REGION ADAPTIVE ADJUSTMENT STRATEGY BASED ON INFORMATION ENTROPY FOR REMOTE SENSING IMAGE SEGMENTATION

For the difficulty of boundary-fitting in region-based algorithms, a region adaptive adjustment strategy based on information entropy is proposed for remote sensing image segmentation. Considering the characteristics of imperfect blocks that cover two homogeneous regions, a selection factor constructed by the spectral coefficient of variation and the information entropy of prior probability representing neighborhood constraint is designed to find the imperfect blocks. Then, the selected imperfect block is split into four equal parts, and new blocks enjoy the same membership as the original block. The model parameters are updated based on the current tessellation. If the fuzzy clustering objective function decrease, the split operation is certainly accepted, otherwise, it will be accepted with a certain probability to avoid local optimum. Finally, the experiments on simulated and multi-spectral remote sensing images show that the proposed strategy can accurately locate the imperfect blocks and effectively fit the boundary of homogeneous regions. * Corresponding author


INTRODUCTION
Image segmentation plays a crucial role in remote sensing image interpretation (Mi and Chen, 2020;Troyagalvis et al., 2015), its main task is to partition the image into a group of homogeneous regions and ensure that (1) the features of pixels in the region is homogeneous and the site of pixels are highly connected in image space (Zhang et al., 2020a), (2) the segmentation boundaries between two homogeneous regions are consistent with the truth boundaries . However, due to the influence of the same ground object with different spectra, high-quality remote sensing image segmentation is always the research of general interest (Löw et al., 2015).
There are many image segmentation methods, such as clustering-based (Gong et al., 2013;Memon and Lee, 2018), statistical-based (Drăguţ et al., 2014;Schmitt et al., 2014), and so on. Clustering-based methods group the pixels according to the dissimilarity between pixels and the clustering center. It is an adaptive iterative optimization algorithm, which is widely used in image processing (Lei et al., 2019). To describe the statistical distribution characteristics, the statistical-based methods are also proposed to improve noise immunity (Permute et al., 2006). Combining the advantages of the two methods, Chatzis and Varvarigou (2008) proposed a statistical-based fuzzy clustering algorithm (HMRF-FCM). The fuzzy theory can deal with the problem that overlapping pixels are difficult to distinguish. It assumes that the pixels in the homogeneous region follow Gaussian distribution, and the dissimilarity is modeled by the negative logarithm of the probability density function. Then, the fuzzy clustering objective function is constructed by weighted dissimilarity measure with membership and adding the KL (Kullback-Leibler ) entropy regularization term. HMRF-FCM has made great achievements in pixel-based segmentation algorithms. However, the ability to overcome noise is still limited (Zhao et al., 2017).
Recently, the region-based algorithm has become the mainstream in remote sensing image segmentation (Kotaridis and Lazaridou, 2021;Zhang et al., 2020b), where the simplest way of regionalization is to divide the image domain into a group of regular blocks (Wang et al., 2016). The regular blocks are difficult to fit the boundary effectively. To improve it, Wang et al. (2015) proposed splitting and merging operations under 他 the Bayesian segmentation framework. However, split or merged blocks are randomly selected, which is not focalization and generates a lot of redundant operations. To find the imperfect blocks purposefully and improve segmentation results, a region adaptive adjustment strategy is proposed in this paper. First, a selection factor constructed from the spectral and spatial aspect is modeled to distinguish imperfect and perfect blocks, where the spectral characteristic is modeled by the spectral coefficient of variation, the spatial characteristic is modeled by the information entropy of prior probability representing neighborhood constraint. Based on the fuzzy clustering segmentation framework, the selected block is divided into four equal parts, and the newly generated blocks inherit the membership of the original one. Finally, the iterative optimization operation is completed under the regionalized HMRF-FCM (Zhao et al., 2017) framework to obtain the optimal segmentation results.

Region adaptive adjustment strategy
Taking regular tessellation as an example, the image Z = {zi (xi, yi): i = 1, ..., n} is divided into a series of regular blocks B = {Bj: j = 1, ..., m}, where i and j are the index of pixels and blocks, n and m are the number of pixels and blocks, (xi, yi) and zi = (zia: a = 1, ..., b) are the position and the spectral vector of pixel i, a and b are the index and the number of bands, respectively.
The visualization model of imperfect blocks is shown in Figure  1, the black frame represents regular blocks, the red frame represents imperfect block, the green frame represents perfect block, the bold blue line represents the boundary of two homogeneous regions (yellow and pink). It can be seen that the characteristics can be described from two aspects of the block itself and the neighboring blocks. Comparing to perfect block B2, there are two kinds of spectral information in the imperfect block B1. It shows that the spectra of the imperfect block will be more discrete. To describe the degree of dispersion, the spectral coefficient of variation of the block is defined as, Where μ(j) and Σ(j) are the mean and covariance of spectra in block j. For the spatial constraints aspect, the labels of neighboring blocks of the imperfect block are more diverse, and the segmentation uncertainty of this block is larger. It means that more information is needed to determine the label of the imperfect block. According to the theory of information entropy, the entropy of prior probability representing neighborhood label constraint is used to describe the diversity.
Where l and k are the index and the number of clusters, respectively, pjl is the prior probability defined by neighborhood system Ω = {Bj': j'~j}, '~' represents the adjacency relation, j' is the index of neighboring blocks. To describe the spatial constraints, the prior probability is modeled based on Markov random field theory, Where L j is the label of block j, δ is the neighborhood influence intensity, when Lj = Lj', η (Lj, Lj') = 1, otherwise η (Lj, Lj') = 0.
Combining the spectral coefficient of variation and information entropy of prior probability, the selection factor is defined as, The higher the value of Sj, the higher the degree of imperfection of the block. Then, the most imperfect block needed to be split is, Block Bh is chosen to split into four equal parts according to the operation, as shown in Figure 2, c is the scale of the block. The newly generated blocks are renumbered counterclockwise as m+1, m+2, and m+3, and their membership is inherited from the original block, i.e. um+1 l = um+2 l = um+3 l =uhl.

Fuzzy clustering segmentation
Based on the block after regular tessellation, the region fuzzy clustering objection function is defined as (Zhao et al., 2017), Where ujl is the membership of block j belonging to cluster l, λ is the coefficient of regularization term, Nj is the number of pixels in block j, djl is the dissimilarity measure defined by the negative logarithm of the probability density function of Gaussian distribution, Where θl = {μl, Σl} is the distribution parameter set, μl and Σl are mean and covariance of the Gaussian distribution to which cluster l follows.
Minimization of the objective function by derivative method, the analytical solution of ujl, μl, and Σl can be obtained,
S6: Stop iteration until the objective function is minimum.

EXPERIMENTS
To highlight the effectiveness of the region adaptive adjustment strategy, the simulated and multi-spectral remote sensing images are tested by two comparison algorithms, HMRF-FCM (Chatzis and Varvarigou, 2008) and the regular tessellation fuzzy clustering algorithm, abbreviated as RT-HMRF-FCM (Zhao et al., 2017). The performance of the proposed algorithm is evaluated qualitatively and quantitatively. It shows that there are many speckle mis-segmentation pixels because of the pixel-based mechanism of HMRF-FCM, as shown in Figures 3(a2) and (a3). The speckle mis-segmentation pixels will increase with spectral complexity. Although RT-HMRF-FCM can effectively overcome the speckle noise, the boundaries between homogeneous regions cannot be fitted smoothly, as shown in Figure 3(b1)-(b3). Comparing Figure 3(b1) and (c1), it can be seen that the imperfect blocks chosen to split are generally distributed on the boundaries of homogeneous regions, which advantageously verifies the effectiveness of the selection factor. Besides, the boundaries are fitted smoothly, which can verify the correctness of the combination of region adaptive adjustment strategy and fuzzy clustering segmentation. The proposed algorithm not only can well fit the boundary, but also avoid speckle noise. In Figure 4, the segmentation results of the HMRF-FCM algorithm is seriously affected by the forest with big spectral variance, as shown in Figure 4(a2) and (a3). For RT-HMRF-FCM, the inner area of homogeneous regions is effectively segmented. However, the boundaries are extremely rough, such as the boundary between farm and forest, as shown in Figure  4(b2) and (b3). The proposed algorithm, benefited by the proposed adaptive selection and splitting strategy, can realize the smooth fitting of boundaries as well as the effective segmentation, as shown in Figure 4(c1) -(c3). , it can be seen that the proposed algorithm has a good ability in finding imperfect blocks and reserving perfect blocks, the segmentation result is better than others. are the comparison of truth boundary and the buffer area of segmentation boundary. The green is right pixels, the red in Figure 6(a1)-(a3), (c1)-(c3) and (e1)-(e3) represents the redundant boundary in segmentation results, the red in Figure  6(b1)-(b3), (d1)-(d3) and (f1)-(f3) represents the deficient boundary in segmentation results. It can be seen that both redundant and deficient boundaries of the proposed algorithm segmentation results are the least compared with others. Figure 6. Buffer area analysis of segmentation boundaries. (a1)-(f1) HMRF-FCM, (a2)-(f2) RT-HMRF-FCM, (a3)-(f3) The proposed algorithm.

CONCLUSION
The pixel-based segmentation has weak noise immunity. However, the region-based algorithms are difficult to fit the boundary smoothly. Focus on the problem, a region adaptive adjustment strategy is proposed in this paper. By analyzing the characteristics of imperfect blocks that cover two or more homogeneous regions, the spectral coefficient of variation based on the block itself and the information entropy of the neighborhood system are modeled to find the imperfect blocks. The most imperfect block is chosen to split into four equal parts.
To avoid local optimum, the split operation will be accepted with a certain probability. A lot of experiments show that the proposed algorithm can find the imperfect blocks accurately, realize the effective segmentation and fit the boundaries smoothly. In the future, other strategies such as merging will be further studied to enhance the performance.