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Medical image segmentation is one of the key technologies in computer aided diagnosis. Due to the complexity and diversity of medical images, the wavelet multi-scale analysis is introduced into GVF (gradient vector flow) snake model. The modulus values of each scale and phase angle values are calculated using wavelet transform, and the local maximum points of modulus values, which are the contours of the object edges, are obtained along phase angle direction at each scale. Then, location of the edges of the object and segmentation is implemented by GVF snake model. The experiments on some medical images show that the improved algorithm has small amount of computation, fast convergence and good robustness to noise.

Image segmentation is used widely in medical fields, such as medical research, clinical diagnosis and treatment, efficacy evaluation, image information processing, surgical planning, computer-assisted surgery, pathological analysis, image-guided surgery and surgical simulation [

At present, the common methods used in the perspective of medical applications include region-based methods, edge-based approach, combination of theoretical tool-specific methods (such as artificial neural networks and deformable model method), the methods based on statistical theory, fractal-based methods and methods based on mathematical morphology [

The earliest deformable model was presented in 1987 in the creative thesis “Snakes: Active Contour Models” of Kass [

In the parametric deformable models, the images segmentation process is to find the parameters that minimize the sum of internal and external energy which have been weighted. Usually, the minimum value is obtained in the image boundary which is the required image region. The energy minimization process is a joint decision of the internal forces and external forces. The internal forces include elastic force and bending force, whose primary role is to prevent excessive bending curve. The main role of the external force is to move the curve toward the boundaries of the image. They both make the curve gradually arrive at the image characteristics region which is the edges of the image. A traditional 2-D parametric deformable model or deformable contour is a curve

where E_{int} is a scalar potential function. The external potential function E_{ext} is derived from the image, so that it takes on its smaller values at the features of interest, such as boundaries. A deformable contour that minimizes must satisfy the Euler equation

To find a solution to Equation (2), the deformable contour is made dynamic by treating x as function of time t as well as s, i.e.

In 1998, Xu proposed a new model, which is called gradient vector flow (GVF) field [

Compared with traditional snake model, the GVF model has made significant improvements, and is widely used in medical image segmentation [

Edge detection plays an important role in image analysis and computer vision. Edges characterize object boundary on the basis of the properties of intensity and texture, which can provide valuable information for further image processing such as image segmentation, image enhancement and image compression. In early years, many edge detection algorithms have been developed [

The application of wavelet transform in image processing has received significant attention and some very efficient wavelet-based multi-scale edge detection algorithms have been proposed [

In 1992, Mallat and Zhong conducted some research on sudden changes in signals and their characteristics under wavelet transforms. They also studied the properties of multi-scale edges through the wavelet theory and showed that the evolution of wavelet, local maxima across scales would characterize the local shape of irregular structure.

The image often is the two-dimensional signal. Suppose

while

dimensional wavelet function are defined as follows:

Suppose

The wavelet transform of

Since Dyadic Wavelet has “zoom” function on analysis of the signal, we only need to increase the magnification by reducing the value of j if we want to watch the details of the signal. The wavelet transform of f at scale 2^{j} is a vector with two components

The Dyadic Wavelet transform of two-dimensional image is

Respectively, the image gradient modulus

Modulus value of wavelet transform is proportional to the gradient vector-valued. Wavelet transform amplitude angle

The comparison of the experimental results shows that the edges extracted using the traditional operator is very wide, more obscure, and has lost a lot of image details. And when the smoothness of the edge is poor, more non-linear noise is retained. However, the wavelet transform modulus maxima approach can accurately position the edges affected by noise and the edge is one pixel wide. On a large scale, the wavelet transform modulus maxima method obtains major edge information. On the small scale, it obtains the details of the edge information. This feature is suitable for us to identify and locate objects from coarse to fine. The experimental results show that wavelet transform can detect weak edge which is not detected by the other algorithms, and has good continuity and smoothness. In short, the image edge detection method based on wavelet transform has a good application in medical image.

of image details. The appropriate threshold can not only get rid of the pseudo-edge of the image, but also remove some noise, while too big threshold may filter out the useful edge information.

First, the edge points of the interested field are detected by using the wavelet transform, and then the Gradient Vector Flow field is constructed on the basis of edge detection results. Then the target segmentation is realized by using the GVF parameter deformable model. We adopt the wavelet transform and the GVF contour model combination algorithm and apply it to a variety of medical image object segmentation and obtain good results. In this paper, the experimental algorithm works on the environment of CPU: Celeron 1.1 GHz, Memory: 256 M, Operating System: Windows Xp and Simulation Software: Matlab 2010a .

In the experiment, we selected five different characteristic of the pictures as the experimental data whose size is 256 × 256. As indicated in

First, we show several examples of the GVF field computations on medical images and demonstrate the limitation of key properties of the GVF deformable contours. The deformable contours were dynamically reparameterized to maintain contour point separation to within 0.5 - 1.5 pixels. All edge maps used in GVF computations were normalized to the range [0, 1].

The GVF model has a much larger capture range and better concavity convergence on simple images. In our experiment, however, the results demonstrate that the GVF model has a poor performance on medical images as shown in

In this paper, we introduce the wavelet modulus maxima method to improve the implementation of the GVF model.

Respectively,

Performance Analysis Image Quality | GVF Algorithm | The Proposed Algorithm | |||
---|---|---|---|---|---|

Initial Contour | Initial Contour | ||||

Inside | Outside or Across | Inside | Outside or Across | ||

Whether the interested region is accurately extracted? | |||||

high-resolution | No | No | Yes | Yes | |

fuzzy | No | No | Yes | Yes | |

concavity | No | No | Yes | Yes | |

noisy | No | No | Yes | Yes | |

homogeneous gray | No | No | Yes | Yes |

Initial Contour | ||||
---|---|---|---|---|

Inside | Outside or Across | |||

Number of Iterations | Running Time | Number of Iterations | Running Time | |

60 | 15.2500 | 50 | 13.6406 | |

160 | 42.5938 | 130 | 36.2813 | |

250 | 81.1406 | 90 | 22.0313 | |

100 | 35.4219 | 30 | 13.0625 | |

30 | 14.8750 | 30 | 9.4844 |

Initial Contour | ||||
---|---|---|---|---|

Inside | Outside or Across | |||

Number of Iterations | Running Time | Number of Iterations | Running Time | |

50 | 10.1094 | 30 | 6.3281 | |

150 | 27.7813 | 125 | 24.00 | |

240 | 48.9531 | 85 | 17.6094 | |

50 | 18.1875 | 20 | 5.5469 | |

15 | 6.4063 | 10 | 3.7656 |

In the future, some investigations into the features and uses of the improved GVF model would be warranted. It would also been done to understand the interplay between the GVF parameters and the wavelet transform parameters and select the parameters adaptively. Likewise, the novel algorithm framework might be useful in defining new improved parametric and geometric deformable models. Finally, making relationship between improved GVF model with other applications in image processing, computer vision, and medical imaging might provide some new insights or even new solutions to existing problems (

Related to the traditional parameters deformable model, the GVF deformable model has been greatly improved, but certain requirements of the initial contour position and more computation time are still needed. Since the wavelet transform has the features of edge detection and noise removal, in this paper, the wavelet transform modulus maxima is introduced into the GVF model to detect the edge of the image and remove the noise and the undesirable details. Experimental results show that the novel algorithm can use less running time to obtain better segmentation results. The dynamic behavior of the GVF model in the energy minimization process manifests that the new algorithm has a wide range of applications, especially in medical image analysis and disease diagnosis.

This Research is funded by the Education Department of Liaoning Province Foundation grant Number LJQ2014033 and University of Science and Technology Liaoning Foundation grant Number 2013RC08.