Hypercomplex Fourier Transforms of Color Images

In recent years, several authors have reported that spectral saliency detection methods provide state-of-the-art performance in predicting human gaze in images (see, e.g., [13]). We systematically integrate and evaluate quaternion DCT-and FFT-based spectral saliency detection [3,4], weighted quaternion color space components [5], and the use of multiple resolutions [1]. Furthermore, we propose the use of the eigenaxes and eigenangles for spectral saliency models that are based on the quaternion Fourier transform. We demonstrate the outstanding performance on the Bruce-Tsotsos (Toronto), Judd (MIT), and KootstraSchomacker eye-tracking data sets.

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“…Although the choice of η is arbitrary, it is not without consequence (see [30,Sec. V]) and can inuence the results.…”

Section: Quaternion Transforms and Transformation Axismentioning

confidence: 99%

Quaternion-Based Spectral Saliency Detection for Eye Fixation Prediction

Schauerte

Stiefelhagen

2012

Lecture Notes in Computer Science

113

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“…The definition of [14] also uses the kernel of (15). If f is a function from R 3 to the Clifford algebra R 3,0 , then…”

Section: A Quaternionic and Clifford Fourier Transformsmentioning

confidence: 99%

Spinor Fourier Transform for Image Processing

Batard

Berthier

2013

IEEE J. Sel. Top. Signal Process.

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Abstract-We propose in this paper to introduce a new spinor Fourier transform for both grey-level and color image processing. Our approach relies on the three following considerations: mathematically speaking, defining a Fourier transform requires to deal with group actions; vectors of the acquisition space can be considered as generalized numbers when embedded in a Clifford algebra; the tangent space of the image surface appears to be a natural parameter of the transform we define by means of so-called spin characters. The resulting spinor Fourier transform may be used to perform frequency filtering that takes into account the Riemannian geometry of the image. We give examples of low-pass filtering interpreted as diffusion process. When applied to color images, the entire color information is involved in a really non marginal process.

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“…The general formula (28) defining the n-D complex signals with single-orthant spectra can be used to derive eight 4-D analytic signals with spectra in 8 octants of the half-space f 1 > 0 (labelled 1,3,5,7,9,11,13,15), representing a 4-D real signal u(x 4 , x 3 , x 2 , x 1 ). Such a signal has in general 16 terms of different parity w.r.t.…”

Section: -D Analytic Signalsmentioning

confidence: 99%

“…The theory of complex (CS) and hypercomplex (HS) signals is a subject of many publications involving mathematicians and engineers [1][2][3][4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%