Subdivision schemes are multi-resolution methods used in computer-aided geometric design to generate smooth curves or surfaces. We propose two new models for data analysis and compression based on subdivision schemes:(a) The ‘subdivision regression’ model, which can be viewed as a special multi-resolution decomposition.(b) The ‘tree regression’ model, which allows the identification of certain patterns within the data. The paper focuses on analysis and mentions compression as a byproduct. We suggest applying certain criteria on the output of these models as features for data analysis. Differently from existing multi-resolution analysis methods, these new models and criteria provide data features related to the schemes (the filters) themselves, based on a decomposition of the data into different resolution levels, and they also allow analysing data of non-smooth functions and working with varying-resolution subdivision rules. Finally, applications of these methods for music analysis and other potential usages are mentioned.
- multi-resolution analysis and approximation
- subdivision schemes