Dynamic B-snake model for complex objects segmentation

Abstract

A close-form B-Snake model using statistics information for 2D objects segmentation is presented in this paper. We called it Dynamic B-Snake Model (DBM). It is able to model the features of the object in training set and guide the B-Snake in the deforming procedure. Compared to other deformable models, the DBM maintains the smoothness of curve while still remain compact representation. Moreover, a method of Minimum Mean Square Error (MMSE) is developed to iteratively estimate the position of those control points in the B-Snake model. As it deforms the segments of the B-Spline at a time, instead of individual points, it is very robust against local minima. Furthermore, in order to use available statistical information about the desired object shape, the Principal Component Analysis (PCA) is applied to model the distribution of knot points of training samples. This allows the deformation of B-Snake to synthesize the shape similar to those in the training set. By applying the proposed B-Snake model to medical images, it is shown that our method is more robust and accurate in comparing with the traditional Snake and Active Shape Model(ASM).

Introduction

Object segmentation is a very important procedure in image analysis, computer vision, and medical imaging. Many medial image analysis applications, like the measurement of anatomical structures, require prior segmentation of the organ from the surrounding tissue. However, it is a difficult task due to the variations of objects and the diversities of image types. For example, one important task in medical imaging is the boundary extraction of the brain ventricle from magnetic resonance (MR) images. But the variations of shapes and sizes of the ventricles with the ages usually make the extraction procedure difficult. Our special interest is the human brain ventricle segmentation in MR images for further study.

The Snake was originally developed by M. Kass [1]. It was curve defined within an image domain which can move under the influence of internal forces from the curve itself and external forces from the image data. Once internal and external forces have been defined, the Snake can detect the desired object boundaries (or other object features) within an image. From the original philosophy of Snake, there are many techniques have been proposed as an alternative method for presenting a curve: Fourier descriptors [2], B-Splines [3], [7], [9], [10], [21], [26], auto-regressive model [4], moments [5], HMM models [6] and wavelets [8], etc. Among these methods, B-Spline representation of the curve stands for an advantage as such a formulation of a deformable model allows for the local control and a compact representation. The flexibility of the curve increases as more control points are added while still remain less parameters compared to other model. Moreover, the internal force is not needed as the smoothness requirement has been implicitly built into the model.

In this paper, we present a closed-form B-Snake model called Dynamic B-Snake Model (DBM) with a Minimum Mean Square Error (MMSE) approach [24]. It possesses three main novelties:

• Internal forces are not required in DBM since the B-Snake representation maintains smoothness via hard constrains implicit in the representation while remains compact representation.

• A method of MMSE is developed to iteratively estimate the position of those control points in the closed B-Snake model. As MMSE deforms the segments of the B-Spline at a time, instead of individual points, it is very robust to against local minima.

• In order to use available statistical information about the desired object shape, the Principal Component Analysis (PCA) has been applied to our B-Snake model. This approach allows the deformation of B-Snake to synthesize the shape similar to those in the training set.

The structure of this paper is arranged as follows. In Section 2, a review of the existing B-Snake model is presented. Section 3 introduces the B-Snake Model with the algorithm for estimating the parameters of B-Snake. In Section 4, the statistic model is given to model the samples of the training set and guide the B-Snake deformation. The simulation results are shown in Section 5. This paper concludes in Section 6.