Local Geometry Variable Conductance Diffusion for Post-Reconstruction Filtering

Variable conductance diffusion (VCD) filtering can preserve edges while smoothing noise in an image. The threshold of the conductance function determines the degree to which a part of the image is smoothed. Traditionally, a constant threshold has been used. The use of a global threshold does not allow for adaptation to local variations within the image. The approach presented in this paper exploits the local geometry of the image and derives the threshold from the variations that are more likely caused by noise than by structural changes. We apply it to simulated noisy reconstructed single-photon emission computed tomographic (SPECT) image sets. For a particular voxel, if a consistent gradient direction is found within its neighborhood, then the variations on the plane perpendicular to the gradient direction are considered as noise and used to derive the threshold. Our results show that, for the same average noise level in the liver, the image contrast from both local geometry and constant threshold VCD filters are higher than those from Butterworth filtering. The local geometry VCD filtering provides images with smoother boundaries than the constant threshold method. Moreover, the contrast loss is less sensitive to the tumor size for the local geometry method.