Multiresolution representation of interval surfaces using subdivision wavelet transform and linear programming
Owing to the imprecision and measure registration, sensors, in general, generate a huge amount of uncertain data, which can be represented as intervals. In this research, we aim at providing a reliable method for the approximation of a measured surface of arbitrary topological type. The technique we based on is called the subdivision wavelet transform (SWT) which has been developed as a useful and efficient means to represent a compact surface of arbitrary topological type at various resolutions. We discover that purely applying the existing wavelet filters in the context of interval surface will lead to a tremendous increase in the widths of the interval data. To remedy this, we employ linear programming (LP) to refine the technique such that the approximated surfaces in low resolutions encloses the intervals of the original data in a very tight way. We also propose a metric called expansion coefficient? for measuring the width changes across various resolutions.
linear programming interval methods multiresolution and subdivision wavelet transform