Spatial Images Feature Extraction Based on Bayesian Nonlocal Means Filter and Improved Contourlet Transform

Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2012, Article ID 467412, 16 pages doi:10.1155/2012/467412 Research Article Spatial Images Feature Extraction Based on Bayesian Nonlocal Means Filter and Improved Contourlet Transform Pengcheng Han and Junping Du Beijing Key Laboratory of Intelligent Telecommunication Software and Multimedia, School of Computer Science, Beijing University of Posts and Telecommunications, Beijing 100876, China Correspondence should be addressed to Junping Du, Received 1 March 2012; Accepted 6 April 2012 Academic Editor: Baocang Ding Copyright q 2012 P. Han and J. Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Spatial images are inevitably mixed with different levels of noise and distortion. The contourlet transform can provide multidimensional sparse representations of images in a discrete domain. Because of its filter structure, the contourlet transform is not translation-invariant. In this paper, we use a nonsubsampled pyramid structure and a nonsubsampled directional filter to achieve multidimensional and translation-invariant image decomposition for spatial images. A nonsubsampled contourlet transform is used as the basis for an improved Bayesian nonlocal means NLM filter for different frequencies. The Bayesian model adds a sigma range in image a priori operations, which can be more effective in protecting image details. The NLM filter retains the image edge content and assigns greater weight to similarities for edge pixels. Experimental results both on standard images and spatial images confirm that the proposed algorithm yields significantly better performance than nonsubsampled wavelet transform, contourlet, and curvelet approaches. 1. Introduction In spatial rendezvous and docking, spatial images are obtained by multisource remote sensors. Spatial images are inevitably mixed with different levels of noise and distortion. The accurate image feature extraction will be helpful for spatial object recognition and can directly influence the success of spatial rendezvous and docking 1, 2. Image feature extraction of spatial images is based on the definition of image features; to some extent, it can be said that it is based on sensitivity changes to image grayscale values for the human eye. Multidimensional image representation can process images for the sparsest representation, especially for 2D image signals 3, 4. This approach identifies optimal high-dimensional 2 Journal of Applied Mathematics Vertical Contours Diagonal Horizontal Wavelet transform decomposition Image contour representation Figure 1: Multidimensional image decomposition. function representation for an image and yields superior image-processing results for an effective solution. A nonlocal means NLM filter uses redundant image information on the basis that structural similarity superimposed on pixel noise is random and noise can be effectively removed using weighted averages 5, 6. Compared to traditional statistical filtering methods, NLM filtering overcomes the constraint of the local neighborhood and extends pixel similarity to block-based similarity, so it is very suitable to deal with spatial images. In this paper, we use a nonsubsampled pyramid structure and a nonsubsampled directional filter to achieve multidimensional and translation-invariant image decomposition for spatial images. A nonsubsampled contourlet transform is used as the basis for an improved Bayesian nonlocal means NLM filter for different frequencies. The Bayesian model adds a sigma range in image a priori operations, which can be more effective in protecting image details. The NLM filter retains the image edge content and assigns greater weight to similarities for edge pixels. Experimental results both on standard images and spatial images confirm that the proposed algorithm yields significantly better performance than nonsubsampled wavelet transform, contourlet, and curvelet approaches. The rest of this paper is organized as follows. Section 2 describes multidimensional image decomposition, with a focus on contourlet and nonsubsampled contourlet transforms NSCTs. Section 3 outlines application of an NLM filter and proposes an improved NLM algorithm based on a Bayesian model. Section 4 applies the improved NLM filter to NSCT, especially NSDFB, to process image features for further extraction. Section 5 compares feature extraction results for the proposed algorithm and other algorithms. Section 6 concludes the paper. 2. Contourlet Transform Decomposition 2.1. Multidimensional Image Decomposition The target of image multidimensional representation is to provide a description of image with less characteristic information. The wavelet transform is a classic image multidimensional representation algorithm that has a good effect on image edge points 7, 8. However, the wavelet transform can capture only limited direction information in the horizontal, vertical, and diagonal directions, as shown in the left side of Figure 1. It is difficult to express image smoothness contours; a better image representation is shown in the right side of Figure 1. Journal of Applied Mathematics 3 Other well-known multidimensional image decomposition algorithms include bandlets, brushlets, edge multidimensional transform, complex wavelets, and wedgelet. However, these algorithms require image edge detection and then summarize a representative adaptive coefficient. A decomposition algorithm that can transform an image into fixed decomposition coefficients is desirable. These coefficients can then be used in a broader context that does rely on edge detection alone but also includes better directional image decomposition. In 2004, Candès and Donoho proposed a curvelet transform that uses a value approximation algorithm for a continuous 2D spatial domain and adds a smooth signal on the basis of a 1D Fourier transform 9. The best approximation deviation is Olog M3 M−2  for curvelet and OM−1  for wavelet transforms. The curvelet transform is first applied to a continuous signal and then combines a multidimensional filter and ridgelet transformation. A second curvelet transform is based on frequency segments and extreme judgment. The curvelet transform is universally applicable to continuous signals, but there will be parallel noise in discrete fields 10. It is also biased in directional image decomposition. The reason is that the typical rectangular sampling mode leads to a priori geometric deviation in decomposition of discrete image signals, especially in the horizontal and vertical directions. This limitation prompted researchers to develop a new multiscale decomposition algorithm that does not depend on edge detection and can decompose images in cross-scale multidimensions. 2.2. Contourlet Transform The conto (...truncated)