A Construction of Dual Wavelet and its Applications in Image Edge Detection

The edge detection is usually used for controlling the automation of pattern recognition in intelligent machines, traffic control and mobile devices security systems. Due to the complex of image control, the dimensions are increasing so that the single wavelet is not able to address some applications, thus, high-dimensional wavelet basis is needed. This paper introduces a construction of dual wavelet for fulfilling the gap. A dual wavelet through the compactly support set/functions which can form the Riesz basis is built up. Based on the mathematic presentation of the construction of the dual wavelet, which is a dual orthogonal with scale function and duality, the constructed dual wavelet is used for an application testing with fingerprint. The proposed approach is compared with Sobel and Canny filter. It is observed that from the results, the proposed dual wavelet outperforms the Sobel and Canny filter in terms of effectiveness and computation time.