Samavati, FaramarzCosta Sousa, MárioHasan, Mahmudul2018-08-272018-08-272018-08-22Hasan, M. (2018). Balanced Multiresolution in Multilevel Focus+Context Visualization (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/32845http://hdl.handle.net/1880/107665Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this thesis can establish a balanced multiresolution (BMR) scheme for images, allowing their balanced decomposition and subsequent perfect reconstruction without the use of any extraordinary boundary filters. We define balanced multiresolution such that it allows balanced decomposition i.e. decomposition of a high-resolution image into a low-resolution image and corresponding details of equal size. Several applications of such a decomposition result in a balanced wavelet transform (BWT) that makes on-demand reconstruction of regions of interest (ROIs) efficient in both computational load and implementation aspects. We find such decomposition and perfect reconstruction based on an appropriate combination of symmetric/antisymmetric extensions near the image and detail boundaries. In our method, exploiting such extensions correlates to performing sample (pixel/voxel) split operations. We demonstrate our general approach for some commonly used symmetric/antisymmetric multiresolution filters. We also show the application of such a balanced multiresolution scheme in constructing an interactive multilevel focus+context visualization framework for the navigation and exploration of large-scale 2D and 3D images. Typically, the given filters are floating-point values, so our BWTs reversibly map integers to floating-point i.e. real values. We extend our balanced multiresolution framework further to construct reversible integer-to-integer BWTs from a given symmetric/antisymmetric decomposition filter vector of width less or equal to four. In our approach, we adjust the linear combination of fine samples suggested by the given decomposition vector using optimal sample split operations in combination with a rounding operation. Such adjustments translate an affine integer combination of fine samples to obtain an integer coarse sample, which closely approximates the floating-point coarse sample suggested by the given decomposition filter vector. The associated translation vectors give us the detail samples. Furthermore, when necessary, we construct every other detail sample differently in order to ensure local perfect reconstruction. Compared to their integer-to-real counterparts, the resulting reversible integer-to-integer BWTs occupy less memory, offer better compressibility, and do not require sample quantization for rendering purposes.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.focus+context visualizationcontextual close-upsymmetric extensionantisymmetric extensionmultiresolutionreverse subdivisionbalanced decompositionperfect reconstructionlossless reconstructionbalanced wavelet transformbalanced integer wavelet transformEducation--MathematicsComputer ScienceEngineering--Electronics and Electricaldoctoral thesis10.11575/PRISM/32845