Quaternion Atomic Function Wavelet for Applications in Image Processing

Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. The main contribution of this work is to develop a Quaternionic Atomic Function Wavelet as a new quaternionic image wavelet transform. This filter have a real part and three imaginary parts (i, j, k) of the Quaternion Atomic Function, as a result we can extract more information from the image by the three phases (φ, θ, φ) of the quaternion representation. The experimental part shows clearly that the phase information of the image is not afected by illumination changes.