Shiftable Complex Directional Pyramid Research Articles

Infrared and visible image fusion based on shiftable complex directional pyramid transform and SUSAN edge detector

Infrared and visible image fusion based on shiftable complex directional pyramid transform and SUSAN edge detector

Exposure fusion via sparse representation and shiftable complex directional pyramid transform

Sparse code theory with the sliding window technique can be used for the efficient fusion of multi-exposure images. However, when the size of the source images is large, this process requires a sig...

RHFMs similarity based nonlocal means image denoising in PDTDFB domain

It is a challenging work to design an edge-preserving image denoising scheme. Nonlocal means methods have been widely adopted as simple algorithms for image denoising, but they tend to overblur the image and sharpen the boundary with many texture details lost. In this paper, we propose a new nonlocal means image denoising approach in shiftable complex directional pyramid (PDTDFB) domain, in which the robust radial harmonic Fourier moments (RHFMs) are utilized. The novelty of the proposed approach includes: (1) PDTDFB based multi-scale structural similarity is explored, which has good robustness to noise interference, (2) Geometric invariant radial harmonic Fourier moments (RHFMs) are introduced into similarity measure function, which can improve the denoising ability. Experimental results demonstrate that our image denoising method can obtain better performances in terms of both subjective and objective evaluations than some other state-of-the-art denoising techniques. Especially, it can preserve edges very well while removing noise.

Image denoising using multivariate model in shiftable complex directional pyramid domain and principal neighborhood dictionary in spatial domain

The major challenge for image denoising is how to effectively remove the noise and preserve the detail information to get better visual quality and higher peak signal-to-noise ratio (PSNR). A new image denoising methods based on combination of multivariate shrinkage model in shiftable complex directional pyramid (PDTDFB) domain and principal neighborhood dictionary (PND) non-local means algorithm in spatial domain is proposed. In PDTDFB domain, the PDTDFB coefficients are modeled as multivariate non-Gaussian distribution taking into account the interscale and intrascale dependency correlation. Then a multivariate shrinkage function is derived by the maximum a posterior (MAP) estimator and the denoised coefficients are obtained. Although the PDTDFB-based algorithm achieves efficient denoising result, it is prone to producing salient artifacts which relate to the structure of the PDTDFB. Principal neighborhood dictionary (PND) is further employed to alleviate the artifacts with small computational load in spatial domain. Experimental results indicate that the proposed method is competitive with other excellent denoising methods in terms of PSNR value and visual quality.

Robust digital watermarking in PDTDFB domain based on least squares support vector machine

Geometric distortion is known as one of the most difficult attacks to resist, for it can desynchronize the location of the watermark and hence causes incorrect watermark detection. It is a challenging work to design a robust image watermarking scheme against geometric distortions. Based on the least squares support vector machine (LS-SVM) geometric distortions correction, we propose a new image watermarking scheme in shiftable complex directional pyramid (PDTDFB) domain with good visual quality and reasonable resistance toward geometric distortions in this paper. Firstly, the PDTDFB decomposition is performed on the original host image. Then, the corresponding lowpass subband is divided into small blocks. Finally, the digital watermark is embedded into host image by modulating the selected lowpass PDTDFB coefficients in small blocks. The main steps of digital watermark detecting procedure include: (1) the PDTDFB decomposition is performed on the test images, and some low-order Gaussian–Hermite moment energy of highpass subbands are computed, which are regarded as the effective feature vectors; (2) the appropriate kernel function is selected for training, and a LS-SVM training model can be obtained; (3) the watermarked image is corrected with the well trained LS-SVM model; and (4) the digital watermark is extracted from the corrected watermarked image. Experimental results show that the proposed image watermarking is not only invisible and robust against common image processing operations such as filtering, noise adding, and JPEG compression etc, but also robust against the geometrical distortions.

Multimodality image fusion by using both phase and magnitude information

In most of complex wavelet based fusion methods, only magnitude (or absolute value) of a complex coefficient is considered and phase information is neglected. However, more salient image features can be determined by the phase. In this paper, a multimodality image fusion algorithm is proposed with the shiftable complex directional pyramid transform (SCDPT), where phase and magnitudes of complex coefficients are jointly considered. Firstly, a novel similarity index (CCC-EM) is presented by combining the circular correlation coefficient (CCC) of relative phase angles and the traditional energy matching (EM) index. When bandpass directional subband coefficients are merged, the CCC-EM index is employed as the similarity measure and three types of regions between source images are determined for each bandpass directional subband. Then, based on some weights or salience measures, different fusion rules are designed for each type of regions. Especially, for regions with similarity in energy and positive or negative correlation relationship in relative phase, the weighted circular variance (WCV) of relative phase angles is employed. When lowpass subband coefficients are merged, the traditional structural similarity index is employed to distinguish different types of regions. For most of regions, the local energy of lowpass subband coefficients is employed as weights or salience measures. While for regions with similar intensity values but different intensity variation directions, an inter-scale based salience measure is defined by combining the local energy of the lowpass subband coefficients and the WCV of the coarsest bandpass directional subband coefficients. Several pairs of multimodality images are fused with the proposed methods. Fusion results demonstrate that the proposed fusion method can extract more salient features (not just in energy) from source images than some other complex wavelet based fusion methods. Especially, more phase information of source images can be preserved into the fused image, which makes the proposed fusion method with higher performance in spatial consistency.

Edge structure preserving image denoising using OAGSM/NC statistical model

It is a challenging work to design an edge structure preserving image denoising. In recent years, Bayes least squares-Gaussian scale mixtures (BLS-GSM) has emerged as one of the most powerful methods for image denoising. Its strength relies on providing a simple and, yet, very effective local statistical description of oriented pyramid coefficient neighborhoods via a GSM vector. This can be viewed as a fine adaptation of the model to the signal variance at each scale, orientation, and spatial location. Combining with Bayes least squares estimator, we describe a method for removing noise from digital images, based on orientation-adapted GSM with nonoriented component (OAGSM/NC) in shiftable complex directional pyramid (PDTDFB) domain in this paper, which can be seen a modified version of the BLS-GSM. By introducing a coarser adaptation level, we model the distribution of PDTDFB coefficients with OAGSM/NC. The statistical model is then used to obtain the denoised coefficients from the noisy image decomposition by Bayes least squares estimator. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.

A new image denoising scheme using support vector machine classification in shiftable complex directional pyramid domain

Edge-preserving image denoising has become a very intensive research topic. In this paper, we propose a new image denoising scheme using support vector machine (SVM) classification in shiftable complex directional pyramid (PDTDFB) domain. Firstly, the noisy image is decomposed into different subbands of frequency and orientation responses using a PDTDFB transform. Secondly, the feature vector for a pixel in a noisy image is formed by the spatial regularity in PDTDFB domain, and the least squares support vector machine (LS-SVM) model is obtained by training. Then the PDTDFB detail coefficients are divided into two classes (edge-related coefficients and noise-related ones) by LS-SVM training model. Finally, the detail subbands of PDTDFB coefficients are denoised by using the different parameters to control the multiscale and multidirectional anisotropic diffusion. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.

Similarity-based multimodality image fusion with shiftable complex directional pyramid

For multimodality images, a novel fusion algorithm based on the shiftable complex directional pyramid transform (SCDPT) is proposed in this paper. As well, with the aid of the structural similarity (SSIM) index, a ‘similarity-based’ idea is employed to distinguish regions with ‘redundant’ or ‘complementary’ information between source imagers before the SCDPT coefficients are merged. A ‘weighted averaging’ scheme for regions with ‘redundant’ information and a ‘selecting’ scheme for regions with ‘complementary’ information are then employed, respectively. When merging the low-pass subband coefficients, the SSIM index in spatial domain (SP-SSIM) is employed as similarity measure, and three types of regions are thus determined. Especially, for regions with similar intensity values but different intensity changing directions between source images, a ‘selecting’ scheme based on gradient and energy is proposed. When merging the directional band-pass subband coefficients, the SSIM index in complex wavelet domain (CW-SSIM) is employed as similarity measure. With the CW-SSIM index, not only the magnitude information but also the phase information of SCDPT coefficients can be employed. Compared to the traditional energy matching (EM) index based fusion methods, the proposed method can better deal with ‘redundant’ and ‘complementary’ information of source images. In addition, because of the shift-invariance of the SCDPT and the CW-SSIM index, the proposed fusion algorithm performs well even if the input images are not well registered. Several sets of experimental results demonstrate the validity and feasibility of the proposed method in terms of both visual quality and objective evaluation.

Image denoising using bilateral filter and Gaussian scale mixtures in shiftable complex directional pyramid domain

For image denoising, the main challenge is how to preserve the information-bearing structures such as edges and textures to get satisfactory visual quality when improving the signal-to-noise-ratio (SNR). Edge-preserving image denoising has become a very intensive research topic. In this paper, we describe a method for removing noise from digital images, based on bilateral filter and Gaussian scale mixtures (GSM) in shiftable complex directional pyramid (also named Pyramidal Dual-Tree Directional Filter Bank, PDTDFB) domain. Firstly, the noisy image is decomposed into different subbands of frequency and orientation responses using a PDTDFB transform. Secondly, the bilateral filter, which is a nonlinear filter that does spatial averaging without smoothing edges, is applied on the approximation subband. Finally, the distribution of detail subbands of PDTDFB coefficients is modeled with GSM, and the statistical model is then used to obtain the denoised detail coefficients from the noisy image decomposition by Bayes least squares estimator. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.

The Shiftable Complex Directional Pyramid—Part II: Implementation and Applications

In Part I ["The shiftable complex directional pyramid-Part I: Theoretical Aspects," IEEE TRANSACTIONS on Signal Processing, vol. 56, no. 10, October 2008], we proposed a novel image decomposition called the shiftable complex directional pyramid. The shiftable, multiresolution and multidirectional image decomposition is constructed by the pyramidal dual-tree directional filter bank (PDTDFB). In this Part II, we consider the design and implementation issues of the PDTDFB and its applications in image processing. The PDTDFB is composed of a multiresolution filter bank (FB) and a pair of directional filter banks (DFB); the design of each FB is considered separately. The binary tree structure of the DFB is modified to minimize the phase delay factor in order to reduce the border artifact in case symmetric extension is used. The filters presented in this paper are designed in frequency domain, and approximated by finite-impulse-response (FIR) filters. Numerical experiments show that the filters from the dual branches approximate the Hilbert transform of those from the primal ones, and the resulting PDTDFB yields acceptable shiftability. The shiftable pyramid decomposition is then tested in image processing applications, including image denoising, texture retrieval and seismic image migration.

The Shiftable Complex Directional Pyramid—Part I: Theoretical Aspects

This paper presents an over-complete multiscale decomposition by combining the Laplacian pyramid and the complex directional filter bank (DFB). The filter bank is constructed in such a way that each complex directional filter is analytical using the dual-tree structure of real fan filters. Necessary and sufficient conditions in order for the resulting multirate filter bank to be shift-invariant in energy sense (shiftability) are derived in terms of the magnitude and phase responses of these filters. Their connection to 2D Hilbert transform relationship is established. The proposed transform possesses several desirable properties including multiresolution, arbitrarily high directional resolution, low redundant ratio, and efficient implementation.