Locating object contours in complex background using improved snakes

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Abstract

An active contour model, called snake, can adapt to object boundary in an image. A snake is defined as an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines or edges. The traditional snake model fails to locate object contours that appear in complex background. In this paper, we present an improved snake model associated with new regional similarity energy and a gravitation force field to attract the snake approaching the object contours efficiently. Experiment results show that our snake model works successfully for convex and concave objects in a variety of complex backgrounds.

Introduction

A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. It belongs to the active contour model in the way that it locks on nearby edges, localizing them accurately. Kass et al. [1] used snakes for interactive interpretation, in which the user-imposed constraint force guides the snake near features of interest. The snake model provides many applications, such as object segmentation, stereo matching and motion tracking [2], [3], [4].

There are two parts in the energy function of the snake model. The first part reflects geometric properties of the contour, and the second part utilizes the external force field to drive the snake [5], [6]. The first part serves to impose a piecewise smoothness constraint, and the second part is responsible for putting the snake near the local minimum of energy. Cohen [7] presented a balloon-like snake model with a pressure force to pass over weak edges and stop at strong edges.

The traditional snakes suffer from a great disadvantage that when an object resides in a complex background, the strong edges may not be the object edges of interest. Therefore, researchers have proposed statistical and variational methods to enrich the energy function and extend its flexibility [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. They calculated the difference between the target object and background using statistical analysis, but these limitations come from the priori knowledge requirements, such as independent probability models and template models. Unfortunately, such priori knowledge is usually unavailable unless the captured images are under very constrained settings. A problem with the snake is that usually a user must place the initial snake points close to the feature of interest. The paper by Li et al. [19] described a variational formulation for geometric active contours that forces the level set function to be close to a signed distance function. They used the level set function to allow flexible initialization.

To allow flexibility of snakes in complex background, we present a new energy term to be added into the gravitation external force field for locating object contours in complex background. The paper is organized as follows. Section 2 briefly reviews the traditional snake model. Section 3 proposes our improved snake model. Section 4 presents the usage of the greedy algorithm and the gravitation external force field. Section 5 provides our experimental results. We draw conclusions in Section 6.

Section snippets

The traditional snake model

A snake is a controlled continuity spline that moves and localizes onto a specified contour under the influence of the objective function. Let a snake be a parametric curve v(s) = [x(s), y(s)], where parameter s  [0, 1]. It moves around the image spatial domain to minimize the objective energy function as defined byEsnake(v)=i=1n[α×Econt(vi)+β×Ecurv(vi)+γ×Eimage(vi)],where α, β, and γ are weighting coefficients that control the snake’s tension, rigidity, and attraction, respectively. The first and

The improved snake model

We observe the following two issues that the snake model fails to locate object contours in complex backgrounds. One is the gray-level sensitivity; i.e., the more abrupt change the gray levels have (e.g. noises), the larger impact on the energy function the snake makes. The other is that the snake mistakenly locates the edges belonging to the background details due to their closeness to the snake point. Fig. 1 shows a disk object in a complex background. If we initialize the snake points

Gravitation external force field and greedy algorithm

In this section, we present gravitation external force field and the greedy algorithm [20], [21] to be used for the active contour. The concept of gravitation external force field is taken from physics. Two objects attract each other by a force, which is proportional to their mass product and inversely proportional to the distance between their mass centers. Based on this concept, we develop an external energy field, called the gravitation energy field (GEF), as given byEgravitation=g(r)rr

Experimental results

We apply both our improved and the traditional snake models on the added salt-and-pepper noise of Fig. 1. The results are shown in Fig. 6. We observe that our model can locate the disk contour, but the traditional model fails. Our model is suitable for random noise or fixed pattern noise. The banding noise is highly camera-dependent, and is the one which is introduced by the camera when it reads data from the digital sensor. Our model may not perform well in an image with such noise.

Fig. 7

Conclusions

We have presented an improved snake model for including the regional similarity energy and the gravitation force field to locate object contours in complex background. The gravitation force field based on gradient is used to make the snake model effective. The regional similarity energy offers the inclusion of the mean intensity difference between the snake and the object. Experiment results show that our snake model works successfully for convex and concave objects in a variety of complex

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