Nonlinear multiresolution techniques with applications to scientific visualization in a haptic environment

This paper develops nonlinear multiresolution techniques for scientific visualization utilizing haptic methods. The visualization of data is critical to many areas of scientific pursuit. Scientific visualization is generally accomplished through computer graphic techniques. Recent advances in haptic technologies allow visual techniques to be augmented with haptic methods. The kinesthetic feedback provided through haptic techniques provides a second modality for visualization and allows for active exploration. Moreover, haptic methods can be utilized by individuals with visual impairments. Haptic representations of large data sets, however, can be confusing to a user, especially if a visual representation is not available or cannot be used. Additionally, most haptic devices utilize point interactions, resulting in a low information bandwidth and further complicating data exploration. Multiresolution techniques can be utilized to address the issues of low information bandwidth and data complexity. Commonly used multiresolution techniques are based on the wavelet decomposition. Such linear techniques, however, tend to smooth important data features, such as discontinuities or edges. In contrast, nonlinear techniques can be utilized that preserve edge structures while removing fine data details. This paper develops a multiresolution data decomposition method based on the affine median filter. This results in a hybrid structure that can be tuned to yield a decomposition that varies from a linear wavelet decomposition to that produced by the median filter. The performance of this hybrid structure is analyzed utilizing deterministic signals and statistically in the frequency domain. This analysis and qualitative and quantitative implementation results show that the afiine median decomposition has advantages over previously proposed methods. In addition to multiresolution decomposition development, analysis, and results, haptic implementation methods are presented.