Reconstruction error characterization and control: A sampling theory approach

Reconstruction is prerequisite whenever a discrete signal needs to be resampled as a result of transformation such as texture mapping, image manipulation, volume slicing, and rendering. We present a new method for the characterization and measurement of reconstruction error in spatial domain. Our method uses the Classical Shannon's Sampling Theorem as a basis to develop error bounds. We use this formulation to provide, for the first time,an efficient way to guarantee an error bound at every point by varying the size of the reconstruction filter. We go further to support position-adaptive reconstruction and data-adaptive reconstruction which adjust filter size to the location of reconstruction point and to the data values in its vicinity. We demonstrate the effectiveness of our methods with 1D signals, 2D signals (images), and 3D signals (volumes).