A multi-scale adaptive thresholding scheme is presented in this study. It was evaluated as a regularization process to filtered back-projection (FBP) for reconstructing clinical PET brain data. Adaptive selection of thresholding operators for each multi-scale sub-band enabled a unified process for noise removal and feature enhancement. A cross-scale regularization process was utilized as an effective signal recovering operator. Together with non-linear thresholding and enhancement operators, they offered remarkable postprocessing to FBP reconstructed data. In addition, such effectiveness was formulated as a regularization process to optimize FBP reconstruction. A comparison study with multiscale regularized FBP (MFBP), standard FBP with clinical settings and iterative reconstruction (OSEM) was reported. The proposed regularization process has shown competitive improvement in the image quality of PET reconstructions when compared to the current state-of-the-art method used in clinical commercial systems (OSEM).

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The radius angle histogram (RAH) is a useful method to retrieve 3D models in the engineering field. This method often requires using the absolute value of the cosine function of the angle between surface normal and radius and usually makes the inner face and outer face indistinguishable. As a result, the retrieval efficiency and precision are insufficient when this method is applied to retrieve models with symmetrical characteristics. In order to improve retrieval efficiency and precision, an improved radius angle histogram method is proposed. This method directly employs the angle between surface normal and radius as the shape descriptor to replace the cosine function of the angle between surface normal and radius. In the process of retrieval, the normalised model coordinates are first established by principal component analysis (PCA). Then local features in each quadrant are extracted and the similarity of the local features is ascertained. Models with a high similarity of local features are obtained and are considered as the retrieval results. Finally, an experiment is described. The simulation results show that the proposed method has higher retrieval efficiency and precision than RAH, especially for symmetrical models. The proposed method is suitable for mechanical component design, especially in the rapid prototyping domain.