The 2D Quaternionic Fourier Transform (QFT), applied to a real 2D image, produces an invertible quaternionic spectrum. If we conserve uniquely the first quadrant of this spectrum, it is possible, after inverse transformation, to obtain, not the original image, but a 2D quaternion image, which generalize in 2D the classical notion of 1D analytical image. From this quaternion image, we compute th...

The Fourier transforms plays a critical role in broad range of image processing applications, including enhancement, restoration, analysis and compression. For filtering of gray scale images 2D Fourier transform is an important tool which converts the image from spatial domain to frequency domain and then by applying filtering mask filtering is done. To filter color images, a new approach is im...

The success of applying generalized complex orthogonal designs as space–time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space–timepolarization block codes. This paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs. One technique is used to build ...

In this paper, we offer and discuss three efficient structural solutions for the hardware-oriented implementation of discrete quaternion Fourier transform basic operations with reduced implementation complexities. The first solution a scheme for calculating sq product, the second solution – a scheme for calculating qt product, and the third solution – a scheme for calculating sqt product, where...

Curves in space are diicult to perceive and analyze, especially when they form dense sets as in typical 3D ow and volume deformation applications. We propose a technique that exposes essential properties of space curves by attaching an appropriate moving coordinate frame to each point, reexpressing that moving frame as a unit quaternion, and supporting interaction with the resulting quaternion ...

In this paper, we apply the quaternion framework for color images to a fragile watermarking algorithm with the objective of multimedia integrity protection (Quaternion Karhunen-Loève Transform Fragile Watermarking (QKLT-FW)). The use of quaternions to represent pixels allows to consider the color information in a holistic and integrated fashion. We stress out that, by taking advantage of the ho...

An improved quaternion switching filter for colour image denoising is presented. It proposes a RGB colour image as a pure quaternion form and measures differences between two colour pixels with the quaternion-based distance. Further, in noisedetection, a two-stage detection method is proposed to determine whether the current pixel is noise or not. The noisy pixels are replaced by the vector med...

Nowadays, almost all images acquired are in color format. Traditional methods process color images by either transforming them into gray scale or dividing them into red, green, and blue components for independent processing, which is definitely not effective in representing color information. Recently, a novel Polar Linear Canonical Transform (PLCT) with parameters in SL(2,<) has been reported,...

Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...