A Quaternion Framework for Color Image Smoothing and Segmentation

Subakan, Özlem N.; Vemuri, Baba C.

doi:10.1007/s11263-010-0388-9

Cited by 106 publications

(46 citation statements)

References 56 publications

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“…We then test , µ 96 = j [57], µ 97 = ( ) / 2 + i k [13], µ 98 = ( 2 8 ) / 68 ! + j k [58], µ 99 = ( ) / 3 + + i j k [1,6,[8][9][10][11][12]15,16] and µ 100 = ( ) / 3 ! !…”

Section: Resultsmentioning

confidence: 99%

Color Image Analysis by Quaternion-Type Moments

et al. 2014

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In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration.We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. ( ) / 3 ! ! i j k appears to be an optimal choice.

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“…We then test , µ 96 = j [57], µ 97 = ( ) / 2 + i k [13], µ 98 = ( 2 8 ) / 68 ! + j k [58], µ 99 = ( ) / 3 + + i j k [1,6,[8][9][10][11][12]15,16] and µ 100 = ( ) / 3 ! !…”

Section: Resultsmentioning

confidence: 99%

Color Image Analysis by Quaternion-Type Moments

et al. 2014

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“…Furthermore, Guo et al applied the quaternion DFT to realize the spectral residual for quaternion images, which reduced the required number of focus of attention shifts to find manually specified objects in test images. This was possible, because quaternions provide a holistic representation of color images in combination with a powerful algebra (see [24]), including the quaternion Fourier transform (see [6]) as well as the recently proposed quaternion cosine transform [7]. However, in contrast to Peters and Itti [21], Hou et al and Guo et al did not evaluate how well their approaches predict human gaze patterns.…”

Section: Related Workmentioning

confidence: 99%

Predicting human gaze using quaternion DCT image signature saliency and face detection

Schauerte

Stiefelhagen

2012

2012 IEEE Workshop on the Applications of Computer Vision (WACV)

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We combine and extend the previous work on DCT-based image signatures and face detection to determine the visual saliency. To this end, we transfer the scalar definition of image signatures to quaternion images and thus introduce a novel saliency method using quaternion type-II DCT image signatures. Furthermore, we use MCT-based face detection to model the important influence of faces on the visual saliency using rotated elliptical Gaussian weight functions and evaluate several integration schemes. In order to demonstrate the performance of the proposed methods, we evaluate our approach on the Bruce-Tsotsos (Toronto) [2] and Cerf (FIFA) [3] benchmark eye-tracking data sets. Additionally, we present evaluation results on the BruceTsotsos data set of the most important spectral saliency approaches. We achieve state-of-the-art results in terms of the well-established area under curve (AUC) measure on the Bruce-Tsotsos data set and come close to the ideal AUC on the Cerf data set -with less than one millisecond to calculate the bottom-up QDCT saliency map.

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“…In signal and image processing, quaternion number based methods are actively researched [3]- [6], [10].…”

Section: Hypercomplex Numbermentioning

confidence: 99%

Fast Hypercomplex Polar Fourier Analysis

Yang

Kamata

2012

IEICE Trans. Inf. & Syst.

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SUMMARYHypercomplex polar Fourier analysis treats a signal as a vector field and generalizes the conventional polar Fourier analysis. It can handle signals represented by hypercomplex numbers such as color images. Hypercomplex polar Fourier analysis is reversible that means it can reconstruct image. Its coefficient has rotation invariance property that can be used for feature extraction. However in order to increase the computation speed, fast algorithm is needed especially for image processing applications like realtime systems and limited resource platforms. This paper presents fast hypercomplex polar Fourier analysis based on symmetric properties and mathematical properties of trigonometric functions. Proposed fast hypercomplex polar Fourier analysis computes symmetric points simultaneously, which significantly reduce the computation time. key words: fast hypercomplex polar Fourier analysis, hypercomplex polar Fourier analysis, Fourier analysis

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A Quaternion Framework for Color Image Smoothing and Segmentation

Cited by 106 publications

References 56 publications

Color Image Analysis by Quaternion-Type Moments

Color Image Analysis by Quaternion-Type Moments

Predicting human gaze using quaternion DCT image signature saliency and face detection

Fast Hypercomplex Polar Fourier Analysis

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