A Data Point-labelled Generalised Hough Transform for ExtractingReflections from Buried Objects in Ground Penetrating RadarScans

Ultra-wide-band radar is used to determine the position and nature of buried objects such as pipes. An antenna, placed just above the surface, is scanned to give a BSCAN" de¯ning the re°ected intensity as a function of the round-trip time of °ight t at a series of positions y. Each buried object gives a generally hyperbolic signal as the range becomes a minimum as the antenna is over the object. The problem is that in general there are many overlapping signals from the di®erent buried objects and many spurious signals arising from extraneous objects such as stones, and from layered structures in the ground. A method is presented for separating the hyperbolic arc arising from a single buried object from other arcs and from noise signals. First an analysis of the BSCAN is made to give the light and dark maximal and minimal positions. This gives two series of discrete data points (yi; ti), de¯ning the light and dark positions of the maxima and minima in the BSCAN. The generalized Hough transform is used to determine generally [n] unknown variables Xj , such as the position Y , depth Z, radius R and medium velocity V for a buried pipe. [n] randomly chosen sets of data points (yi; ti), are solved analytically to give the [n] solutions Xj . The process is repeated many times. Each time an [n]-dimensional accumulator space in the unknown variables is incremented, conventionally by 1, or more generally by a weight re°ecting the error analysis of the set of data points. The most probable values of the unknown parameters Xj within the selected area of interest in (y; t) space are given by the peaks in the accumulator space. The method has been extended by recording the [n] data points (yi; ti), contributing to each element of the accumulator space. Two associative stores are used. One conventionally describes the [n]-dimensional accumulator space. The second notes for each element in the ¯rst associative store, the [n] sets of data points (yi; ti) which have contributed to this particular element. The most intense element in the accumulator space is located and the neighboring elements contributing to the peak located, for example, by thresholding the accumulator space. A histogram may then be made over all data points, counting the number of times that each data point has been included within the accumulator space elements de¯ned as contributing to the located peak. Those data points which contribute many times to the peak in accumulator space are labeled" as belonging to the arc leading to the located peak. Those data points with no contributions, or only a few contributions and so below a chosen threshold, remain unlabeled. Having so labeled" the data points contributing to the re°ection from an object, the ¯nal parameters are easily found by a conventional least squares method over the labeled data points. The method will be demonstrated on real radar data from buried pipes.