Fast Computation of the Difference of Low-Pass Transform

Authors:
James L. Crowley;Richard M. Stern
Affiliations:
Robotics Institute, Carnegie-Mellon University, Pittsburgh, PA 15213.;Department of Electrical Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213.
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1984

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Abstract

This paper defines the difference of low-pass (DOLP) transform and describes a fast algorithm for its computation. The DOLP is a reversible transform which converts an image into a set of bandpass images. A DOLP transform is shown to require O(N2) multiplies and produce O(N log(N)) samples from an N sample image. When Gaussian low-pass filters are used, the result is a set of images which have been convolved with difference of Gaussian (DOG) filters from an exponential set of sizes. A fast computation technique based on ``resampling'' is described and shown to reduce the DOLP transform complexity to O(N log(N)) multiplies and O(N) storage locations. A second technique, ``cascaded convolution with expansion,'' is then defined and also shown to reduce the computational cost to O(N log(N)) multiplies. Combining these two techniques yields an algorithm for a DOLP transform that requires O(N) storage cells and requires O(N) multiplies.