Balanced multiresolution for symmetric/antisymmetric filters

• Devised balanced multiresolution (BMR) schemes allow balanced decomposition.
• Constructed balanced wavelet transform (BWT) allows perfect reconstruction.
• BWT provides efficient access to previously extracted details on demand.
• We eliminate the need for using extraordinary boundary filters.
• BMR schemes use symmetric/antisymmetric extensions at image and detail boundaries.

Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this article can establish a balanced multiresolution 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. Such a balanced decomposition makes on-demand reconstruction of regions of interest efficient in both computational load and implementation aspects. We find this balanced 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. Our general approach is demonstrated for some commonly used symmetric/antisymmetric multiresolution filters. We also show the application of such a balanced multiresolution scheme in real-time focus+context visualization.

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