Detection of linear features using a localized Radon transform with a wavelet filter

Warrick, A.; Delaney, P.A.

doi:10.1109/icassp.1997.595363

Cited by 14 publications

(10 citation statements)

References 10 publications

(2 reference statements)

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“…The local use of the Radon transform (RT) [25] has been often advocated for 1-D pattern detection and orientation estimation [1], [26], [27]. The RT of the image is defined as For a 1-D pattern, the RT is constant along for , whereas for it yields a tomographic slice equal to the cross section.…”

Section: Radon Transformmentioning

confidence: 99%

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Maximum Likelihood Orientation Estimation of 1-D Patterns in Laguerre-Gauss Subspaces

Claudio

Jacovitti

Laurenti

2010

IEEE Trans. on Image Process.

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A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

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Section: Radon Transformmentioning

confidence: 99%

“…The LG-CH representation of the 1-D pattern (26), contaminated by additive noise, is (27) where the vector represents the noise projection in the OS. By (23), it is obtained by transforming as the real-valued column vector , of length , which contains the 2-D HG expansion of the noise component.…”

Section: One-dimensional Pattern Model In Noisementioning

confidence: 99%

Maximum Likelihood Orientation Estimation of 1-D Patterns in Laguerre-Gauss Subspaces

Claudio

Jacovitti

Laurenti

2010

IEEE Trans. on Image Process.

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“…The second category of wavelet approach applies wavelets for image de-noising and feature extraction. The wavelet transform is applied to the projections in order to isolate features of interest (such as edges) and reconstruct the images only from those features [16], [17]. The third category identified is a regularisation approach, called the Wavelet-Vaguelette decomposition [18], which is a wavelet analogue of the singular value decomposition.…”

Section: Introductionmentioning

confidence: 99%

Wavelet-Based Image Reconstruction for Hard-Field Tomography With Severely Limited Data

Terzija

McCann

2011

IEEE Sensors J.

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We introduce a new wavelet-based hard-field image reconstruction method that is well suited for data inversion of limited path-integral data obtained from a geometrically sparse sensor array. It is applied to a chemical species tomography system based on near-IR spectroscopic absorption measurements along an irregular array of only 27 paths. This system can be classified as producing severely limited data, where both the number of viewing angles and the number of measurements are small. As shown in our previous work, the Landweber iteration method allows stable solution of this tomography problem by incorporating suitable a priori information. In the new method, a 2-D discrete wavelet transform has been used as a smoothing function. We present a method of designing the optimal waveletbased smoothing function, depending on a priori knowledge of the subject. The significance of the particular wavelet filter selected is considered in terms of the accuracy of reconstruction of the spatial location and shape of the gas distribution. Results are presented for simulated phantoms using different sensor arrays and for experiments with propane plumes, showing excellent spatial localization and quantification. The computational time of the iterative algorithm is significantly reduced by applying the wavelet transform method. Some of our conclusions are applicable to other hard-field tomographic modalities in applications where similar constraints may be encountered.

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“…In other words, (19) According to the property (3) the outputs of the wavelet transform in Fig. 4 are uncorrelated, so the extracted features are uncorrelated.…”

Section: ) If ϕ 1 (X) Is a Wavelet Functionmentioning

confidence: 99%

“…Magli et al [18] use Radon transform and 1-D continuous wavelet transform to detect linear patterns in the aerial images. Warrick and Delaney [19] use a localized Radon transform with a wavelet filter to accentuate the linear and chirp-like features in SAR images. Leavers [20] uses the Radon transform to generate a taxonomy of shape for the characterization of abrasive powder particles.…”

mentioning

confidence: 99%

Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms

Jafari-Khouzani

Soltanian-Zadeh

2005

IEEE Trans. on Image Process.

137

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A new rotation invariant texture analysis technique using Radon and wavelet transforms is proposed. This technique utilizes the Radon transform to convert the rotation to translation and then applies a translation invariant wavelet transform to the result to extract texture features. A k-nearest neighbors (k-NN) classifier is employed to classify texture patterns. A method to find the optimal number of projections for the Radon transform is proposed. It is shown that the extracted features generate an efficient orthogonal feature space. It is also shown that the proposed features extract both of the local and directional information of the texture patterns. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. To test and evaluate the method, we employed several sets of textures along with different wavelet bases. Experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent texture analysis methods.

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Detection of linear features using a localized Radon transform with a wavelet filter

Cited by 14 publications

References 10 publications

Maximum Likelihood Orientation Estimation of 1-D Patterns in Laguerre-Gauss Subspaces

Maximum Likelihood Orientation Estimation of 1-D Patterns in Laguerre-Gauss Subspaces

Wavelet-Based Image Reconstruction for Hard-Field Tomography With Severely Limited Data

Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms

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