For local smooth regions in multifocus images, it is difficult to judge whether they are in focus or not, whether using human eyes or special focus measures. We propose to classify the images into smooth and nonsmooth regions based on structural similarity index. Quaternion wavelet transform (QWT), as a novel tool of image analysis, has some superior properties compared to discrete wavelet transform, such as nearly shift-invariant wavelet coefficients and phase-based texture representation. We use the local variance of the QWT phases to detect the focus position for the pixels belonging to the nonsmooth image regions. Thus, binary images of the left-focus, right-focus, and smooth region, e.g., there are two different focuses, are obtained. Then, the connected components labeling algorithm is exploited to label the two binary images containing the focus position information, and the regions with focus measure errors are transferred between the two binary images. The fusion result is finally acquired through three weighted binary images combined with the original multifocus images. Furthermore, we conduct several experiments to verify the feasibility of the proposed fusion method. The performance is demonstrated to be superior to current methods.
Speckle reduction is a difficult task for ultrasound image processing because of low resolution and contrast. As a novel tool of image analysis, quaternion wavelet (QW) has some superior properties compared to discrete wavelets, such as nearly shift-invariant wavelet coefficients and phase-based texture presentation. We aim to exploit the excellent performance of speckle reduction in quaternion wavelet domain based on the soft thresholding method. First, we exploit the characteristics of magnitude and phases in quaternion wavelet transform (QWT) to the denoising application, and find that the QWT phases of the images are little influenced by the noises. Then we model the QWT magnitude using the Rayleigh distribution, and derive the thresholding criterion. Furthermore, we conduct several experiments on synthetic speckle images and real ultrasound images. The performance of the proposed speckle reduction algorithm, using QWT with soft thresholding, demonstrates superiority to those using discrete wavelet transform and classical algorithms.
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