COMPUTER VISION,GRAPHICS, AND IMAGE PROCESSING ]I, 280-293 (1983) NOTE Application of the One-Dimensional Fourier Transform for Tracking Moving Objects in Noisy Environments* SARAHA. RAJALA, ALFY N. RIDDLE, AND WESLEY E. SNYDER North Carolina State University, Electrical Engineering Department, Box 52 75, Raleigh, North Carolina 2 7650 Received July 20, 1982 In Riddle and Rajala (Fifteenth Asilomar Conference on Circuits, Systems and Computers, November 1981), an algorithm was presented which operates on an image sequence to identify all sets of pixels having the same velocity. The algorithm operates by performing a transforma- tion in which all pixels with the same two-dimensional velocity map to a peak in a transform space. The transform can be decomposed into applications of the one-dimensional Fourier transform and therefore can gain from the computational advantages of the FFT. The aim of this paper is the concern with the fundamental limitations of that algorithm, particularly as relates to its sensitivity to image-disturbing parameters as noise, jitter, and clutter, A modifica- tion to the algorithm is then proposed which increases its robustness in the presence of these disturbances. 1. INTRODUCTION This paper contains the development of an algorithm for identifying the tracks of moving objects in noisy environments. An example application is a sensor on a downward-looking space platform whose objective is to detect moving aircraft. Even if the background can be assumed constant, simple differencing techniques are inadequate to detect a low amplitude target in the presence of camera jitter or clutter (time-varying spatially correlated noise). A technique is presented in this paper which characterizes a target uniquely by its motion. That motion, over time, creates a track. These tracks, as well as the objects creating the tracks, can be identified using an algorithm which is based on the application of the one-dimensional Fourier transform. The result is an ability to simultaneously acquire the tracks of, and identify, resolved and unresolved targets in the presence of noise. 2. BACKGROUND Sophisticated algorithms for tracking multiple targets in environments with addi- tive noise exist, and a good review of these techniques is presented in [2]. These algorithms basically fall into two categories, non-Bayesian and Bayesian, and are ~/11 used in active tracking systems (i.e., radar). Both approaches, although quite robust, require a large number of computations for each new update. An alternative approach [3] combines successive sets of two-dimensional frames and then screens these using a 3 × 3 pixel window. The result is a simple, computationally efficient algorithm. This algorithm, however, requires two major assumptions: (1) the target *This work was sponsored in part by NASA Langley Research Center Grant NAG-I-20. 280 0734-189X/83/020280-14503.00/0 Copyright © 1983 by Aettdernie Press. Inc. All rights of reproductionin any formreserved.