Phases measure of image sharpness based on quaternion wavelet

• Introduce the quaternion wavelet transform (QWT) into the sharpness measurement.
• The relationship between the blur degree and the QWT coefficients is found.
• One proposed metric is uniform to the different images with the same blur degree.

We present two novel and simple image sharpness metrics based on the quaternion wavelet transform. The result of quaternion wavelet decomposition can be transformed into the form of one magnitude with three phases (ϕ, θ, ψ). We exploit the new interpretation of phases (ϕ, θ) through the distributions of quaternion wavelet coefficients, and from the characteristics of these two phases, we construct two simple but effective sharpness metrics. We use quaternion wavelet transform to decompose the natural images, and then find the relationship between the blur degree and the distribution histograms of high/low frequencies coefficients of the two phases, respectively. We employ the variance of coefficients distribution to detect the blur degree and achieve the function of sharpness metric. Finally, experiments are conducted on natural images and the results indicate that the proposed metric can exhibit better performance than existing sharpness metrics, such as variance, image gradient, wavelet and eigenvalue based methods. The most important feature of one proposed metric is that it can provide consistent results for different natural images with the same blur degree, which of the other is robust to noise.