Conference Paper

Determining multiscale image feature angles from complex wavelet phases

DOI: 10.1007/11559573_61 Conference: Proceedings
Source: DBLP

ABSTRACT In this paper, we introduce a new multiscale representation for 2-D images named the inter-coefficient product (ICP). The ICP is a decimated pyramid of complex values based on the dual-tree complex wavelet transform (DT-CWT). The complex phases of its coefficients correspond to the angles of dominant directional features in their support regions. As a sparse representation of this information, the ICP is relatively simple to calculate and is a computationally efficient representation for subsequent analysis in computer vision activities or large data set analysis. Examples of ICP decomposition show its ability to provide an intuitive representation of multiscale features (such as edges and ridges). Its potential uses are then discussed

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Available from: Julien Fauqueur, Jul 16, 2014
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    • "Some other applications exploit the local phase information across scales of the complex wavelet such as the description of texture images [8], the detection of blurred images [9] and object recognition [10]. The investigation of local phase in the same orientation and the same scale is based on the dual-tree complex wavelet transform [11] and the complex directional filter bank (CDFB) [12]. Therefore an accurate statistical model of the phase of the complex wavelet coefficients can be beneficial to the developments in the image processing community. "
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    ABSTRACT: With the assumptions of Gaussian as well as Gaussian scale mixture models for images in wavelet domain, marginal and joint distributions for phases of complex wavelet coefficients are studied in detail. From these hypotheses, we then derive a relative phase probability density function, which is called Vonn distribution, in complex wavelet domain. The maximum-likelihood method is proposed to estimate two Vonn distribution parameters. We demonstrate that the Vonn distribution fits well with behaviors of relative phases from various real images including texture images as well as standard images. The Vonn distribution is compared with other standard circular distributions including von Mises and wrapped Cauchy. The simulation results, in which images are decomposed by various complex wavelet transforms, show that the Vonn distribution is more accurate than other conventional distributions. Moreover, the Vonn model is applied to texture image retrieval application and improves retrieval accuracy.
    Signal Processing 01/2011; DOI:10.1016/j.sigpro.2010.06.014 · 2.24 Impact Factor
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    • "In addition, the coefficient phases across scales at an edge are aligned [4], [5]. These intrascale and interscale relationships have been used in some image-processing applications (e.g., in [3]–[7]). All of these point out the significance of the magnitude and phase information of complex coefficients. "
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    ABSTRACT: In this paper, we propose the complex Gaussian scale mixture (CGSM) to model the complex wavelet coefficients as an extension of the Gaussian scale mixture (GSM), which is for real-valued random variables to the complex case. Along with some related propositions and miscellaneous results, we present the probability density functions of the magnitude and phase of the complex random variable. Specifically, we present the closed forms of the probability density function (pdf) of the magnitude for the case of complex generalized Gaussian distribution and the phase pdf for the general case. Subsequently, the pdf of the relative phase is derived. The CGSM is then applied to image denoising using the Bayes least-square estimator in several complex transform domains. The experimental results show that using the CGSM of complex wavelet coefficients visually improves the quality of denoised images from the real case.
    IEEE Transactions on Signal Processing 08/2010; 58(7-58):3545 - 3556. DOI:10.1109/TSP.2010.2046698 · 3.20 Impact Factor
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    • "It has been stated in [12] that the local phase varies linearly with the distance from features and in [28], the authors also have observed that the phase of a 1-D DTCWT coefficient is consistently linear with respect to the feature offset (distance to the step). However, the proof for this relationship has not been given. "
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    ABSTRACT: In this paper, we develop a new approach which exploits the probabilistic properties from the phase information of 2-D complex wavelet coefficients for image modeling. Instead of directly using phases of complex wavelet coefficients, we demonstrate why relative phases should be used. The definition, properties and statistics of relative phases of complex coefficients are studied in detail. We proposed von Mises and wrapped Cauchy for the probability density function (pdf) of relative phases in the complex wavelet domain. The maximum-likelihood method is used to estimate two parameters of von Mises and wrapped Cauchy. We demonstrate that the von Mises and wrapped Cauchy fit well with real data obtained from various real images including texture images as well as standard images. The von Mises and wrapped Cauchy models are compared, and the simulation results show that the wrapped Cauchy fits well with the peaky and heavy-tailed pdf of relative phases and the von Mises fits well with the pdf which is in Gaussian shape. For most of the test images, the wrapped Cauchy model is more accurate than the von Mises model, when images are decomposed by different complex wavelet transforms including dual-tree complex wavelet (DTCWT), pyramidal dual-tree directional filter bank (PDTDFB) and uniform discrete curvelet transform (UDCT). Moreover, the relative phase is applied to obtain new features for texture image retrieval and segmentation applications. Instead of using only real or magnitude coefficients, the new approach uses a feature in which phase information is incorporated, yielding a higher accuracy in texture image retrieval as well as in segmentation. The relative phase information which is complementary to the magnitude is a promising approach in image processing.
    Signal Processing Image Communication 01/2010; 25(1-25):28-46. DOI:10.1016/j.image.2009.09.003 · 1.15 Impact Factor
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