Elsevier

Signal Processing

Volume 83, Issue 1, January 2003, Pages 67-78
Signal Processing

Multiresolution image segmentation integrating Gibbs sampler and region merging algorithm

https://doi.org/10.1016/S0165-1684(02)00377-8Get rights and content

Abstract

This work approaches the texture segmentation problem by incorporating Gibbs sampler (i.e., the combination of Markov random fields and simulated annealing) and a region-merging process within a multiresolution structure with “high class resolution and low boundary resolution” at high levels and “low class resolution and high boundary resolution” at lower ones. As the algorithm descends the multiresolution structure, the coarse segmentation results are propagated down to the lower levels so as to reduce the inherent class-boundary uncertainty and to improve the segmentation accuracy. The computational complexity and frequent occurrences of over-segmentation of Gibbs sampler are addressed and the computationally and functionally effective region-merging process is included to allow Gibbs sampler to start its annealing schedule at relatively low pseudo-temperature and to guide the search trajectory away from local minima associated with over-segmented configurations.

Introduction

Image segmentation is the essential and usually the first stage in image analysis and computer vision systems. Its applications can be found in a wide variety of areas such as remote sensing, vehicle and robot navigation, medical imaging, surveillance, target identification and tracking, scene analysis, product inspection/quality control, etc. It is also frequently cast as an optimization problem wherein the partitioning of the target image corresponding to the optimal value of an objective function is sought [3], [12], [14], [17], [19]. The appropriateness of the objective function dictates the accuracy of the segmentation results. However, formulating an appropriate objective function is usually one of the most difficult parts in an optimization problem. The ubiquitous local optima in the landscape of the objective function necessitate proper mechanisms to guide the algorithm away from them.

Moreover, segmenting texture images is not a trivial task due to various reasons. First of all, textures consist of primitives and tiny edges (intensity fluctuation) which can cause false response to conventional edge detectors, while texture boundaries do not appear as conventional edges between homogeneous regions, and thus, often go undetected by conventional edge detectors [6].

Another major difficulty of texture segmentation arising from the contextual characteristic of texture is the compatibility of texture symbol (what class the texture belongs) with the position symbol (where the texture boundary is) [18]. If we take a big block of a textured image into consideration by using a large analysis window, we get high confidence in which class of texture this area contains. However, we lose confidence in where the texture boundary may be. On the other hand, if we confine the analysis in a smaller window, the confidence in boundary position increases at the expense of compromising the certainty of texture class. This problem, known as “class-boundary uncertainty” [18], calls for remedy and poses a tough challenge to all segmentation algorithms. It is this reason that motivates the adoption of the multiresolution approach in this work.

Thirdly, to be considered effective and practicable in a wide variety of application areas, a segmentation algorithm must work without human supervision or intervention. To achieve this objective, the algorithm should not require a priori knowledge about the number of texture classes and the types of textures contained in the target images. The later requirement means that it is preferable not to have a training phase before the algorithm is commissioned. This requirement is sensible because if the training phase were needed, than when textures outside the training set present in the images, the algorithm would have difficulty identifying them.

In the last few decades, a wide variety of image segmentation techniques have been reported in the literature [1], [3], [4], [7], [8], [10], [11], [12], [13], [14], [15], [17]. Among them, Markov random field is one of the most frequently utilized techniques [1], [4], [7], [8], [12], [13], [17]. However, despite its local characteristic (also known as Markovianity), which allows a global optimization problem to be solved locally, Markov random field is still a computation intensive method, especially when they are used in conjunction with stochastic relaxation schemes [16] such as simulated annealing (SA) [5], [17]. With simulated annealing, to guarantee the convergence to the global optimal, the annealing schedule has to start with a sufficiently high pseudo-temperature. Unfortunately, it is non-trivial to tell how high is sufficient, and the higher the starting temperature is, the longer the schedule will take.

Generally speaking, given the inherent merit of MRF's local characteristic, to make Markov random field a more efficient segmentation technique, the following requirements have to be met.

  • No a priori knowledge about the number of texture classes and the types of textures contained in the images is required.

  • The objective function has to appropriately characterize the problem domain.

  • When simulated annealing is adopted, a mechanism allowing the schedule to start from relatively low temperature should be utilized in order to accelerate the convergence rate and to stay away from the local optima. However, the computational cost of the mechanism must be insignificant relative to that of the MRFs.

The approach reported by Wilson and Li in [17] is a typical combination of MRFs and simulated annealing, known as Gibbs sampler [5]. By using the idea of set of indispensable labels (SOIL) [9] and exploiting the local feature differences, their work requires no a priori global knowledge about the number of texture classes and the types of textures contained in the images. The satisfactory experimental results demonstrate that their technique is effective. However, without meeting the last two requirements mentioned above, their algorithm has to start at high temperature and may still converge to local minima, yielding over-segmented results. It is our intention to propose an improved algorithm in this work, which meets all the three aforementioned requirements to circumvent the shortcomings of Gibbs sampler in general and the algorithm of [17] in particular.

The rest of the paper is organized as follows. Section 2 discusses the methodology and drawbacks of the previous work [17]. The core of the modified multiresolution Gibbs sampler and the region-merging algorithm are proposed in Section 3. A set of experiments is conducted in Section 4. Section 5 concludes the work.

Section snippets

Methodology and drawbacks of the previous work

In work [17], when Gibbs sampler is applied for texture segmentation, the algorithm is comprised of two sequential processes: a region process making use of regional data followed by a boundary process making use of boundary information. Both of the two processes employ Gibbs sampler. However, besides providing a smoother visual effect, the boundary process does not contribute significant accuracy improvement. The decisive role is played by the region process. Therefore, in this work, we will

Multiresolution Gibbs sampler

In the context of texture segmentation, what we want to achieve is to assign a proper class label to each pixel in an image based on the observed data. An equivalent statistical description of this problem is that we want to know the posterior probability distribution P(X|Y) where X is the label configuration and Y is the observed data. According to Baye's theorem, this posterior probability can be expressed in terms of a prior probability P(X) and the conditional probability of the observation

Experiments

Like most approaches, the segmentation process in this work follows the features extraction process. Since the main purpose of this work is to investigate the performance of the segmentation process, without loss of generality, feature set in this work includes only the mean gray value, a common feature adopted in discriminating textures. However, readers are reminded that appropriate features other than mean gray value can be incorporated with the proposed segmentation algorithm since the

Conclusions

In this work, we have addressed the drawbacks of Gibbs sampler (i.e., the combination of Markov random field and simulated annealing) when it is applied to texture segmentation problem due to its short-range interaction among sites and local “sibling competition”. In attempt to circumvent these drawbacks, we also pointed out that given the inherent merit of MRF's local characteristic, to make Gibbs sampler a more efficient segmentation technique, the following requirements have to be met.

  • No a

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