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Non-linear deformations are useful for applications where users face highly cluttered visual displays, either due to large datasets, or visualizations on small screens, or a combination of both, that increases the density of the data and makes the perception of patterns difficult. Non-linear deformations have been used to magnify significant/cluttered regions in data visualization, for the purpose of reducing clutter and enhancing the perception of patterns. General deformation methods (e.g. logarithmic scaling and fish-eye views) suffer from several drawbacks, since they do not consider the prominent features that must be preserved in the visualization. This work introduces a hierarchical approach for non-linear deformation that aims to reduce visual clutter by magnifying significant regions, and lead to enhanced visualizations of two/three-dimensional datasets on highly cluttered displays. The proposed approach utilizes an energy function, which aims to determine the optimal deformation for every local region in the data, taking the information from multiple single-layer significance maps into account. The problem is subsequently transformed into an optimization problem for the minimization of the energy function under specific spatial constraints. The proposed hierarchical approach for the generation of the significance map, surpasses current methods, and manages to efficiently identify significant regions and achieve better results.

A Hierarchical Magnification Approach for Enhancing the Insight in Data Visualizations