Showing papers on "Contourlet published in 2005"

The contourlet transform: an efficient directional multiresolution image representation

Abstract: The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.

Nonsubsampled contourlet transform: construction and application in enhancement

Abstract: We present the nonsubsampled contourlet transform and its application in image enhancement. The nonsubsampled contourlet transform is built upon nonsubsampled pyramids and nonsubsampled directional filter banks and provides a shift-invariant directional multiresolution image representation. Existing methods for image enhancement cannot capture the geometric information of images and tend to amplify noises when they are applied to noisy images since they cannot distinguish noises from weak edges. In contrast, the nonsubsampled contourlet transform extracts the geometric information of images, which can be used to distinguish noises from weak edges. Experimental results show the proposed method achieves better enhancement results than a wavelet-based image enhancement method.

Nonsubsampled contourilet transform: filter design and applications in denoising

Abstract: In this paper we study the nonsubsampled contourlet transform. We address the corresponding filter design problem using the Mc-Clellan transformation. We show how zeroes can be imposed in the filters so that the iterated structure produces regular basis functions. The proposed design framework yields filters that can be implemented efficiently through a lifting factorization. We apply the constructed transform in image noise removal where the results obtained are comparable to the state-of-the art, being superior in some cases.

Beyond wavelets: New image representation paradigms

Abstract: It is by now a well-established fact that the usual two-dimensional tensor product wavelet bases are not optimal for representing images consisting of different regions of smoothly varying greyvalues, separated by smooth boundaries. The chapter starts with a discussion of this phenomenon from a nonlinear approximation point of view, and then proceeds to describe approaches that have been suggested as a remedy. The methods can be sorted roughly into two groups: Adaptive geometry-based approaches such as wedgelets and related constructions on one hand, and directional frames, such as curvelets or ridgelets, on the other. We discuss wedgelets and curvelets in more details, as representatives of the different branches. These systems are first described in the continuous setting, and their construction is motivated by a discussion of their nonlinear approximation properties. We then present digital implementations of the schemes. For wedgelets and related transforms, we present a new method which results in a significant speedup, in comparison to preexisting implementations. We also give a short description of the contourlet approach to discrete curvelets. In the last section, we present the results of nonlinear approximation experiments, comparing wedgelets, contourlets and wavelets, and comment on the potential of the new techniques for image coding.

Improved denoising of images using modelling of a redundant contourlet transform

Abstract: In this work we investigate the image denoising problem. One common approach found in the literature involves manipulating the coefficients in the transform domain, e.g. shrinkage, followed by the inverse transform. Several advanced methods that model the inter-coefficient dependencies were developed recently, and were shown to yield significant improvement. However, these methods operate on the transform domain error rather than on the image domain one. These errors are in general entirely different for redundant transforms. In this work we propose a novel denoising method, based on the Basis-Pursuit Denoising (BPDN). Our method combines the image domain error with the transform domain dependency structure, resulting in a general objective function, applicable for any wavelet-like transform. We focus here on the Contourlet Transform (CT) and on a redundant version of it, both relatively new transforms designed to sparsely represent images. The performance of our new method is compared favorably with the state-of-the-art method of Bayesian Least Squares Gaussian Scale Mixture (BLS-GSM), which we adapted to the CT as well, with further improvements still to come.

Adaptive watermarking schemes based on a redundant contourlet transform

Abstract: We are interested in the adaptive watermarking approaches and in directional multiresolution image transforms. In this paper, a novel watermarking technique based on a redundant contourlet transform is presented. In contrast to the wavelet transform widely used for image watermarking, to our best knowledge, this is the first time contourlets are applied to this field. The goal of this work is to investigate whether the contourlet with their extra feature of directionality and the explicit introduction of redundancy would provide any significant advantages over the wavelets in terms of watermark robustness and invisibility. Our approach uses directional subbands to generate weighing masks that identify significant image features. The redundancy being introduced brings simplicity and accuracy for mask processing. To prove the validity of our approach, we give experimental results, compare our algorithm to a wavelet-based adaptive watermarking technique and assess watermarking performance in terms of robustness and invisibility.

An improved pyramid for spatially scalable video coding

Abstract: This paper discusses an improved pyramid for spatially scalable video coding. We introduce additional update steps in the analysis and the synthesis of the Laplacian pyramid. Our pyramid is able to control efficiently the quantization noise energy in the reconstruction. Hence, it provides improved coding performance when compared to the standard Laplacian pyramid. Moreover, our pyramid does not require biorthogonal filters as they should be used for the frame reconstruction of the Laplacian pyramid. Therefore, low-pass filters can be chosen that suppress aliasing in the low-resolution images efficiently and, hence, permit efficient motion compensation. The experimental results demonstrate coding gains of up to 1 dB for both images and image sequences when compared to the standard Laplacian pyramid.

Image denoising using translation-invariant contourlet transform

Abstract: The contourlet transform, one of the recent geometrical image transforms, lacks the feature of translation invariance due to subsampling in its filter bank (FB) structure. In this paper, we develop a translation-invariant (TI) scheme of a general multi-channel multidimensional FB and apply our findings to the contourlet transform to obtain a TI contourlet transform (TICT). Further, we employ the proposed TICT for image denoising, where we show that a significant improvement in the PSNR values as well as visual results is gained. Moreover, we demonstrate that this proposed denoising scheme outperforms the TI wavelet denoising approach for most experiments. We also introduce a less-redundant variety of the TICT, where we merely make the first stage of contourlets, translation invariant. We show that this transform, which we call semi-TICT (STICT), achieves a performance near that of the TICT in image denoising.

A contourlet-based method for writer identification

Abstract: Handwriting-based writer identification is a hot research topic in the field of pattern recognition. Typically, there are four modes of writer identification: on-line text-dependent, on-line text-independent, off-line text-dependent, off-line text-independent; and off-line text-independent is the most challenging problem among them because many valuable writing features are not available in this case, such as shape features, dynastic writing information and etc. In this paper, we focus on the text-independent writer identification based on off-line Chinese handwriting and present a new contourlet-based GGD (Generalized Gaussian Density) method. This novel method achieves a good experiment result in our experiments.

Wavelet-based Contourlet Packet Image Coding

Abstract: The contourlet transform is a new directional transform, which is capable of capturing contours and fine details in images. We recently introduced the wavelet-based contourlet transform (WBCT) that is a non-redundant version of the contourlet transform, and appropriately used this transform for image coding. In this paper, we introduce the concept of wavelet-based contourlet packets (WBCP), which is similar to the notion of wavelet packets (WP). Using WBCP, we have the flexibility of choosing the most proper basis based on a criterion. In this work, we utilize WBCP for image coding to extend our previous work that was based on WBCT for image coding. Our simulation results show that the proposed WBCT packets provide both visual and PSNR improvements over WBCT. Moreover, for texture images the results outperform those of WP, visually, while achieve comparable PSNR values.

Contourlet Based Image Recovery and De-noising Through Wireless Fading Channels

Abstract: The contourlet transform consists of two modules: the Laplacian Pyramid and the Directional Filter Bank. When both of them use perfect reconstruction filters, the contourlet expansion and reconstruction is a perfect dual. Therefore, the contourlet transform can be employed as a coding scheme. The contourlet coefficients derived above can be transmitted through the wireless channel in the same way as transmitting the original image, where the transmission is prone to noise and block loss. However, the reconstruction at the receiver performs differently if the image is transmitted directly or coded by the contourlet transform. This paper studies the performance of the contourlet coding in image recovery and denoising. The simulation results show that for general images the contourlet transform is quite competitive to the wavelet transform in the SNR sense and in visual effect. Further, the contourlet transform can be used in a wireless face recognition system to extract the unique feature that other transforms can not discover, For face recognition system, the recovery of the original image is not essential any more; therefore, the resources on the image reconstruction from the contourlet coefficient can be saved.

Unsupervised image segmentation using contourlet domain hidden markov trees model

Abstract: A novel method of unsupervised imagesegmentation using contourlet domain hidden markov trees model is presented. Fuzzy C-mean clustering algorithm is used to capture the likelihood disparity of different texture features. A new context based fusion model is given for preserve more interscale information in contourlet domain. The simulation results of synthetic mosaics and real images show that the proposed unsupervised segmentation algorithm represents a better performance in edge detection and protection and its error probability of the synthetic mosaics is lower than wavelet domain HMT based method.

Bi-orthogonal filter banks with directional vanishing moments [image representation applications]

Abstract: In this paper we study 2D nonseparable filter banks that annihilate information along a certain discrete direction. This is done by having filters with directional vanishing moments (DVM). We study the approximation property of such filters and the design problem providing conditions for its solvability. In particular, we completely characterize the solution and propose a design procedure utilizing the mapping technique. Nonlinear approximation experiments with the contourlet transform indicate that compared with the traditional filters, the new filters designed with DVM provide gains in SNR and visual quality due to their short size.

Color texture retrieval through contourlet-based hidden Markov model

Abstract: Two statistical models for color texture retrieval based on a hidden Markov model (HMM) in the contourlet domain are described in this paper. Through a contourlet transformation, each color component of an image is decomposed into a set of directional subbands with texture details captured in different orientations. By exploiting inter-scale dependencies and in-band spatial dependencies, the distribution of the coefficients in each subband triplet (subbands of three color components at the same scale with the same orientation) can be estimated using a vector hidden Markov model. The Kullback-Leibler distance (KLD) is used to measure the difference between the distributions of query texture images and those of images in the database. The experimental results show the proposed retrieval systems yield high retrieval rates and better visual quality as compared with previous methods employing hidden Markov models for luminance component alone.

Contourlet image coding based on adjusted SPIHT

Abstract: Contourlet is a new image representation method, which can efficiently represent contours and textures in images. In this paper, we analyze the distribution of significant contourlet coefficients in different subbands and propose a contourlet image coding algorithm by constructing a virtual low frequency subband and adjusting coding method of SPIHT (Set Partitioning in Hierarchical Trees) algorithm according to the structure of contourlet coefficients. The proposed coding algorithm can provide an embedded bit stream, which is very desirable in heterogeneous networks. Our experiments demonstrate that the proposed coding algorithm can achieve better or competitive compression performance when compared with traditional wavelet transform with SPIHT and wavelet-based contourlet transform with SPIHT, which both are embedded image coding algorithms based on two non-redundant transforms. At the same time, benefiting from genuine contourlet adopted in the proposed coding algorithm, more contours and textures in the coded images are preserved to ensure superior subjective quality.

Contourlet image coding based on adjusted SPIHT

Abstract: Contourlet is a new image representation method, which can efficiently represent contours and textures in images. In this paper, we analyze the distribution of significant contourlet coefficients in different subbands and propose a contourlet image coding algorithm by constructing a virtual low frequency subband and adjusting coding method of SPIHT (Set Partitioning in Hierarchical Trees) algorithm according to the structure of contourlet coefficients. The proposed coding algorithm can provide an embedded bit stream, which is very desirable in heterogeneous networks. Our experiments demonstrate that the proposed coding algorithm can achieve better or competitive compression performance when compared with traditional wavelet transform with SPIHT and wavelet-based contourlet transform with SPIHT, which both are embedded image coding algorithms based on two non-redundant transforms. At the same time, benefiting from genuine contourlet adopted in the proposed coding algorithm, more contours and textures in the coded images are preserved to ensure superior subjective quality.

Denoising of images with multiplicative noise corruption

Abstract: Multiplicative noise is signal dependent and is difficult to be removed without impairing image details. It causes difficulties for many real world imaging applications. Previously, a hypothesis test based wavelet denoising algorithm had been proposed with promising results. In this paper, the algorithm has been further studied by fitting it into the framework of contourlet transform, an emerging two-dimensional technique for image processing and analysis. The developed contourlet denoising algorithm has been evaluated with standard test images, yielding successful results. It has also been demonstrated that the proposed algorithm outperformed the original wavelet based approach.

A Method for Image De-noising Based on the Contourlet Transform Using Recursive Cycle Spinning

Abstract: A new method for image de-noising which colligated the strongpoint of Contourlet transform and Recursive Cycle Spinning was presented.Due to the lack of translation invariance of the Contourlet transform,image de-noising by coefficient thresholding would lead to Gibbs-like phenomena(lead to artifacts).Recursive Cycle Spinning was employed to avoid the artifacts.The experimental results indicate that the method can get better visual effect and PSNR value compared with the methods like wavelet image de-noising using the Recursive Cycle Spinning.

Reduced feature texture retrieval using contourlet decomposition of luminance image component

Abstract: In this paper, a texture retrieval system based on directional hidden Markov model (HMM) in the contourlet domain is described. Through a contourlet transform, a directional multiscale transformation, the luminance component of an image can be decomposed into a set of directional subbands with texture details captured in different orientations at various scales. By exploiting in-band spatial dependencies, the distribution of the coefficients in each subband, which is modeled as a Gaussian mixture, is estimated using a directional hidden Markov model. We compare retrieval systems on the basis of retrieval rate and find that the proposed HMM exploiting in-band luminance dependencies provides reasonable results with much fewer features.

Multi-scale image segmentation based on contourlet-domain hidden markov trees model

Abstract: Based on the statistics characteristics of contourlet coefficients,a new multi-scale image segmentation method(CHMTseg)combining Contourlet domain hidden Markov trees model with multiscale Bayesian approaches was presented.A novel weighted neighborhood model was given for preserving more inner-scale information in Contourlet domain.The pixel level segmentation based on Gauss mixture model and the multiscale fusion method based on the new contextual model were provided.In experiments,synthetic mosaic image,aerial image and SAR image were selected to evaluate the performance of the method,and the segmentation results were compared with wavelet domain HMTseg method.For synthetic mosaic texture image,miss classed probability was given as the evaluation of segmentation results.Experiment results show that the method not only has better performance in edges and anisotropy information detection but has lower missed classed probability,and it can achieve satisfied segmentation results for real images.

Comparative Analysis of Decimation-Free Directional Filter Bank with Directional Filter Bank: In Context of Image Enhancement

Abstract: This paper presents a new directional analysis tool namely decimation-free directional filter bank, and its comparison with directional filter bank Outputs of directional filter bank are maximally decimated (smaller in size) due to the presence of decimators Multi-rate identities are used to push all these decimators to the right of filters By doing so, frequency scrambling produced in directional filter bank due to non-diagonalization of overall downsampling matrix is removed No interpolation prior to image enhancement is required in decimation-free directional filter bank, as it was mandatory step before enhancement in directional filter bank Artifacts produced due to interpolation can be misleading in situation like medical images, and aerial images These artifacts are avoided in decimation-free directional filter bank as it requires no interpolation Artifacts produced due to aliasing and folding during downsampling were also avoided in decimation-free directional filter bank due to absence of decimators Synthesis in decimation-free directional filter bank at any stage, can be achieved by just simply adding all the images, as it was not the case with directional filter bank

Image enhancement via fusion based on laplacian pyramid directional filter banks

Abstract: Based on the directionality of images and combining the direction information with multiple resolution analysis, an image enhancement idea via fusion based on directional filter banks is presented in this paper. Combining with LP analysis further, an image fusion method based on LPDFB is given in the paper. Using the experiments to compare the results, they prove its feasibility and validity.

Image Segmentation Method Based on Wavelet Decompositon and Neural Network

Abstract: Firstly, the image was decomposed by wavelet transform to multiresolution image. Multiresolution image pyramid was constructed by multiresolution image. Secondly, the noise of image was better reduced in wavelet transform domain. Finally, the image was segment by classification method of Kohonen neural network that increases speed and accuracy of classification.

Filter design for directional multiresolution decomposition

Abstract: In this paper we discuss recent developments on design t ools and methods for multidi mensional “lter banks inthe context of directional multiresolution representations. Due to the inherent non-separability of the “ltersand the lack of multi-dimensional factorization tools, one generally has to overcome factorization by indirectmethods. One such method is the mapping technique. 1–3 In the context of contourlets we review methodsfor designing “lters with directional vanishing moments (DVM). The DVM property is crucial in guaranteeingthe non-linear approximation ecacy of contourlets. Our approach allows for easy design of two-channel linear-phase “lter banks with DVM of any order. Next we study the design via mapping of nonsubsampled “lterbanks. Our methodology allows for a fast implementation through ladder steps. The proposed design is thenused to construct the nonsubsampled contourlet transfor m which is particularly eciently in image denoising,as experiments in this paper show.Keywords: Multidimensional Filter Banks, Cont ourlets, Nonlinear Approximation

SAR image edge detection based on contourlet-domain hidden Markov models

Abstract: We present a new approach to edge detection on synthetic aperture radar (SAR) images based on contourlet-domain hidden Markov tree (CD-HMT) model. In the contourlet transform, a double filterbank structure, pyramidal directional filterbank, is employed by first using Laplacian pyramidal decomposition and then a local directional filterbank. Compared with the wavelet transform, the contourlet transform not only can capture multiresolution and local information of an image, but obtain its directional information in a flexible way by using different number of directions at different scales. This non-separable two-dimensional transform is a new alternative to and improvement on separable wavelets for the representation of an image. On the other hand, HMT is a tree-structured probabilistic graph that can capture the statistical properties of contourlet coefficients at different scales and directions where each coefficient is considered as an observation of its hidden state variable which indicates whether the coefficient belongs to singularity structures or not. Herein, the state "1" represents the location belonging to singularity structure, and state "0" not. CD-HMT model is firstly trained by Expectation-Maximization (EM) algorithm before the Viterbi algorithm is utilized to uncover the hidden state sequences based on maximum a posterior (MAP) estimation. Moreover, we take into account the effect of speckle on the detection performance for singularity structures. Finally, the thinning post-processing procedure is performed to obtain the edge map of an SAR image. Experiments on both simulated speckled and real SAR images demonstrate the feasibility and effectiveness of our approach with the performance outperforming the classical Canny edge detector.

Improvement of the image enlargement method based on the Laplacian pyramid representation

Abstract: Summary form only given. It is necessary to predict unknown higher-frequency components that are lost by sampling for enlarging digital images. Based on the Laplacian pyramid representation, the prediction of unknown higher-frequency components is equivalent to the prediction of a known higher-resolution Laplacian image. We have proposed the higher resolution method based on the Laplacian pyramid representation. However, the Laplacian pyramid representation was considered for image compression. Thus, we think that the bandwidth of the Gaussian filter for image compression is not optimal for digital image enlargement. In this paper, we proposed a new enlargement method for digital images with the variable bandwidth of Gaussian filter.

Color image compression: early vision and the multiresolution representations

Abstract: The efficiency of an image compression technique relies on the capability of finding sparse M-terms for best approximation with reduced visually significant quality loss. By ”visually significant” it is meant the information to which human observer can perceive. The Human Visual System (HVS) is generally sensitive to the contrast, color, spatial frequency...etc. This paper is concerned with the compression of color images where the psycho-visual representation is an important strategy to define the best M-term approximation technique. Digital color images are usually stored using the RGB space, television broadcast uses YUV (YIQ) space while the psycho-visual representation relies on 3 components: one for the luminance and two for the chrominance. In this paper, an analysis of the wavelet and contourlet representation of the color image both in RGB and YUV spaces is performed. A approximation technique is performed in order to investigate the performance of image compression technique using one of those transforms.

Window shrink contourlet coefficients for image denoising

Abstract: An adaptive image denosing technique was proposed to achieve the tradeoff between details retain and noises removal. In order to achieve this objective, the contourlet transform was introduced and a new threshold method, namely CWinShrink, is presented. It shrinks the contourlet coefficients with adaptive shrinkage factors. The shrinkage factors were calculated with reference to the sum of squares of the contourlet coefficients within the neighborhood window. This approach achieves enhanced results for images those are corrupted with additive Gaussian noise. In numerical comparisons with various methods, for a set of noisy images (the PSNR range from 10.86dB to 26.91dB), the presented method outperforms VisuShrink and Wiener filter in terms of the PSNR. Experiments also show that this method not only keeps the details of image but also yields denoised images with better visual quality.