Diffusion equation quantification: selective enhancement algorithm for bone metastasis lesions in CT images

<i>Objective.</i>Diffusion equation (DE) imaging processing is promising to enhance images showing lesions of bone metastasis (LBM). The Perona-Malik diffusion (PMD) model, which has been widely used and studied, is an anisotropic diffusion processing method to denoise or extract objects from an image effectively. However, the smoothing characteristics of PMD or its related method hinder extraction and enhancement of soft tissue regions of medical image such as computed tomography (CT), typically leaving an indistinct region with ambient tissues. Moreover, PMD expands the border region of the objects. A novel diffusion methodology must be used to enhance the LBM region effectively.<i>Approach.</i>For this study, we originally developed a DE quantification (DEQ) method that uses a filter function to selectively provide modulated diffusion according to the original locations of objects in an image. The structural similarity index measure (SSIM) and Lie derivative image analysis<i>L</i>-value map were used to evaluate image quality and processing.<i>Main results.</i>We determined superellipse function with its ordern=4as a better performing filter for the LBM region. DEQ was found to be more effective at contrasting LBM for various LBM CT images than PMD or its improved models when the filter was a positive exponential similar function. DEQ yields enhancement agreeing with the indications of positron emission tomography despite complex LBM comprising osteoblastic, osteoclastic, mixed tissues, and metal artifacts, which is innovative. Moreover, DEQ retained high quality of image (SSIM> 0.95), and achieved a low mean value of the<i>L</i>-value (<0.001), indicative of our intended selective diffusion compared to other PMD models.<i>Significance.</i>Our method improved the visibility of mixed tissue lesions, which can assist computer visional framework and can help radiologists to produce accurate diagnose of LBM regions which are frequently overlooked in radiology findings because of the various degrees of visibility in CT images.