The Curvelet Transform

Ma, Jianwei; Plonka, Gerlind

doi:10.1109/msp.2009.935453

Cited by 408 publications

(117 citation statements)

References 63 publications

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“…However, images in two dimensions also have discontinuities along lines and curves. As wavelets ignore the geometric properties of objects with edges and do not exploit the regularity of the edge curves [16]- [17], they exhibit large wavelet coefficients in all scales for edges in the image.…”

Section: Proposed Methodsmentioning

confidence: 99%

Using Curvelet transform for watermarking based on amplitude modulation

Lari

Ghofrani

McLernon

2013

SIViP

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In this paper we propose a precise and robust watermarking scheme based on the technique called amplitude modulation. A watermark is embedded in a color image by modifying the pixel values in the blue channel. At the receiver, the watermark bits are retrieved using a prediction system, by a linear combination of nearby pixel values around the embedded pixels, and without having the original image. Because amplitude modulation is a spatial-domain watermarking method, it may not be robust enough, i.e. incapable of exact watermark retrieval. In order to enhance the bit retrieval, we apply a Gaussian mask to equalize the luminance intensity; we employ the pixel value replacing technique to enhance the prediction performance; and we use two additional bits as a geometrical reference. In addition, we demonstrate that choosing an improper location (like singularities) for watermarking will lead the prediction system to malfunction. In order to increase the robustness, we propose using the Curvelet transform to detect singularities such as lines and curves and prevent the system from using these locations in an image for embedding the watermark bits. The experimental results indicate that our proposed method has a better performance in comparison with two other similar approaches and in addition it is robust against various geometrical and non-geometrical attacks as well as having a good imperceptibility.

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Section: Proposed Methodsmentioning

confidence: 99%

Using Curvelet transform for watermarking based on amplitude modulation

Lari

Ghofrani

McLernon

2013

SIViP

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“…Compared to wavelet and similar transforms, it can be said that curvelet transform can represent curve-like features with greater sparsity [11]. CT is closely related to frequency-domain wedge filters, short-time Fourier transform, wavelet transform, Gabor wavelet transform, ridgelet transform, contourlet transform and other directional wavelet transforms.…”

Section: Curvelet Transform Subband Statistical Momentsmentioning

confidence: 99%

“…All together parabolic scaled (unequal stretching at different axis) with D j , rotated with R θℓ and translated with k = (k 1 , k 2 ) ∈ R 2 versions of φ give the spatial curvelet family. The spatial curvelet family can be given in Equation (11).…”

Section: Curvelet Transform Subband Statistical Momentsmentioning

confidence: 99%

Synthetic Aperture Radar Image Clustering with Curvelet Subband Gauss Distribution Parameters

Uslu

Albayrak

2014

Remote Sensing

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Curvelet transform is a multidirectional multiscale transform that enables sparse representations for signals. Curvelet-based feature extraction for Synthetic Aperture Radar (SAR) naturally enables utilizing spatial locality; the use of curvelet-based feature extraction is a novel method for SAR clustering. The implemented method is based on curvelet subband Gaussian distribution parameter estimation and cascading these estimated values. The implemented method is compared against original data, polarimetric decomposition features and speckle noise reduced data with use of k-means, fuzzy c-means, spatial fuzzy c-means and self-organizing maps clustering methods. Experimental results show that the curvelet subband Gaussian distribution parameter estimation method with use of self-organizing maps has the best results among other feature extraction-clustering performances, with up to 94.94% overall clustering accuracies. The results also suggest that the implemented method is robust against speckle noise.

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“…However, the advantage of wavelet transform is to reflect the singularity of the signal, that is, it can optimally represent the low-dimensional function with singular singularity, and cannot optimally represent the high-dimensional function with singular singularity or singularity. Therefore, there is a need for a better or "sparse" function representation than wavelet transform to take full advantage of the geometrical properties of the image, that is, multi-scale geometric analysis of images, and Donoho et al [2] proposed Curvelet transformation theory. The first generation of digital Curvelet transform implementation is more complex, requires a series of sub-band decomposition, smooth block, regularization and ridgelet analysis and a series of steps, and the decomposition of the pyramid pyramid also brought a huge amount of data redundancy, Candes et al [3] [4] have proposed a simpler and easier to understand the fast Curvelet transform algorithm, that is, the second generation of the Curvelet (Fast Curvelet transform).…”

Section: Introductionmentioning

confidence: 99%

Smoke Classification based on curve transform

Tang¹,

Dai²,

Yin³

2017

Proceedings of the 2017 2nd International Conference on Machinery, Electronics and Control Simulation (MECS 2017)

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Abstract:Smoke classification based on video image plays an important role in the performance of fire warning system. This paper presents a smoke classification algorithm based on frequency domain information processing. It is a feature in the video stream image region, which is based on the frequency domain analysis of smoke characteristics. In this paper, a method of extracting features based on Curvelet transform is proposed. Firstly, the multi-scale decomposition of the smoke pattern is preprocessed, and then the effective Curvelet coefficients are extracted as far as possible. At the same time, the selected coefficients as a feature, and finally to the Support Vector Machine classifier to achieve the identification of smoke. The experimental results show that the method can effectively classify the smoke in the frequency domain.

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The Curvelet Transform

Cited by 408 publications

References 63 publications

Using Curvelet transform for watermarking based on amplitude modulation

Using Curvelet transform for watermarking based on amplitude modulation

Synthetic Aperture Radar Image Clustering with Curvelet Subband Gauss Distribution Parameters

Smoke Classification based on curve transform

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