Fuzzy relations applied to minimize over segmentation in watershed algorithms

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Abstract

This paper presents a novel method to minimise the over-segmentation that inherently results after applying a watershed algorithm. The proposed technique characterises each of the segmented regions and then employs the composition of fuzzy relations to group together similar regions.

Introduction

Most image applications are based on the extraction and analysis of meaningful features, which may be hard to distinguish from all the information contained in the image. A simplification step is then needed to filter out the required features, which can then be further processed either by a computational algorithm or by a human operator. Segmentation is a widespread image simplification operation, essential in most content-based imaging systems. Tracking segmented objects in video, image retrieval from databases and image pattern recognition are just some examples. Many different approaches exist to achieve segmentation. Roughly classified, they can be divided into three categories (Bueno et al., 2001). Segmentation without modelisation of the image, where low-level image processing algorithms belong to, Segmentation with an available model, such as deformable models and knowledge-based models, and Hybrid segmentation models. As for the first type of algorithms, the method works well on images with high SNR, good contrast and strong homogeneity. The second category of algorithms is indeed more robust but its success still is limited by the difficulty to incorporate the knowledge about the shapes to segment; also, there is a loss of generality as the implementation becomes application dependant, and finally, the intervention of an operator is frequently required to incorporate the a priori information. The same concerns remain valid for the approaches contained in the third category. Among the low-level algorithms, the watershed segmentation, initially proposed by Beucher and Lantuéjoul (1979), has been widely used and has provided satisfactory results when the SNR and homogeneity conditions, mentioned above, are met. Otherwise the result may exhibit over-segmentation, which is undeniably the huge inconvenience of this approach. On the other hand, watersheds have the valuable advantage of partitioning the image and always returning a set of closed contours even in low contrast conditions. A variation algorithm to the watersheds, the marker-based watershed (Meyer and Beucher, 1990) has been proposed to avoid the over-segmentation problem. In this technique there are as many final regions as markers in the image. The problem is that automatic placement of the markers is difficult and thus, is often done by an operator. Also, the accuracy on the contours obtained is diminished depending on the number of markers placed in the image. In this paper a novel method to minimise the inherently watersheds over-segmentation is proposed, delivering thus, a simplified image with meaningful closed contours. In order to reduce the partition complexity, the use of fuzzy relations to cluster similar regions is implemented. The algorithm has been applied on some generic images and MRI medical images for which ground-truth segmentations have been defined.

The rest of the paper is as follows: Section 2 explains the watershed implementation employed for the segmentation of images. In Section 3 the details of the fuzzy algorithm applied to minimise over-segmentation are presented. Section 4 shows meaningful results. Finally Section 5 presents the conclusions of this paper.

Section snippets

Watershed segmentation

The watershed segmentation is a technique developed from morphological algorithms, which follows a geological analogy. The image to be segmented can be considered as a topographical surface, S, where the grey levels or image intensities, I(x, y) = I(s) correspond to altitude values. A minimum at an altitude value j, mj, in this landscape, is a dip in the ground surrounded by strictly higher land. A catchment basin, CBi(mij), is then the area around the minimum mij in S where water falling on it

Over-segmentation minimisation

The proposed approach is based on the application of the Fuzzy C-means algorithm together with composition of Fuzzy relations.

The Fuzzy C-means algorithm is one of the most widely used clustering algorithms. It was initially proposed by Bezdek (1973). It is an unsupervised algorithm, based on the minimisation of a fuzzy objective function, which is based on the intra-class scatter of the given data. The algorithm performs a partition of the data into c clusters and c centres, one for each

Results

In order to demonstrate the efficiency of the proposed method, some experiments were carried out on different types of images: Firstly the ‘Peppers’ image shown in Fig. 1 was processed. This is a 128 × 128 8-bits coded image (256 grey value levels). The resulting watershed image contains 682 basins. When the latter image is processed with the proposed algorithm, the number of basins is reduced to only 90. The resulting simplified mosaic and watershed image are shown in Fig. 2.

Then a second

Conclusions

Over-segmentation is an intrinsic problem appearing when the watershed transform is used. In this paper a new algorithm is proposed to merge similar regions to allow simplifying the segmented image. The composition of fuzzy relations is proposed to group together regions with similar grey value level under the constraint that only adjacent regions can be merged. Experimental results show to diminish the number of regions in the over-segmented image from 70% to 85%. Thus, by running the proposed

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