The highly limited bandwidth (and high cost of bandwidth when available) of ground-aircraft and aircraft-ground data links necessitates maximal compression of radar-generated weather pictures for transmission to and from aircraft. Compression of pictorial data is a subject of much research. However, general-purpose picture compression algorithms seldom achieve compression ratios better than an order of magnitude. Specific compression schemes optimized for weather data hold the promise of higher degrees of compression. One such class of schemes is based on contour representation of weather fields. The contours may be represented by, e.g., elliptical or polygonal segments, each represented by a few parameters which may be transmitted over the data link for reconstruction of the contours at the receiving end. This paper reports a novel method of compressing generalized weather radar reflectivity contours by a limited number of control points, and retrieving the contours using spline interpolation. We have achieved compression ratios exceeding a hundred while preserving the meteorologically significant features in the data field. The results are compared with other available methods in terms of compression factor and fidelity of reproduction.

Contour Tracing

The 2-D reflectivity distribution is converted into a binary image by applying a threshold. Any threshold may be applied, but it is more meaningful to choose one of the six threshold values specified by the National Weather Service (NWS) corresponding to different levels of severe weather phenomena. The boundary separating an area of 0's from an area of 1's is called a contour. Contours enclosing a zone of 1's are called 'region contours', and boundaries within these region contours which enclose only 0's are called 'holes'. It is possible for region contours and holes to be nested, i.e. there may be region contours within holes, and so on.

We use the radial sweep algorithm to trace the contours. However, this algorithm does not automatically trace internal structures of contours such as holes, region contours inside them, and nested contours. Further, it traces only one contour at a time, only after the contour has been initiated through a search procedure. We overcome these limitations by using the Pavlidis' scheme, applying it recursively to trace nested holes and region contours.

Extracting Control Points

Typical reflectivity contours present a rather zig-zag appearance. The aim is to capture the shape of the curve faithfully with a limited number of significant points. A novel scheme for extracting these control points is proposed in this paper. We first average the given contour over a sliding segment to obtain a smoothed curve. The deviation of each point on the original contour from the nearest point on the smoothed curve is calculated. From this data, the points of crossing between the original contour and the smoothed curve are determined and stored. Points with maximum deviation lying between two consecutive crossings are taken as control points. If the distance between two adjacent crossings is large (greater than a threshold), additional control points are introduced by bisecting the arcs (of original contour) between the control point and the crossings on both sides.

This scheme works in most situations, but may not extract proper control points for smooth contours and small contours (e.g. contours with < 20 points). The control points for such contours are extracted by considering uniformly spaced points along the contour.

Figure 1: Original PPI image

Contour Transmission and Reconstruction

The thresholds used for encoding are stored in a look-up table, and only the indices need to be transmitted to minimize bit requirements. The closed contours for any given threshold are numbered. Further, a tag bit of 0 and 1 is used to distinguish region and hole contours respectively. The control points for each numbered contour are transmitted in terms of their coordinates, referenced relative to the contour?s minimum bounding rectangle for minimizing bit requirements.

At the receiving end, the contours are retrieved using the B-spline fit on the control points, employing a special technique to handle closed curves. A boundary fill algorithm is used to fill the interior of each region contour (identified by its tag bit), excluding any embedded holes, with the color corresponding to its threshold value. Superposition of filled contours of all valid threshold levels would display the total reflectivity picture to the pilot.

Figure 2: A raw contour (gray line) obtained by 30-dB thresholding, and its smoothed version (black line). Control points are shown as small black squares.

Performance Evaluation

The performance of the compression scheme is evaluated by the compression ratio it provides and contour reproduction fidelity. We have derived an expression for the bit requirements for the compressed image in terms of the number of control points, contour sizes, and other secondary parameters. Based on this the compression ratio can be evaluated.

The compression algorithm has been tested using WSR-88D radar reflectivity Level II data (512 x 512 pixels). NOAA standard color table ('legend') is used for displaying the reflectivity, with the background (originally black) changed to white (Fig. 1).

The largest-area contour appearing in the 30-dB-threshold section of the picture is shown in Fig. 2 in raw form and after smoothing it over 10% of the contour length. Root Mean Square Error (RMSE) obtained for this contour using the methods of Gertz and Grappel (US patent 5363107) and Burdon (Patent 6614425) are 1.1348 and 1.2104 respectively, while our scheme has resulted in 1.1197 when 66 control points are transmitted, yielding a compression ratio of 112. This level of compression is very high compared with any of the general-purpose image compression schemes. The reconstructed image (Fig. 3) is found to retain all of the meteorologically significant features of the original image. Further, the computational time even on a medium-speed (1.8. MHz) Pentium PC remains within a few percent of typical radar scan periods, permitting real-time compression and reconstruction of the images.

Figure 3: Reconstructed PPI image