The Color Clifford Hardy Signal: Application to Color Edge Detection and Optical Flow

This paper introduces the idea of the color Clifford Hardy signal, which can be used to process color images. As a complex analytic function's high-dimensional analogue, the color Clifford Hardy signal inherits many desirable qualities of analyticity. A crucial tool for getting the color and structural data is the local feature representation of a color image in the color Clifford Hardy signal. By looking at the extended Cauchy-Riemann equations in the high-dimensional space, it is possible to see the connection between the different parts of the color Clifford Hardy signal. Based on the distinctive and important local amplitude and local phase generated by the color Clifford Hardy signal, we propose five methods to identify the edges of color images with relation to a certain color. To prove the superiority of the offered methodologies, numerous comparative studies employing image quality assessment criteria are used. Specifically by using the multi-scale structure of the color Clifford Hardy signal, the proposed approaches are resistant to a variety of noises. In addition, a color optical flow detection method with anti-noise ability is provided as an example of application.

Facial Expression Classification Using Rotation Slepian-based Moment Invariants

Rotation moment invariants have been of great interest in image processing and pattern recognition. This paper presents a novel kind of rotation moment invariants based on the Slepian functions, which were originally introduced in the method of separation of variables for Helmholtz equations. They were first proposed for time series by Slepian and his coworkers in the 1960s. Recent studies have shown that these functions have an good performance in local approximation compared to other approximation basis. Motivated by the good approximation performance, we construct the Slepian-based moments and derive the rotation invariant. We not only theoretically prove the invariance, but also discuss the experiments on real data. The proposed rotation invariants are robust to noise and yield decent performance in facial expression classification.