Research

IMAGE SEGMENTATION USING B-SPLINE LEVEL-SET MODELS

Abstract

We developped a new formulation of level-set where the implicit function is modelled as a continuous parametric function expressed on a B-spline basis. Starting from the level-set energy functional, this formulation allows computing the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-splines parameters. We also show that each step of this minimization may be expressed through a separable convolution operation, which yields a very efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can explicitly be controlled via the degree and the scale of the chosen B-spline kernel.

Experiments

The behaviour of this approach has been illustrated on simulated images as well as experimental images from various fields. The segmentation experiments are based on the Chan-Vese functional, which aims at partitioning the image into regions with piecewise constant intensity.

B-spline level-set segmentation results of various kind of images

Demonstration

The proposed approach can be tested in real time using the following JAVA applet demonstrator.

Start the Java Applet (Java 1.3)

Related papers

• Olivier Bernard, Denis Friboulet, Philippe Thevenaz, Michael Unser. Variational B-spline level-set method for fast biomedical segmentation. In IEEE International Symposium on Biomedical Imaging (ISBI’ 08), Paris, France, 2008.
  

IMAGE SEGMENTATION USING RBF-BASED LEVEL-SET MODELS

Abstract

The partial differential equation (PDE) driving level set evolution in segmentation is usually solved using finite differences schemes. In this paper we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well-suited to collocation in the framework of segmentation. In addition CSRBFs allow to reduce the computation cost using a kd-tree based strategy for neighbourhoods representation. Moreover, we show that the usual reinitialisation step of the level set may be avoided by simply constraining the l1-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e. new zero level components), which are difficult to obtain using reinitialisation. The behaviour of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3D CT bone images and echocardiographic ultrasound images.

Experiments

The proposed segmentation approach has been applied to 3D CT images of calcaneus bone. Due to its complex topology, calcaneus bone is an attractive example for testing our approach.

Segmentation of 3D CT images of calcaneus bone.

Related papers

• Arnaud Gelas, Olivier Bernard, Denis Friboulet, Rémy Prost. Compactly supported radial basis functions based collocation method for level-set evolution in image segmentation. In IEEE Transactions on Image Processing, volume 16, no. 07, pp. 1873-1887, 2007.
  
  
• Olivier Bernard, Basma Touil, Arnaud Gelas, Rémy Prost, Denis Friboulet. A RBF-based multiphase level set method for segmentation in echocardiography using the statistics of the radiofrequency signal. In IEEE International Conference On Image Processing (ICIP’ 07), San Antonio, Texas, USA, volume 3, pp. 157-160, 2007.
  
  
• Arnaud Gelas, Joel Schaerer, Olivier Bernard, Denis Friboulet, Rémy Prost. Radial basis functions collocation methods for model based level-set segmentation. In IEEE International Conference On Image Processing (ICIP’ 07), San Antonio, Texas, USA, volume 2, pp. 237-240, 2007.
  
  
• Olivier Bernard, Basma Touil, Arnaud Gelas, Rémy Prost, Denis Friboulet. Segmentation of myocardial regions in echocardiography using the statistics of the radio-frequency signal. In Functional Imaging and Modeling of the Heart (FIMH’ 07), Salt Lake City, UT, USA, pages 433-442, 2007.
  

MYOCARDIUM SEGMENTATION IN ECHOCARDIOGRAPHIC IMAGES

Abstract

This work presents an algorithm for segmentation of ultrasound images based on the statistics of the radio-frequency (RF) signal. We first show that the Generalized Gaussian distribution can reliably model both fully (blood pool) and partially (tissue area) developed speckle in echocardiographic RF images. We then show that this probability density function (pdf) may be used in a maximum likelihood framework for tissue segmentation. Results are presented on both simulations and ultrasound cardiac images of clinical interest.

Experiments

The ability of the proposed method to segment echocardiographic images from RF signal using Generalized Gaussian was tested on ultrasound cardiac images acquired in vivo.

Segmentation of an echocardiographic image acquired in vivo for a Parasternal long axis orientation.

Related papers

• Olivier Bernard, Basma Touil, Arnaud Gelas, Rémy Prost, Denis Friboulet. Segmentation of myocardial regions in echocardiography using the statistics of the radio-frequency signal. In Functional Imaging and Modeling of the Heart (FIMH’ 07), Salt Lake City, UT, USA, pages 433-442, 2007.
  
  
• Olivier Bernard, Jan D'hooge, Denis Friboulet. Segmentation of echocardiographic images based on statistical modelling of the radio-frequency signal. In European Signal Processing Conference (EUSIPCO’ 06), Florence, Italy, pages Article ID cr2205, 4 pages, 2006.
  
  
• Olivier Bernard, Jan D'hooge, Denis Friboulet. Segmentation d’images échocardiographiques par contours actifs implicites : exploitation de descripteurs statistiques de régions. In GRETSI, Louvain-la-Neuve, Belgium, pp. 359-362, 2005.

PROSTATE SEGMENTATION IN ECHOGRAPHIC IMAGES

Abstract

We present a simple, robust and computationally efficient additional global deformation terms such as tapering and method for the semi-automatic segmentation of the prostate in TRUS (Transrectal Ultrasound) image. The method relies on a variational formulation based on a deformable super-ellipse and a region energy based on the assumption of a Rayleigh distribution. Instead of using the classical level-set approach, we directly insert the implicit representation of a deformable super-ellipse into the energy to minimize. This yields a super-ellipse evolution able to accurately segment prostate and surrounding tissues while handling boundary gaps on the contour.

Experiments

The ability of the proposed method to segment prostate structures was tested on ultrasound images acquired in vivo.

Examples of prostate segmentation on four prostate Cartesian images.

Related papers

• Laurent Saroul, Olivier Bernard, Didier Vray, Denis Friboulet. Prostate segmentation in echographic images: a variational approach using deformable super-ellipse and Rayleigh distribution. In IEEE International Symposium on Biomedical Imaging (ISBI’ 08), Paris, France, 2008.