Issue No. 02 - February (1984 vol. 6)
James L. Crowley , Robotics Institute, Carnegie-Mellon University, Pittsburgh, PA 15213.
Richard M. Stern , Department of Electrical Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213.
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.
R. M. Stern and J. L. Crowley, "Fast Computation of the Difference of Low-Pass Transform," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 6, no. , pp. 212-222, 1984.