Submitted to IEEE Transactions on Computer Graphics and Visualization Reconstruction Error Characterization and Control: A Sampling Theory Approach Raghu Machiraju and Roni Yagel Department of Computer and Information Science The Advanced Computing Center for the Arts and Design The Ohio State University Abstract 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 Sam- pling 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 vary- ing 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 effec- tiveness of our methods with 1D signals, 2D signals (images), and 3D signals (vol- umes). 1. Introduction Reconstruction is the process of recovering a continuous function from a set of samples. It is one of the fundamental operations in computer graphics and imaging. Many algorithms, such as texture mapping, image registration, image transformation (e.g., rotation, scaling), and volume rendering, transform a raster (2D or 3D) from a source space to a target space. All these algorithms must recon- struct the underlying function in either space. Given the essential nature of the reconstruction opera- tion, it is surprising that, although much work has been expended in the design of reconstruction filters, not much attention has been paid to characterize and control its numerical accuracy. Inaccurate reconstruction can manifest in image artifacts and make subsequent operations error prone. The work described here is aimed to give the user, for the first time, the ability to set a point-wise error bound. Unlike existing methods, which use frequency domain analysis to guarantee some global error bound, we use spatial domain error analysis to guarantee that, for a given threshold ε, the differ- ence between the reconstructed function and the real function is not more than ε at any point in the source space. Our spatial domain analysis culminates in a formal expression for the error bound at