), a 'n log(n)' algorithm is proposed to compute the distance by propagation until a given distance to the contour is reached. In this paper, we present two improvements: 1) We estimate the Euclidean distance to the interpolated surface for all voxels that are neighbors to the surface; and 2) We apply a fast approximation of the Distance Transform only in the narrow band, which, in turn, reduces the complexity of 'n log(n)' to 'n', where 'n' is the size of the narrow band.

Figure 2 shows the results obtained with two techniques. The top line displays the initial isosurface, and the bottom line displays the isosurface of the zero level set after 130 iterations, using Fast Marching on the left, and using Fast Chamfer Distance on the right.

Reference

Krissian K, Westin CF. Fast and accurate redistancing for level set methods. In RM Diaz, AQ Arencibia, eds., Computer Aided Systems Theory (EUROCAST'03). Las Palmas de Gran Canaria, Spain: Universidad de Las Palmas de Gran Canaria, 2003;48-51.

Bibtex entry

@INPROCEEDINGS{krissianEUROCAST03,
  author         = {Karl Krissian and Carl-Fredrik Westin},                    
  title          = {Fast and Accurate Redistancing for Level Set Methods},     
  editor         = {Roberto Moreno Diaz and Alexis Quesada Arencibia},         
  booktitle      = {Computer Aided Systems Theory (EUROCAST'03)},              
  pages          = {48--51},                                                   
  month          = {February 24--28},                                          
  year           = {2003},                                                     
  address        = {Las Palmas de Gran Canaria, Spain},                        
  publisher      = {Universidad de Las Palmas de Gran Canaria}
}

Grants

NIH P41-RR13218 (NAC), CIMIT

Research areas

Level Sets, Segmentation, Vessels