The random monogenic signal

Olhede, Sofia C.; Ramírez, David; Schreier, Peter J.

doi:10.1109/icip.2012.6467404

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Tests to check the properness of quaternion random vectors were proposed in [5], [6]. Quaternion properness has then found applications among which widely-linear processing [7], [8], detection [9], [10], ICA [11], [12], adaptive filtering [8], [13], study of random monogenic signal [14], quaternion VAR processes [15], Gaussian graphical models [16] and directionnality in random fields [17].…”

Section: Introductionmentioning

confidence: 99%

The geometry of proper quaternion random variables

Bihan

2017

Signal Processing

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Section: Introductionmentioning

confidence: 99%

The geometry of proper quaternion random variables

Bihan

2017

Signal Processing

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“…So far, work on monogenic signals has focussed only on the deterministic case. Aside from our own conference paper [29], we are not aware of any work that has been performed on a random monogenic signal. In Section III, we investigate the second-order statistical properties of random monogenic signals for stationary random fields, and in Section IV, we examine these properties for the special and important cases of isotropic, geometrically anisotropic, and unidirectional random fields.…”

Section: Introductionmentioning

confidence: 99%

Detecting Directionality in Random Fields Using the Monogenic Signal

Olhede

Ramírez

Schreier

2014

IEEE Trans. Inform. Theory

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Detecting and analyzing directional structures in images is important in many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. Classifying a structure as directional or non-directional requires a measure to quantify the degree of directionality and a threshold, which needs to be chosen based on the statistics of the image. In order to do this, we model the image as a random field. So far, little research has been performed on analyzing directionality in random fields. In this paper, we propose a measure to quantify the degree of directionality based on the random monogenic signal, which enables a unique decomposition of a 2D signal into local amplitude, local orientation, and local phase. We investigate the secondorder statistical properties of the monogenic signal for isotropic, anisotropic, and unidirectional random fields. We analyze our measure of directionality for finite-size sample images, and determine a threshold to distinguish between unidirectional and non-unidirectional random fields, which allows the automatic classification of images.

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The random monogenic signal

Cited by 2 publications

References 15 publications

The geometry of proper quaternion random variables

The geometry of proper quaternion random variables

Detecting Directionality in Random Fields Using the Monogenic Signal

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