Scan conversion of radar images

I. INTRODUCTION

Scan Conversion of Radar Images

KENT NICKERSON

SIMON IIAYKIN, Fellow, IEEE McMaster University

Radar images which are sanlpled in a Cartesian formal, rather

than in the polar convention, avail themelves to modern displays and image processing techniques. The object of scan conversion is

to resarnple a polar-sampled image into a Cartesian format while retaining integrity of the geonletry and content of the image.

Linear interpolation and decimation in hvo dimensions

in the context or scan conversion is reviewed. Appropriate approximations of the nonlinear relationship between Cartesian

and polar coordinates are then made lo allow the application of

the linear interpolation theory to produce a number of practical scan conversion algorilhms. Together with an image preliltering process which is applied to areas which require decimation, an

effective scan conversion scheme is finally presented.

Digital raster scan displays in real aperture radar systems may be refreshed at video rates, independent of the antenna scanning rate, and offer a choice of display phosphors and colors. A rectangular (Cartesian) raster scan display also lends itself to easy application of two-pass and space-invariant image processing operators. The former consists of a series of two one-dimensional processes along different axes in order to effect a two-dimensional result, and so requires an orthogonal image sampling lattice such as one with Cartesian coordinates. Space-invariant operators, specifically in convolutional filtering, have kernels which are fixed and invariant of the region of operation, allowing simple transversal filter implementation. If the scale of the spatial impulse response of a two-dimensional operator is to be geometrically invariant as well as invariant with respect to the image sampling lattice, the lattice must be geometrically regular, that is, Cartesian. To summarize, then, a digital raster scan display, with its Cartesian sampling lattice, has advantages over traditional analog plan-position indicator (PPI) displays, including the natural and easy application of two-pass and space-invariant operations.

Since monostatic real-aperture radar data is naturally acquired in terms of range and azimuth, that is, in polar coordinates, and is digitized accordingly, one must address the difficult problem of resampling the polar data onto a Cartesian lattice for raster scan display. This procedure is called scan conversion. It will be shown that this may not be performed simply, but that some approximate methods exist that provide a compromise between accuracy and simplicity.

In Section 11, the geometry of the polar-to-Cartesian scan conversion problem is discussed. Section I11 contains a brief review of the sampling process in one dimension, which is extended in Section IV to a review of twodimensional interpolation. In Section V, the previous theory is applied to the problem of scan conversion. Section VI presents a prefiltering process as an aid to the practical methods covered in Section V. Finally, the application of previously developed scan conversion methods to real and artificial images is demonstrated.

The remainder of this paper is organized as follows:

II. GEOMETRY OF SCAN CONVERSION

Regular sampling of radar returns can be seen as sampling the observed landscape with a polar lattice, as shown in Fig. l(a). Upon presentation of such data on a Cartesian raster scan display, a geometrically distorted image called a “B-scan” [ l ] is seen, as sketched in Fig. l(b). Scan conversion is employed to yield the desired Cartesian sampled representation of the landscape of Fig. l(c). This last geometrically

Manuscript received August 21, 1987.

IEEE Log No. 26876.

Authors’ address: Communications Research Laboratory, McMaster University, 1280 Main St. West, Hamilton, Ontario, Canada, L8.5 4K1.

0018-9251/89/0300-0166 $1.00 @ 1989 IEEE

166 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-25, NO. 2 MARCH 1989

e = o

Fig. l(a). Polar sampling of terrain by radar.

I - - - -1 Fig. l(b). B-scan Cartesian display of polar-sampled terrain.

-

NICKERSON & HAYKIN: SCAN CONVERSION OF RADAR IMAGES 161

Fig. l(c). PPI display with polar-to-Cartesian scan conversion.

Fig. 2. Photographs of radar returns in B-scan and PPI formats.

correct display is traditionally known as the PPI representation. Fig. 2 contains photographs of a scan sector of actual radar returns in the B-scan and PPI forms.

N by N pixels from a complete B-scan image of A range cells by B azimuth sweeps, as in Figs. l(b) and l(c). Assigning the continuous coordinate pairs (p, 0) and ( x , y ) , respectively, to the B-scan sketch and PPI

Assume that one wishes to create a PPI picture of

sketch, the geometric transformation may be written as

p = U ( X ~ + Y ~ ) ” ~ , U = 2 A / N (la)

In the discrete domain, when x and y a re integers (but not p and e), one sees upon examination of (1) that the scan conversion problem is difficult for two reasons: 1) Each B-scan coordinate is a function of both PPI coordinates, necessitating resampling in two dimensions, as opposed to successive one-dimensional passes. 2) The geometrically variant sampling interval of the polar lattice, reflected in the nonlinear forms of (l), renders conventional linear interpolation and decimation of limited use. In spite of these discouragements, a review of linear resampling is given next.

Ill. REVIEW OF RESAMPLING IN ONE DIMENSION

Resampling of one sequence into another can be visualized as a recovery of a continuous signal which would produce the original sequence, followed by sampling this reconstituted signal at the desircd new rate. Consider a discrete sequence x(n) with a sampling period T made from a continuous signal s(t). Suppose also that a new sequence y(n) with a sampling period T’ is desired from x ( n ) . Recovery of s ( t ) may be attempted by a convolution of x ( n ) with a continuous interpolation function h(t) to give an estimate i ( t ) [2, 31:

00

? ( t ) = x( t )h ( t - r ) d r . (2) 1, Noting that x ( t ) is defined only at = nT, n E I , and sampling the reconstituted signal with period T’, one obtains

00

y ( k ) = x(n)h(kT’ - nT). (3) n = - m

Taking H ( w ) as the Fourier transform of h(t) , the Nyquist sampling theorem says that s ( t ) may be perfectly and uniquely reconstructed (e.g., s ( t ) = s(1) ) from a sequence x ( n ) if H ( w ) has the form of an ideal low-pass filter with cutoff at w = n/T. This assumes that ~ ( t ) is strictly bandlimited in the first place before sampling, and that x ( n ) is infinitely long. Fig. 3(a) illustrates this for the case where T >_ T’. In the case of decimation, where T’ > T , s ( t ) must be further bandlimited to a cutoff of w = n/T’, as shown in Fig. 3(b). For either case, this form of H ( w ) corresponds to the following ideal interpolation function:

hi(t) = [sin(nf/~)]/(nt), T = max(T,T’). (4)

The infinite extent of the sinc function in (4) makes it impractical to implement, and impossible to apply to a finite sequence. I f x ( n ) is finite, convolution with

Fig. 3(a). Signal and spectra for ideal interpolation (T > T’).

- 0

t

another sequence of length m will render a result with nt - 1 less valid samples than x ( n ) . For these reasons, alternate and more tractable, albeit suboptimal, forms of h(t) are used for implementation in finite impulse response (FIR) filter forms. However, with any form of h( t ) with limited spatial extent, the frequency response H ( w ) will not absolutely reject images of the baseband spectrum of x ( n ) , as shown in Fig. 4, and so pass energy in the shaded regions to give rise to aliasing. Therefore, a compromise must be made between the spatial extent of h(t) and its rejection of aliasing components. Popular and practical alternative resampling schemes which are briefly described below include “nearest neighbor”, linear, and cubic interpolation.

Nearest neighbor, or zero-order, interpolation,

For the case of decimation (T < T’), ho(r) may be modified to assign y ( n ) the unweighted average of the N nearest points, where

N = nearest integer(T’/T) + 1.

Another intuitive method offering greater accuracy is linear or first-order interpolation, which assigns to the resample point an average of the two adjacent original samples, the average being weighted according to proximity of the samples. If one defines the two original points x1 and x2 about the point y (n ) , that is,

x1 = x[integer part(nT’/T)]

x:! = x[integer part(nT‘/T) + 11 (7)

involves the assigning of each sample of sequence y the nearest sample of sequence x in the case of interpolation (T < T’). This yields

and defines A as the normalized delay y ( n ) with respect to XI:

y (n) = x [nearest integer (nT’/T)]. (5 ) A = (nT’/T) - integer part(nT’/T) (8)

The corresponding zero-order form of h( t ) is

ho(t) = 1, It1 < T / 2

then the linearly interpolated point value is the weighted average:

168 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-25, NO. 2 MARCH 1989

- W/T fl/T

A I

A , .I

Inspection of (9) yields the interpolation function:

h l ( t ) = 1 - Itl/T, It1 < T (10)

= 0, It( > T .

Again, in decimation, hl( t ) may be modified by substituting T’ for T in (lo), with care taken for proper normalization.

One may continue the trend toward higher polynomial (Lagrangian) interpolation schemes, where a polynomial of order N - 1 is fit to the N points most local to the new sample point [4]. One may also truncate or taper the ideal interpolation function of (4). Whichever approach is taken, a compromise is always made between flatness of passband and sharpness of transition band in the choice of a finite h(t) .

For the case where the bandwidth of s ( f ) , and hence ~ ( n ) , is much less than what is available (bandwidth << w/Ts-’), so that T’ << T , elementary schemes such as nearest neighbor may be used with no appreciable aliasing. However, in other cases, an interpolation filter of greater complexity may be required to provide a strong enough stopband to bring aliasing to an acceptable level.

f ig . 5(a). Rectilinear sampling lattice.

\

\

Fig. 5(b). Reciprocal lattice with baseband cell.

IV. TWO-DIMENSIONAL INTERPOLATION

The previous discussion on one-dimensional interpolation may be extended to two dimensions in the case of a rectilinear sampling lattice. Consider such a lattice with basis sampling vectors T I and T2, as shown in Fig. 5(a). The baseband of the two-dimensional discrete Fourier transform is then bounded in a “reciprocal cell” [5], as in the region shaded in Fig. 5(b), by the vectors w1 and w2 where

~1 .T I = ~2 .T2 = 2~ ( I l a>

W ~ . T ? = W ~ . T ~ = O . (1 Ib) and

Consider also the resampling of an image with basis sampling vectors T1 and T2 to another rectilinear lattice with a basis of Ti and Ti, as shown in Fig. 6(a). Fig. 6(b) illustrates the corresponding reciprocal cells bounded, respectively, by w1, w2, and w i , w;. In one dimension, in order to prevent aliasing, the reconstituted continuous signal of (2) must be bandlimited to the lesser Nyquist rate of the original and resampled sequences. For the same reason, information in the Fourier domain in the two-dimensional case must be limited to the area of intersection of the original and resamplcd image reciprocal cells, shown as the shaded region in Fig.


Fig. 6(a). Xvo rectilinear sampling lattices.

- i j :

Fig. q b ) . Common baseband of reciprocal lattices.

6(b). Thus, the Fourier transform H(wl,w2) of the ideal interpolation function h(tl,t2) is a constant within the reciprocal cell intersection, and zero elsewhere.

Having obtained the two-dimensional interpolation function, the reconstituted image 3(tl, t2) may be found from a discrete original x ( n , m ) :

to yield the resampling equation:

y (k , l ) = y y l x ( W n ) h ( k T ~ - ~ T I , ~ T ~ - ~ I T ’ ) . (13) m n

For the special case where the original and resampled images are to differ only in scale, so that T1 = aT\ and TZ = bT;, with a,b constants, the interpolation function becomes separable,

allowing implementation of (13) in two one-dimensional passes.

If the interpolation problem is reduced to a two-pass operation, as represented by (14), a two-dimensional linear (first-order) interpolation scheme, called bilinear interpolation, may b e derived. Referring to Fig. 7, suppose a sample point S with fractional coordinates A p and A8, with respect to the lower left-hand original sample Sm, is to b e estimated from the surrounding four points. Application of the linear interpolation of (9) in the p dimension, followed

Fig. 7. Scenario for bilinear interpolation.

by the same in the 8 dimension, gives

S = (1 - A8)[(l- Ap)Sw + APSIO]

+ A8[(1- &)sol + APSII]

= (1 - A8)(l- Ap)& + AO(1- Ap)Sol

+ Ap(1- A8)Slo + ApA8Sll

= awSm + UOlSOl + 40SlO + UllS11. (15) Higher order interpolation functions a re used and

recommended for remotely sensed images, notably bicubic interpolation [6], which estimates a sample point from its sixteen (16) surrounding samples. However, for the purposes of this paper, only bilinear interpolation is used.

V. APPLICATION OF INTERPOLATION TO SCAN CONVERSION

To reword the two points made at the beginning of this paper from the PPI to B-scan transformation described by (l), in light of resampling theory: 1) the different sampling lattices preclude separable interpolation functions as in (14), and so also scan conversion routines separable into one-dimensional components, and 2) the B-scan data is acquired in polar coordinates, and so does not lend itself to linear interpolation to Cartesian coordinates.

Therefore, the given theory cannot yield an exact solution, but it can still serve as a guide for approximate but practical approaches to scan conversion. Three schemes are presented: 1) ray tracing, 2) space-variant interpolation, and 3) space semi-invariant interpolation.

A. Ray Tracing

This process is a “quick and dirty” scan convcrsion method where the B-scan returns a re directly assigned to the PPI pixel with the nearest integer part of (1) as a coordinate. This is equivalent to zero-order interpolation, with a half sample period shift, since if a number of B-scan returns map to the vicinity of one PPI pixel, only the last return encountered is assigned, not necessarily the closest. Therefore, ray tracing is at best equivalent to zero-order interpolation, which is

170 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRqNIC SYSTEMS VOL. A E S - 2 5 , NO. 2 MARCH 1989

I- N/2 -1 1% i -----I Rg. 8. Local rectangular approximation to polar lattice.

n A

@ I P I AI111111111

4

Fig. 9. Two-dimensional interpolation using local rectangular approximation.

already inferior to bilinear and bicubic interpolation. As such, it is subject to aliasing artifacts such as the case where resampled straight lines take on a staircase appearance, as is seen in the zero-order example of Fig. 14.

Another defect of ray tracing is the absence of any guarantee that all PPI pixels will be addressed, especially at large radii, unless pixels at small radii are greatly and needlessly oversampled. Fig. 8, which shows a B-scan polar lattice superposed on the display PPI lattice, demonstrates this. Note that while PPI pixel P2 may be assigned either B3 or B4 (not necessarily the closest), PI has no candidate samples. Such “holes” result in a regular Moire pattern of unassigned PPI pixels which is at least annoying. Such holes can be removed by “fill-in” schemes based on known hole locations or by median filter discrimination [7]. It is concluded, then, that ray tracing is a simple scan conversion process which is flawed by susceptibility to aliasing and a requirement for B-scan oversampling or fill-in algorithms. If more sophisticated methods cannot b e considered, aliasing may be reduced somewhat for small radii through prefiltering as described in Section VI.

B. Space-Variant Interpolation

In the manner of Fig. 6(a), Fig. 9 illustrates the resampling of the polar lattice onto the Cartesian one. Noting that the polar sampling lattice which is naturally imposed is at least locally rectangular, a local Cartesian sampling grid may be approximated as shown. The Fourier transform of the best interpolation function for the region can then be calculated from the baseband intersection of the transforms of the local Cartesian grid and the PPI display grid, as in the manner of Fig. 6(b). However, the ideal interpolation function thus defined for a locality is evidently infinite in extent, which is opposed to the requirement of spatially limited interpolation. Thus the question begged is one of the best compromise between locality of the interpolation function in space and in frequency. Without models of radar images and of human recognition, it is proposed here that a maximum extent of the interpolation function be set according to results as judged by an experienced radar operator.

The computational complexity of this “ideal” interpolation scheme is high and is therefore not considered for a fast scan conversion, especially in the time required for one radar scan, as would be desirable. One could strike a compromise between computational difficulty and accuracy by defining a Cartesian grid, not for every point of the PPI display, but for a lesser number of local regions. This approximation is further pursued in the next subsection.

C. Semivariant Interpolation

Let a closer examination be made of the range of interpolation functions required by the space-variant interpolation scheme of the last section. On its inner circle of sketches, Fig. 9 shows the local rectangular approximations of the radar B-scan range-azimuth cells at a fixed range superimposed o n the PPI display cells (which a re square for convenience) at strategic


x (0)

f High Order Prefilter Response

Low Order Interpolator Response

Prgfiltered

Alias Energy Alias Energy without Prefilter with Prefilter

Fig. 10. Reduction of decimation aliasing through prefiltenng.

positions. The outer circle of sketches illustrates superposition of the corresponding reciprocal cells in the frequency domain, the PPI reciprocal cells remaining square. For positions 1 and 3, the required bandlimiting is to the shaded intersections of the reciprocal cells. Note that in terms of the polar p,8 coordinates, these a re identical.' The corresponding interpolation function in both cases is the product of two sinc functions in the orthogonal p,O dimensions, and can therefore be applied to the B-scan image in separate one-dimensional passes in the form of (14). Such happy symmetry is spoiled somewhat for other positions than 1 and 3, the greatest deviation occurring halfway between at position 2. The shaded rectangle of the reciprocal cell diagram of position 2 is identical in p and 8 to that of 1 or 3, but the black areas represent needlessly discarded information and admitted energy which may introduce aliasing. Adjusting the extent of the bandlimited area for position 2 is seen, then, as a compromise between aliasing and loss of valid information. However, the decision either way is dependent on what constitutes the more serious picture degradation. If, therefore, the interpolation error represented by the black areas is acceptable, the job of interpolation of the B-scan samples to the PPI form can be separated into a problem of two independent dimensions.

-

INote that filtering is not required in the azimuthal direction i n this example, since the B-scan data ia already bandlimited i n this dimension.

While it has been shown that approximate bandlimiting may be performed for a fixed range by a simple two-pass filtering, it is observed that the azimuthal extent of the range azimuth cells are proportional to radius. Therefore, while all radar sweeps along radius are interpolated equally, the scale of the azimuthal interpolation function for the B-scan image is inversely proportional to radius.

Another consideration is the finite length kernel which must be used, since the B-scan image has a finite length in range and is, at best, cyclic in azimuth. A compromise must therefore be made between the quality of bandlimiting and the amount of distorted data at the ends of finite sequences when convolved with the kernel. Noting that perfect bandlimiting is not relevant in the face of approximations already made, a simple truncation of the sinc function is used for the filtering kernel with easy conscience.

VI. PREFILTERING

Being thus able to approximate scan conversion as interpolation separated into the p and 8 coordinates, finer points may be examined in terms of one dimension.

one-dimensional interpolation, when the sample rate of the new sequence exceeds the original, o r when the new sequence has a lesser rate. In the first case, the interpolation function must be of a sufficient order to provide a passband which adequately rcjects spectral

Two basic cases a re encountered in

172 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-25, NO. 2 MARC11 1989

images of the baseband of the original sequence. The second case, known as decimation, involves a necessary reduction in the baseband of the original sequence, such that the spectral images do not overlap when the sampling rate is reduced. If the degree of decimation is high, the interpolation function required to give adequate bandlimiting may have a large spatial extent with a correspondingly high computational load. Fig. 10 illustrates the alternative of (zero phase) prefiltering the original sequence for bandlimiting. This is followed by decimation with a simple interpolation function h(t) , with frequency response H(w) (in this example the linear form of (10)). Note that for a fair degree of decimation, the amount of energy picked up from the spectral images by a low-order interpolator is reduced. Therefore, the use of prefiltering yields increasing benefit with increasing degrees of documentation. However, prefiltering becomes of less and finally no use as the new sequence sampling rate becomes comparable and finally exceeds the rate of the original. This defines the role of prefiltering as a way of allowing the use of a spatially small interpolation function under all conditions of resampling.

of a PPI image of radius N / 2 pixels from a B-scan image of A range cells by B azimuth cells, the ratio of the PPI sampling rates in range and azimuth to the B-scan rates determines the degree of prefiltering. Referring to Fig. 8, the radial sampling ratio along the Cartesian axes is N/2A, while the azimuthal ratio is 2wr/B, where r = (x2 + y2) ' I2 is the radius in PPI coordinates. From (la), r = Np/2A, making the azimuthal ratio in terms of the B-scan radial coordinate p r N / A B . Therefore, the prefiltering kernels Wp and We to be applied radially and azimuthally, respectively, to the B-scan data prior to interpolation are the truncated sinc functions:

Wp(nz) = (l /nn)sin(Nsnt/2A), if A > N/2,

Returning to the original problem of the formation

Int I < integer(4A/N)

We(n) = ( l /~n t ) s in (pa2Nn/AB) , if A B > Nap ,

In1 < integer(2AB/Npa) (16b)

so that

2AB N*P 4AIN -

BP@+ c Bp-m,e-nWp(nt>We(n>. n=-2AB/Nxp m=-4AIN

(17a) Taking advantage of the fact that W ( n ) = W(-n) for a zero-phase interpolator, we can rewrite

2ABINrp 4AIN B@ + Bpe + 2 Bp-m,e-nWp(nz)We(n).

n = l m = l

(17b)

No filtering is applied in the radial direction if A < N / 2 or in the azimuthal direction if A B < Nap. The second set of conditions on nz and n in (16) corresponds to truncation of Wp and WO at the second zero, in keeping with the previously stated requirement that these kernels be localized.

With the B-scan image now properly bandlimited with respect to the PPI sampling grid through prefiltering, interpolation proper may now proceed with the use of a fixed interpolation function.

VII. APPLICATION TO RADAR IMAGE

In performing a real life scan conversion, the B-scan image was prefiltered, followed by the use of a bilinear interpolator as described in Section IV. Although, to simplify visualization, the scan conversion process was portrayed directly as resampling a polar lattice into a Cartesian one, interpolation is now viewed in the B-scan domain. As shown in Fig. 11, raster scans of a PPI image transform to secants and cosecants, according to ( l ) , when the B-scan lattice is represented as Cartesian. Suppose a PPI pixel transforms to a point S with the nonintegral B-scan coordinates ps and 8,. Defining the coordinates of the four surrounding samples in the manner of Fig. 7, the samples are identified

where

p = integer part@,); 8 = integer part(0,)

with the fractional coordinates:

Equation (15) may then be applied to obtain a value for S . Interpolation is performed in the B-scan domain, but not because the PPI domain approach is not equally valid. The sampling lattices remain locally rectilinear in either domain, yielding equal results. However, in the B-scan domain, only one transformation is required per interpolation. Fig. 12 is a photograph of a B-scan display with an entire scan of radar data. It is in two parts meant to be concatenated. The total image is composed of 1920 azimuth cells by 512 range cells, with the latter spanning a range ratio of 16. Therefore the effective coordinate of the first sample is 512/16 = 32, resulting in dimensions of A = 544 and B = 1920. In order to scan convert to a PPI image with a diameter of 1023 pixels, as measured from pixel centers, the sampling ratios are N/2A = 0.94 and N r p / A B = p/325. Therefore, no radial prefiltering is required, but the B-scan's azimuthal records out to a radius of 324 require prefiltering. In


PPI B-Scan

Fig. 11. Interpolation in B-scan domain.

Fig. 12. Full scan of radar data in B-scan format.

this case, then, (15) was implemented thus:

~ 9 1 P

Bp0 +- Bp,~-,,(l/lrn)sin(np/103), p < 325. n = - M 9 / p

(19) Sincc the radar scan was complete, the liberty of

applying circular convolution was used in azimuth filtering. Note that for the closest range ( p = 32), the prefilter kernel is of length 41-certainly beyond the bandlimiting capability of a bilinear interpolation scheme! The PPI picture of Fig. 13 was formed raster by raster by transforming each pixel's PPI coordinate into the B-scan domain and applying

Fig. 13. Bilinear scan converted PPI image.

bilinear interpolation. Although this process is a laborious task for a general purpose computer, the first author has proposed a dedicated processor to perform semivariant scan conversions [7].

As a better test of the accuracy of the different scan conversion methods discussed, three schemes were applied to an artificial B-scan image consisting of simple bar patterns in two different widths, such that a radial spoke pattern would be produced upon conversion. Since such patterns are regular and have high spatial frequency content, owing to sharp changes in image brightness, even slight aliasing suffered during resampling is expected to show prominently. The three conversion methods tested are 1) zero

174 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-25 , NO. 2 MARCH 1989

Fig. 14. Scan conversion of bar pattern using various interpolation schemes.

order interpolation without prefiltering, 2) bilinear interpolation without prefiltering, and 3) bilinear interpolation with prefiltering.

The results of Fig. 14 can be divided into two rcgions, a decimation region within 64 percent of total image radius and an outer interpolation region. In the latter region, the improvement a bilinear scheme offers over a zero-order interpolation is obvious, but both suffer appreciable decimation aliasing. However, dramatic improvement in the conversion result is achievcd by application of a prefilter previous to interpolation.2

2’I11e radial variations of average intensity in the decimation (i.e., prefiltered) region of the image are due to failure to renormalize the prefilter kernel after truncation.

In view of the ability of the prefiltered bilinear interpolation to render such a result from a difficult test pattern, it is proposed by the authors that this method of scan conversion is adequate for any set of real radar returns.

REFERENCES

[ l ] Skolnik, M. I. (1%2) Introduction to Raahr Systems. New York: McGraw-Hill, 1962.

Interpolation and decimation of digital signals-a tutorial review. Proceedings ofthe IEEE, 69 (Mar. 1981), 301.

Digital image processing. In Proceedings of the NATO Advanced Study Institute, Bonas, France, June 23-July 4, 1980.

A digital signal processing approach to interpolation. Proceedings of the IEEE, 61 (June 1973), 699-701.

Elements of X-Ray Difiaciion, App. 15. Reading, Mass.: Addison-Wesley, 1956.

Cubic convolution interpolation for digital image processing. IEEE Transactions on Acoustics, Sound, and Signal Processing, 29 (1981), 1153.

Enhancement of ice radar images. Master‘s thesis, McMaster University, Hamilton, Ontario, Canada, 1986.

[2] Crochiere, R. E., and Rabiner, L. R. (1981)

[3] Simon, J. C., and Haralick, R. M. (Eds.) (1980)

141 Schafer, R. W., and Rabiner, L. R. (1973)

1.51 Cullity, B. D. (1956)

[6] Keyes, A . B. (1981)

[7] Nickerson, K. (1986)

Kent Nickerson was born in Goderich, Ontario, Canada in 1958. He received the Honours B.Sc. degree in co-op applied physics from University of Waterloo in 1981. Following a period of industrial employment as a design engineer, he received the M.S. degree in electrical engineering with distinction in 19% from McMaster University, Hamilton, Ontario, Canada.

Mr. Nickerson is now on the research staff at McMaster University’s Communications Research Laboratory. He has been involved in physics-related research at several institutions as a co-operative program undergraduate, and is a self-taught electronics designer through personal experimentation in music synthesis. His research interests lie in imaging systems and with his present work in optical computation.

Simon IIaykin (SM’70-FS2) received the B.Sc. (First-class Honours) in 1953, Ph.D. in 1956, and D.Sc. in 1967, all in electrical engineering from the Univcrsity of Birmingham, England.

Dr. Haykin is presently Director of the Communications Research Laboratory and Professor of Electrical and Computer Engineering at McMaster University, Hamilton, Ontario. His research interests include image processing, adaptive filters, adaptive detection, and spectrum estimation with applications to radar.

In 19S0, he was elected Fellow of the Royal Society of Canada. He is co-recipient of the Ross Medal from the Engineering Institute of Canada and the J. J. Thomson Premium from the Institution of Electrical Engineers, London. He was awarded the McNaughton Gold Medal, IEEE (Region 7), in 19%. He is a Fellow of the IEEE.

NICKERSON 6( HAYKIN: SCAN CONVERSION OF RADAR IMAGES 175

Documents

Scan conversion of radar images