“Reconstruction filters in computer-graphics” by Mitchell and Netravali

Problems of signal processing arise in image synthesis because of transformations between continuous and discrete representations of 2D images. Aliasing introduced by sampling has received much attention in graphics, but reconstruction of samples into a continuous representation can also cause aliasing as well as other defects in image quality. The problem of designing a filter for use on images is discussed, and a new family of piecewise cubic filters are investigated as a practical demonstration. Two interesting cubic filters are found, one having good antialiasing properties and the other having good image-quality properties. It is also shown that reconstruction using derivative as well as amplitude values can greatly reduce aliasing.

1. Brown, Earl F., “Television: The Subjective Effects of Filter Ringing Transients”, Journal of the SMPTE, Vol. 78, No. 4, April 1969, pp. 249-255.
2. Catmnll, Edwin, Alvy Ray Smith, “3-D Transformations of Images in Scardine Order”, Computer Graphics, Vol. 14, No. 3, pp. 279-285.
3. Cook, Robert L., “Stochastic Sampling in Computer Graphics”, ACM Trans. Graphics, VoL 5, No. 1, January 1986.
4. Cook, Robert L., personal communication, August, 1987.
5. Crow, Franklin C., “The Aliasing Problem in Computer- Generated Shaded Images”, Comm. ACM, Vol. 20, No. 11, November 1977, pp. 799-805.
6. Dippe, Mark A. Z. and Erling Henry Wold, “Antialiasing Through Stochastic Sampling”, Computer Graphics, Vol. 19, No. 3, July 1985, pp. 69-78.
7. Duff, Tom, “Splines in Animation and Modeling”, State of the Art in Image Synthesis, SIGGRAPH 86 Course Notes.
8. Hou, Hsich S., Harry C. Andrews, “Cubic Splines for Image Interpolation and Digital Filtering”, IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. ASSP-26, No. 6, December 1978, pp. 508-517.
9. Keys, Robert, G, “Cubic Convolution Interpolation for Digital Image Processing”, IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. ASSP-29, No. 6, December 1981, pp. 1153-1160.
10. Mettz, Pierre, and Frank Grey, “A Theory of Scanning and its Relation to the Characteristics of the Transmitted Signal in Telephotography and Television,” Bell System Tech. J., Vol. 13, pp. 464-515, July 1934.
11. Mitchell, Don P., “Generating Antialiased Images at Low Sampling Densities”, Computer Graphics, Vol. 21, No. 4, July 1987, pp. 65-72.
12. Netravali, Arun N., Barry G. Haskell, Digital Pictures: Representation and Compression, New York, Plenum, 1988.
13. Park, Stephen K., Robert A. Schowengerdt, “Image Reconstruction by Parametric Cubic Convolution”, Computer Vision, Graphics, and Image Processing, Vol. 23, No. 3, September 1983, pp. 258-272.
14. Petersen, Daniel P., David Middleton, “Reconstruction of Multidimensional Stochastic Fields from Discrete Measurements of Amplitude and Gradient”, Information and Control, Vol. 7, pp. 445-476.
15. Schreiber, William F., Donald E. Troxel, “Transformation Between Continuous and Discrete Representations of Images: A Perceptual Approach”, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-7, No. 2, March 1985, pp. 178-186.
16. Shannon, Claude E., “Communication in the Presence of Noise.”, Proc. IRE Vol. 37, 19,49, pp. 10-21.
17. Whitted, Turner, “An Improved Illumination Model for Shaded Display”, Comm. ACM, Vol. 23, No. 6, June 1980, pp. 343-349.