Two-dimensional discrete Hilbert transform and computational complexity aspects in its implementation

Bose, N.K.; Prabhu, K.

doi:10.1109/tassp.1979.1163261

Cited by 18 publications

(2 citation statements)

References 9 publications

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“…There is no known exact solution for a 2-D Hilbert transform, which transforms images into pure analytic images. However, most of them transform images into pseudo-analytic images [41]. In order to obtain a pseudo-analytic image, we have used a Fourier transform based algorithm,…”

Section: Recovery Of a Directional 2-d Chirp Imagementioning

confidence: 99%

Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains

Serbes

Durak

2010

Communications in Nonlinear Science and Numerical Simulation

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Section: Recovery Of a Directional 2-d Chirp Imagementioning

confidence: 99%

Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains

Serbes

Durak

2010

Communications in Nonlinear Science and Numerical Simulation

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“…The Hilbert transform commonly used to derive the quadrature filters is defined formally only for the 1-D domain, as it requires causality. An approximate expansion of the Hilbert transform into the 2-D domain is possible for oriented filters [57], [63], [64]. The Hilbert transform for our oriented filters design (two-orientation case) was computed by setting to zero the fast Fourier transform values of the filtered image in half of the frequency domain orthogonal to the direction of the filter.…”

Section: B No Need For Quadrature Filtersmentioning

confidence: 99%

Feature detection algorithm based on a visual system model

Peli

2002

Proc. IEEE

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An algorithm for the detection of visually relevant luminance features is presented. The algorithm is motivated and directed by current models of the visual system. The algorithm detects edges (sharp luminance transitions) and narrow bars (luminance cusps) and marks them with the proper polarity. The image is first bandpass filtered with oriented filters at a number of scales an octave apart. The suprathreshold image contrast details at each scale are then identified and are compared across scales to find locations in which the signal polarity (sign) is identical at all scales, representing a minimal level of phase congruence across scales. These locations maintain the polarity of the bandpass-filtered image. The result is a polarity-preserving features map representing the edges with pairs of light and dark lines or curves on corresponding sides of the contour. Similarly, bar features are detected and represented with single curves of the proper polarity. The algorithm is implemented without free (fitted) parameters. All parameters are directly derived from visual models and from measurements on human observers. The algorithm is shown to be robust with respect to variations in filter parameters and requires no use of quadrature filters or Hilbert transforms. The possible utility of such an algorithm within the visual system and in computer vision applications is discussed.

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The stabilization of two‐dimensional non‐symmetric half‐plane recursive filters via the discrete Hilbert transformations

Reddy

Sathyanarayana

Swamy

1991

Circuit Theory & Apps

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SUMMARYThe discrete Hilbert transform (DHT) relations for 2D semicausal signals have been introduced. An alternative algorithm to stabilize non-symmetric half-plane (NSHP) recursive filters by applying the DHT directly in the nonsymmetric half-plane is presented. The results of the direct DHT (DDHT) stabilization procedure are compared with the method of quarter-plane DHT (QDHT) stabilization after transforming the NSHP polynomia1 into the quarterplane by application of an appropriate transformation. It is observed that the proposed scheme produces the same stable NSHP filter as that obtained through the QDHT method.

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Two-dimensional discrete Hilbert transform and computational complexity aspects in its implementation

Cited by 18 publications

References 9 publications

Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains

Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains

Feature detection algorithm based on a visual system model

The stabilization of two‐dimensional non‐symmetric half‐plane recursive filters via the discrete Hilbert transformations

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