A spatially adaptive retinex variational model for the uneven intensity correction of remote sensing images
Introduction
It is well known that the remote sensing image acquisition process is complicated, which usually results in radiometric errors. The two main reasons for the errors are sensor malfunction and the external interference. Even if the imaging system is in working order, radiometric errors will still accompany the external interference. The external factors include: non-uniform illumination; atmospheric attenuation brought about by atmospheric scattering and absorption; and terrain attenuation brought about by terrain elevation, aspect, slope, and so on. Therefore, remote sensing images usually have an uneven intensity distribution, color cast, etc. In this paper, we are concerned with the uneven intensity distribution that is caused by the non-uniform illumination in aerial remote sensing images. Since remote sensing data is very important for image classification, change detection, and other applications [1], [2], [3], it is extremely important to carry out radiometric correction.
The traditional correction methods are either absolute or relative radiometric correction. Most forms of absolute radiometric correction are based on physical theory, which is extremely complex. This often requires huge amounts of information, including atmospheric and sensor properties for the acquisition date of the satellite scene, and so on. For the majority of the archived satellite images, this information is not available [4], [5], [6]. Thus, relative radiometric correction has been developed, which normalizes multiple satellite scenes to match a referenced one. To date, a few methods based on single-scene image enhancement have been applied to adjust uneven illumination, including the homomorphic filter (HF) and histogram equalization (HE). The HF can adjust the illumination, but it suffers from the problem of color distortion [7], [8], [9]. The HE can redistribute the intensity distribution [9], [10], [11], [12], [13]; however, the results may sometimes turn out to be even more uneven [9]. Furthermore, a unique solution does not exist for multiband histogram matching [14].
Color perception techniques based on the human visual system (HVS) have also been developed to correct the uneven intensity distribution [6]. When the illumination level is very low, the rods in the retina play a leading role. Thus, the HVS cannot identify the color very well [15], [16], [17]. However, the HVS has the ability to perceive the colors of a scene almost independently of the spectral electromagnetic composition of uniform illumination, i.e., color constancy [6]. The first contribution in this field was the retinex theory proposed by Land and McCann [18], [19]. Subsequently, other path-based algorithms have been proposed based upon different path geometry [20], [21], [22]; however, these approaches can be time-consuming.
In the image processing field, PDE-based models and variational techniques have been very popular [23], [24], [25], [26], and have also been developed for uneven intensity correction. According to retinex theory, researchers have decomposed the image intensity as a product of the illumination and reflectance intensity. With the assumption that the illumination varies smoothly, Poisson equation type retinex algorithms have been proposed [27], [28], [29], [30]. Based on this assumption, a variational framework for the retinex was proposed by Kimmel et al. [31]. In this framework, the illumination intensity is first estimated by a variational model, and it is then removed to obtain the reflectance intensity. Recently, according to the reflectance piecewise constant assumption, Michael et al. [32] and Li et al. [6] proposed a total variation (TV) model and a perceptually inspired variational method for the retinex, respectively. In [32], the relationship and the fidelity term between the illumination and reflectance are considered. In [6], both the L2 norm prior and the TV prior are used; furthermore, the “gray world” (GW) assumption [33] is also considered. Although these methods did show improvements, there are still shortcomings with both models.
In this paper, a spatially adaptive retinex variational model is proposed. Here, the spatial information is used to constrain the TV regularization strength of the reflectance. In the edge pixels, a weak regularization strength is enforced to preserve detail, and in the homogeneous areas, a strong regularization strength is enforced to eliminate the uneven intensity. In addition, we take the essentials features of both [6], [32], in that the GW assumption and the fidelity term between the illumination and reflectance are also considered in the proposed model. Moreover, the split Bregman optimization algorithm is employed to solve the proposed model.
The remainder of this paper is organized as follows. In Section 2, we review retinex theory and the perceptually inspired retinex variational framework. The spatially adaptive retinex variational model is described in detail in Section 3. The experiments are presented in Section 4. Finally, conclusions are drawn in Section 5.
Section snippets
Retinex theory
Recently, more attention has been paid to color perception techniques based on the HVS [6], [34]. Here, we review the first contribution in this field: retinex theory. The basic model is as follows:where is the observed image, is the uneven or even illumination distribution, and represents the object reflectance , which is related to the physical characteristics of the material object. In order to reduce the product expression, (1) is converted into the logarithmic form, as
The proposed model
In [32], Michael et al. assumed that the reflectance component was piecewise constant, and used the TV prior as the regularization term. In this paper, the same assumption is adopted.
In addition, it is very important to note that the TV regularization strength of the reflectance should be associated with the spatial information of the reflectance. In the edge pixels, a weak regularization strength is enforced to preserve detail, and in the homogeneous area, a strong regularization strength is
Experimental results and discussion
In this section, extensive simulated experiments and real-life experiments are presented to verify the effectiveness of the proposed model. In this paper, we compare the results of the proposed model with the models of Michael’s model [32] and Li’s model [6]. In the simulated experiments, four common quantity evaluation indexes (PSNR [6], [45], MSE [6], [46], SSIM [47], GSIM [48]) based on the reference image are used to evaluate the recovery results. Since clear images in real-life experiments
Conclusion
This paper presents a spatially adaptive retinex variational model for uneven intensity correction. In this model, the spatial information is used to constrain the TV regularization strength of the reflectance, which effectively preserves the details. The relationship and the fidelity term between the illumination and reflectance are also considered. Moreover, the split Bregman optimization algorithm is employed to solve the proposed model. Extensive experiments were undertaken with both
Acknowledgements
The authors would like to thank the editors and the anonymous reviewers for their valuable suggestions. This work was supported in part by the Nation Basic Research Program of China (973 Program) under grant no. 2011CB707103, the National Natural Science Foundation of China under Grants 41271376, Hubei Natural Science Foundation under Grant 2011CDA096, Program for Changjiang Scholars and Innovative Research Team in University (IRT1278), and the Fundamental Research Funds for the Central
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