Elsevier

Image and Vision Computing

Volume 54, October 2016, Pages 12-21
Image and Vision Computing

Iterated random walks with shape prior*

https://doi.org/10.1016/j.imavis.2016.07.005Get rights and content

Highlights

  • New framework using random walks combining a distance-based prior with a region term

  • Prior weighted by a confidence map to reduce influence of the prior in certain areas

  • A refinement might be applied using a narrow band.

  • Our approach was tested with natural and medical images giving satisfactory results.

Abstract

We propose a new framework for image segmentation using random walks where a distance shape prior is combined with a region term. The shape prior is weighted by a confidence map to reduce the influence of the prior in high gradient areas and the region term is computed with k-means to estimate the parametric probability density function. Then, random walks is performed iteratively aligning the prior with the current segmentation in every iteration. We tested the proposed approach with natural and medical images and compared it with the latest techniques with random walks and shape priors. The experiments suggest that this method gives promising results for medical and natural images.

Introduction

Image segmentation has an important and fundamental role in computer vision. The purpose of image segmentation is to localize objects or regions of interest in a certain image. Segmentation is still very challenging because it must deal with several issues such as occlusion, weak edges or lack of contrast of the object to segment. In order to solve these issues, many methods have been implemented but the problem is still open.

In this work, we focus on the random walks algorithm. Random walks based image segmentation is a graph-based segmentation method proposed by Leo Grady [1] in 2006. This technique has become very popular because it can deal with weak boundaries efficiently, and the extension to 3D and the multi-label segmentation is straightforward [1]. According to the author, random walks can outperform the well-known graph cuts [2] in terms of weak boundaries, since the latter is more susceptible to the “small cuts” problem in the presence of weak boundaries [1]. Moreover, random walks do not require any complex technique to be extended to multi-label segmentation unlike graph cuts which usually use sophisticated alpha-beta methods [3].

Generally, images are not separable via intensity information. Thus, a shape prior may be incorporated in order to separate the object of interest from the image. There are some techniques to incorporate prior knowledge into random walks. For example, a pedestrian segmentation method is developed using random walks with a shape prior in Ref. [4]. A pedestrian shape prior model is built averaging the training data for every pose, as well as averaging all training data to obtain a general prior model. The resulting shape models are integrated into the random walks formulation. The modified random walks is applied for every shape model separately, and the final segmentation is the one with higher probability. A similar work was proposed by Baudin et al. in Ref. [5] applied to the skeletal muscle. The prior term is derived from learning a Gaussian model based on previous segmentations of the thigh muscles in a training set. The segmentations in both works may fail when the average model is too different from the target image or the registration is not very accurate. The same issues may occur in Ref. [6] where the algorithm relies on a probabilistic atlas as a prior knowledge. Therefore, Baudin et al. proposed a new technique to handle large scale deformations by allowing the model to evolve in a low-dimensional shape space of valid segmentations. The authors extended the random walks algorithm introducing principal components into the formulation in which shape deformation is constrained to remain close to PCA shape space built from training examples [7]. However, the method only yields an approximate solution and PCA can neither deal properly with probabilities nor allow representing shapes which differ too much from standard shapes [8]. Therefore, they suggest as a future direction to find a different shape space more compatible with probabilities such as a barycentric model. A similar work using PCA is presented in Ref. [9] but it is also very sensitive to the average shape. In order not to be constrained to the average shape, the guided random walks were proposed [10] where the closest subject in a given database is retrieved to guide the segmentation. If there is no matching case in the database to guide the segmentation, the conventional random walks algorithm is performed. The guided random walks method is applied to the target image guided by every sample in the training dataset. It returns the segmentation with the highest overlap between the segmentation result and the manually segmented training sample, or it performs the conventional random walks if there is not enough overlap in the training set. The limitations of this method are that all the samples of the training data must be considered and if there is not a good match, it only relies on the conventional random walks. Random walks with shape prior have also been used in video tracking and segmentation [11], [12]. In Ref. [11], a human segmentation method from a video is implemented in which a model of the human shape is used as a prior and the segmentation likelihood is propagated. In Ref. [12], the segmentation result is also propagated as a prior mask and a spatial cue, obtained from the prior, and a colour cue are fused using Bayesian inference. A disadvantage of these tracking methods is that they can propagate errors.

Besides incorporating the prior, Leo Grady also extended the method to include unary node information as the data term of graph cuts and added a non-parametric probability density model that allows localization of disconnected objects, and eliminates the requirement for user-specified labels [13]. The author only used the intensity profile to estimate the probability densities. In our paper, we use this framework to incorporate the shape prior into the random walks formulation. The shape prior information and the region term constitute the probability density model. The closest works to this paper are based on graph cuts with prior knowledge [14], [15], [16].

The contribution of this paper is to combine a prior probability map computed using a distance map of the aligned shape prior with a k-means based region term into the random walks formulation, making the process iterative to guide the prior with the current segmentation. This technique is more flexible than probabilistic maps or atlas-based methods. This shape prior has been widely used in iterative graph cuts and we apply it to random walks due to its numerous advantages mentioned above. In the remainder of this paper, we explain the details of the proposed method and show the segmentation results when applying it to both natural images and medical images of the human cochlea.

Section snippets

Random walks segmentation

An image can be represented as a graph where the nodes are the pixels of the image, and the weights represent the similarity between nodes. Vertices marked by the user as seeds are denoted by Vm and the rest by Vu. Given some seeds, vjVm, random walks assign to each node, viVu, the probability, xis, that starting from that node, it first reaches a marked node, vjVm assigned to label gs. The segmentation is then completed by assigning each free node to the label for which it has the

Iterative segmentation algorithm

The pose of the object to segment is usually unknown causing that the shape prior may not be properly defined or aligned to the target object. In order to alleviate this issue, the segmentation is made as an iterative process to guide the prior in the following way. Given some seeds for the background and the foreground, the shape prior is placed close to the foreground seeds and the distance map from the shape is calculated. Then, the proposed random walks considering region and distance prior

Results

The proposed method is tested on two different types of data sets. One data set is based on natural images, where most of the images are obtained from PASCAL VOC 2011 [20]. The other data set is obtained from micro-CT images of the human cochlea. The cochlea segmentation is performed in 3D.

The method is compared with the latest techniques using random walks with shape prior such as guided random walks [10], constrained random walks [4] and PCA-based random walks [9]. All parameters are

Conclusion

We presented a new framework for image segmentation using random walks that are able to deal with weak boundaries efficiently. We incorporate a distance map prior weighted by a confidence map into the random walks segmentation. Distance map priors have been widely used in level sets and graph cuts but not in random walks. The combination of the distance map prior with a region term into random walks provides accurate segmentations. Then, the random walks algorithm is performed iteratively to

Acknowledgments

The research leading to these results received funding from the European Union Seventh Frame Programme (FP7/2007–2013) under grant agreement 304857, HEAR-EU Project.

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*

This paper has been recommended for acceptance by Shishir Shah.

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