Characterization of growing lettuce from density contours—I. Head selection

Characterization of growing lettuce from density contours—I. Head selection

0031 3202/81/050333 08 $02.00/0 Pergamon Press Ltd. Pattern Recognition Society Pattern Rectglnitum Vol. 13, No, 5. pp. 333 340. 1981 Printed in Grea...

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0031 3202/81/050333 08 $02.00/0 Pergamon Press Ltd. Pattern Recognition Society

Pattern Rectglnitum Vol. 13, No, 5. pp. 333 340. 1981 Printed in Great Britain,

C H A R A C T E R I Z A T I O N OF G R O W I N G LETTUCE F R O M DENSITY C O N T O U R S - - I . HEAD SELECTION T. F. SCHATZKIand S. C. WltT Western Regional Research Center, Albany, CA 94710, U.S.A. and D. E. WILKINS

and D. H. Lf~NKER

Agricultural Research Station, Salinas, CA 93901, U.S.A. (Received 11 December 1979; received for publication 1 July 1980)

Abstract - Image processing techniques have been applied to the (one-dimensional) density profiles one obtains when rows of growing iceberg lettuce are scanned with a moving X-ray source. Separation of the Xray scan into individual head clusters is achieved by a valley seeking algorithm which depends, in turn, on a fast convex hull algorithm, which is described. Remaining clustering errors are recognized by n-space linear partitioning, resulting in an overall error rate of about 2~,,. Such levelsof accuracy are required in the present applications which involve the breeding of experimental plant varieties and the management of commercial fields. This is one in a series of papers using moving scanners to characterize standing row crops. I-D clustering Convex hull X-ray densitometry Lettuce Breedinglines Automatic harvesting

The success of these methods in predicting market acceptability suggested that they might be expanded to Over 200,000 acres of lettuce (largely iceberg head yield information about the growing crop before lettuce) are currently hand harvested and packed in the harvest and to provide for further needed improveU.S.A. annually, requiring approximately seven mil- ment of harvest selection. Specifically, a time series lion hours of hand labor. Lettuce is a row crop, i.e., it is analysis of significant parameters might enable pregrown in rows with roughly constant spacing between diction to be made as to date of harvestability and crop plants, with furrows every two rows to allow for expected - of particular interest to growers. Further, irrigation and access for labor or machinery. Head the knowledge of the distribution of such parameters would be of interest to geneticists who are breeding for lettuce first develops outer or wrapper leaves and a loose interior before a head actually forms and fills in. uniformity. Finally, more precise harvest selection This 'filling in' or maturation occurs irregularly. In criteria will decrease the number of incorrectly harvested heads. While much of this information can be, and order to harvest the crop, trained, skilled crews of hand is presently, obtained from sampling of heads among harvesters must pass through a given field from one to the growing crop, sampling is limited, expensive, and three times, feel heads for firmness and selectively cut not feasible when the crop is very small, as in only the mature heads. In keeping with trends towards experimental plots. An ,automatic, non-destructive automation of labor-intensive operations, researchers have studied mechanical harvesters for a number of method is thus desired. years. ~L2~ Successful mechanization has been hamA large number of strip charts were produced by pered by the need for a selector capable of accurately recording the output of an X-ray selector developed by and consistently determining head maturity without Lenker and Adrian for a mechanical harvester. These injuring the head. The physical properties which charts recorded integrated mass (in a I o n cone correlate to market acceptability are density, volume, perpendicular to the row) as a function of ground firmness, and size of the head. ~3~Several groups have coordinate [parallel to the row, Fig. l(a)]. The harvesdeveloped selecting devices which measure or estimate ter traversed selected fields of growing lettuce on one or more parameters on standing heads to several dates. Significant marketing parameters predict these market properties. 12'4"s'6~ Two of these (weight, volume and density) of heads which were subdevices, the gamma ray selector of Garrett and Talsequently harvested were available as well. In order to leyt51 and the X-ray selector of Lenker and Adrian,~6~ use the strip charts (or more precisely, their computerpredict head marketability by measuring the in- readable equivalent) for the above purposes it was tegrated water content in the beam, i.e., through the necessary to first develop an algorithm to recognize head. The accuracy of these selectors has been shown individual heads, a classical one-dimensional clusterto equal or surpass that of hand selection.~71 ing problem. Further, it was necessary to select those INTRODUCTION

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Fig. 1. X-ray absorption contours of section of lettuce row approximately 2 days before maturity; Salinas variety. (a) Strip chart from X-ray scanner: ~ = hand separations. (b) Computer back-plot of digitized data. Machine separation indicated by low vertical bars. (c) Strip chart from "in situ-trimmed' heads. characteristics of the absorption curve representing each head which could predict the market parameters associated with that head, a problem of feature selection. A regression from the selected features to the market parameters was obtained next. Distribution functions of market parameters could then be predicted (and compared to the raw data). From the temporal dependence of these distribution parameters current and future distributions can be predicted and used for breeding information as well as for planning of future harvests. This paper reports on data recording, clustering and feature selection. A companion publication (a~ addresses the regression, distribution, time series and selection problems. A future publication will describe firmware for gathering the X-ray signal directly in computer readable form. This is part of an ongoing study of using remote sensing hardware and software concepts in a close-in mode to identify growing plants with respect to size, disease, maturity, or other selector criteria. DATA One row each of Great Lakes 66A, Monterey, and Salinas (breeding line 67-345-7) crisp head lettuce were raised in sections of two commercial fields in Salinas, California, the major lettuce growing area in the U.S.A. Plants were spaced on 25-30 cm centers, with

occasional larger gaps where plants did not germinate, died, etc; 75-160 heads were grown in each row. A steel stake was inserted into the ground after every tenth head for later calibration purposes. Sixty and 66 days after seeding in field 2, and 51, 54, 64 and 68 days after seeding in field 7, X-ray scans of the growing lettuce were taken using a mechanical harvester equipped with an X-ray scanner (9) using a tracking speed of about 20 cm/sec. Note that optimum maturity occurred at about 68 days in field 2, 62 days in field 7.(s} On 5 of the 6 occasions when scans were made, a section, comprising one-half or one-third of all initial heads in the field being scanned, was harvested. Each head was then trimmed of frame and wrapper leaves, and the weight and volum~e of the trimmed head were measured. Trimming was done to mimic market place practice where loose outer leaves are discarded prior to shelving. Approximately 50% by weight ofthe growing head is so discarded (25% at harvest, 25% at point of sale). In some cases, standing heads were trimmed after the initial scan without cutting the root ; these 'in situ trimmed' heads were re-scanned before they were harvested and measured as described above [Fig. 1(c)]. In these cases discarded leaf weight was also obtained. This allowed a later estimate of which part of the scan signal might be attributed to discarded leaves alone.

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The X-ray signal, after filtering and log amplifi- into regions corresponding to single heads and regions cation, was recorded on one channel of the strip where no head is present. This appears to be a problem recorder. This signal was calibrated after each run of edge detection since what is required is clearly the using beam stops, and a corresponding linear calib- beginning and end of each head. However, virtually all ration was applied to the y-coordinates after strip edge detectors seek the boundary (generally in 2chart digitization. The harvester traverse speed, after dimensional space) between regions of constant grey filtering (t.c. --- 0.3 sec-l) was recorded on the other scale [see e.g. Shapiro(l°'11)]. The resulting step channel [Fig. l(a)]. Visual inspection of the speed function is assumed degraded because of noise. An channel recording indicated that the selector speed exception is the work of Demuth (12) who assumes a had a coefficient of variation of 2-3% over a given row. parametric form for the grey scale plus noise and fits The x-axis was corrected to account for the manually the signal by least square techniques. The X-ray signal measured distance between first and last stakes; no for a single head is not of constant grey scale. For an correction was made within a row, i.e. the speed idealized solid sphere the signal is that of a semicircle; channel information was not used. ]'Note the 2% for a hollow sphere it is the difference between two difference in stake-to-stake distance between Fig. 2(a) semicircles ; a shape which is recognizable in Fig. l(a). Furthermore, the high frequency component of the and (c).] The strip charts were digitized on a large graphic signal is not random but corresponds to the absorptablet. Strip chart segments displaying about 20 heads tion by individual leaves. This may be most easily (75 cm chart length) were digitized with a crosshair seen by comparing Figs l(a) and l(c); one notes very accuracy limit of _+0.1 mm and short range non- similar profiles when the interior section of the head is linearity of less than 0.25%. Points zt = (x~,y~) were rescanned. Because of the unknown pdf of the leaf selected to correspond to observed maxima, minima, signal, edge detection methods do not seem applicable. and places where the slope of the trace changed Wc seek a completely non-parametric separation suddenly (essentially where d 2 l / d t ~ > c, where I is the algorithm, such as is provided by clustering. Regions of signal, t is the time axis, and c is a large constant). high density are to be combined while regions of low Approximately 60 x, y pairs were taken per head. The density act as separation. Isolated clumps (weeds or digitized data was stored in computer-readable form edge leaves not part of the main head - see below) are and then back-plotted to the same scale. Plots were to be eliminated. No ad hoc restrictions regarding the compared to the original strip chart by overlay and number of heads in a given traverse distance are to be where necessary, corrections made to the digitized applied (there may be missing heads which died or did data to assure faithful reproduction [Fig. l(b)]. not germinate). A solution to the problem is suggested by ISODATA, (13) modified to operate in l-D, with CLUSTERING The data of Figs l(a) or 2(a) or (c) is to be partitioned added birth and death rules. An attempt to apply

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T.F. SCHATZKI,S. C. WITT,D. E. WILKINSand D. H. LENKER

ISODATA to the present problem is in progress. A disadvantage of I S O D A T A is, however, that it is global; the entire data vector is treated at once. It is more desirable, and less demanding on data storage, that heads be recognized and segmented as data is obtained in real time. The valley-seeking algorithm, presented below, will recognize a head before the signal rises to the top of the next adjacent head or drops to background level. Post-scan processing, using a classical decision hyperplane, (t*) although necessary, is kept to a minimum. The digitized data were separated into individual heads (1) visually ('hand-separated') and (2) by a clustering algorithm ('machine-separated'). Hand cuts were made by inspection of the strip charts. Heads were tentatively identified from the knowledge that ten wore present between adjacent stakes; in problematic cases, the position and shape of the same head on later scans was used as well. The actual partition between heads was then chosen as the first rise above background if the signal dropped that low [for example heads 52-53, Fig. l(a)], or a minimum between heads (heads 54-55) or roughly in the middle of the low signal (heads 51-52). F r o m Fig. 2(c) it is clear that such partitioning is relatively straightforward for lettuce one week from maturity. F o r younger heads ['Fig. 2(a)], independent knowledge of head positions derived from later scans over the same field, as described above, is essential for hand separation. Hand-separation may be viewed as manual clusteri n g Its purpose is, of course, to develop a target which a machine clustering algorithm is to match as closely as possible. We seek to partition the data, z~, into individual heads, preferably without advance knowledge of the number of heads in a field. The method used here is one of valley detection. We search downfield (left to right on Figs i or 2), recognize the appearance of a low density region and cut off the head to the left. This requires storage of but a few more z~ than those for one head. This method depends on having an absolute criterion for a low density region and thus requires rather uniform appearance of heads. This criterion is met here. We recognize a low density region (a 'valley') whenever any Yi between two 'adjacent high points' is less than • times the smaller of the two, where ce is a fixed fraction. The 'adjacent high points' are members of the convex hull being generated [see below and the dotted line in Fig. l(b)]. Once a valley is recognized the cut is applied at its minimum and the hull is redrawn to the cut. A cut is also made whenever the signal drops below a minimum, y~ < ~,, basically the base line. The material so cut away may well consist solely of the wrapper and frame leaves. To avoid counting loose leaves as a head, each cut 'head' is inspected and if its area falls below a fixed criterion (~/o of running area average) it is discarded. The complete cut algorithm flow diagram is shown in Fig. 3(b). Choice of a,/~ and ~, is discussed below.

Convex hull algorithm Let Z , = {z~ = (x, y~), i = 1.... n} be a set of points in R 2 with x~ monotonic (x~ > xj if i > j). [An example of Zn would be a sequence of digitized points of an Xray scan, as in Fig. l(b).] A 'straddling chord o f f shall be a line between z~ and zk (~Z~) for any i < j < k. We define a quantity Cn as a subset of Z~ with the following property: zl ~ Cn if each straddling chord o f j lies below zl. By 'lies below' we mean y (XJ) < YJ, where y (xi) lies on the straddling chord, zl and z~ are understood to be part of C~. The C~ we so define is, of course, simply a part of the usual convex hull of Z~, i.e. if we replace y~ by - y ~ and repeat the above process, the two partial convex hulls so found together comprise the entire convex hull of Z,. (In a simplistic way the C~ can be thought of as drawing a plastic bag tightly over a head - this is, of course, the motivation for the convex hull.) We require an efficient algorithm to establish C~, given Z~. Since n is finite we could always test all straddling chords, but this is 0(n 3) tests. A more efficient test can be created from the following consideration. Ct = {zt} and C2 = {zt, z2}, since the end points are always included. Suppose Ck has been found for k < n. If zj¢Zk but zj~Ck then z~EC~, for all l, k < I < n, for the set of all straddling chords of j in Z~ is a proper subset of all straddling chords ofj in Z~. On the other hand z~+t ¢Ck+1. Our required algorithm then proceeds as follows. Put Ca in a stack. Add zk + i. Test the contents of the stack for membership in Ck+ 1. Any discards are discarded forever as members of C,. This requires but 0(K 2) tests or O(nKz) overall, where K is the number of members of Ck, and N of Cn; typically K << k, N << n, K/k ~ N/k and K = 0(N). We introduce yet another compression of our algorithm which reduces the test of the stack for membership of Ck+l from 0(K 2) to 0(K), as follows. Draw chord (z~, zk + 1), where zj = z_ 2 is the element of the stack currently two below zk+ 1 = Zo. (Initially zj will be the penultimate number of Ck.) Test the single member of the stack between z~ and zk + 1 (z_ 1). If it is below the chord, discard it from the stack and repeat by drawing a chord from zk+l to the next deeper member of the stack. If it is above the chord the stack will contain exactly the elements of Ck + ~. We do not prove this last statement, it follows directly from the geometry in this case. Thus we need to make at most but K - 1 tests (K - I is achieved if C~+t = {z~, zh+ 1}) and our total test for C~ takes between 0(n) and O(nK) tests. The flow diagram for this algorithm is shown in Fig. 3(a) (where Ck is shown as CVH~). Note that this convex hull algorithm is ideally suited for microprocessors since it is based on a last-in first-out pop-up stack. Graham ~s~ and Jarvis ~16~ have also described methods for finding the convex hull of points in R z. Our algorithm is a somewhat improved version of the latter, particularly adapted to the present case of an ordered, infinite data stream and close interlocking with a valley-seeking algorithm. The computational

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Fig. 3. (a) Flowchart for convex hull algorithm. efficiency of the present algorithm at large n would fall between that of (is) and, (1~) while for n ~ 50, the present case, it would probably be superior to either. Three kinds of head recognition errors can arise from the cutting algorithm described. The algorithm can fail to separate two closely adjacent heads ; we call this a merge. The algorithm can cut a head in two, keeping two heads where one should be; we call this a split. The algorithm can find a valid head but reject it completely on the minimum area criterion ; we call this a miss. A fourth kind of error, where the cut occurs at a point different from that of the hand decision, in effect moving part of one head to another, is not considered an error as such for the local head count remains valid and no certainty attaches to the hand decision in any case ; such errors were quite common. Of course, such a move will affect the resulting values, e.g. while one head gains in area the adjacent head will lose. Merges,

splits and misses are identified when the machine head recognition is compared with the hand decisions. [Two merges (including the only 3-head merge in the data) and a miss (last head) are noted in Fig. 2(b).] The fraction, f, of those three kinds of errors which arise will, for a given field, depend on the adjustable cutting parameters ~, fl and 7- Since head separation is most difficult for young lettuce we inspected two stretches of 40 of the youngest heads in each field and adjusted o~ and ~ to minimize errors (clearly a trade-off is involved). We chose ~ = 0.4, fl = 0.33 and 7 --- 0.6 g cn1-2. For these parameters we found 42 merges, 8 splits and 45 misses among the 1490 heads scanned. Among the 45 misses were 20 heads which were dead or would die before harvest (heads were scanned up. to 4 times before harvest); these heads tended to be small, of course. On the other hand, 51 such dead or dying

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Fig. 3. (b) Flowchart for machine separation algorithm Negative subscripts refer to elements of current CVH stock. heads were not missed. If the distribution of only fraction of splits and merges is clearly low, these errors healthy heads is wanted the errors would be roughly are concentrated in the young rows, M / N reaching compensatory. In any event a miss rate of 3% is not values as high as 11%. Since m/s -~ 3 we note that this serious and would affect any distribution only at the frequency of merges will cause an overestimation of s 2 low end. N o further correction was made for misses. by a factor of 2. There is thus considerable motivation to reduce M and S even further. If the true distribution of samples is normal, which we show in another publication,(s) it is straightforward The crucial variable here is the width, WD, of each to show that the computed mean of the size distri- head. It is reasonable to suppose that an unusually bution becomes wide machine-selected head is two merged heads, while two adjacent narrow heads may well have S-M resulted from a split. Accordingly, we carried out a E(m) -= m -m N multi-dimensional pattern recognition search for an indicator of merges and splits based on width and while the computed variance becomes other parameters. We find indeed that the inequality S 2 - 3s 2) + ~-(m M z + s2), E(s 2) --- s 2 + ~--~(m W D / W D > 2.97 - 0.87 ( A R / A R ) indicates a merge; this criterion identifies all but 7 of the merges while each to first order in 1/N. Here S and M are the number incorrectly indicating 5 non-merged heads as merges. of splits and merges among N samples and we have (The partitioning surface is not very critical; the assumed that a split results in two equal parts, the criterjon W D / W D > 1.57 does almost as well.) Here A R is the area under the head and the overscores splitting and merging samples occurring at random among the normal distribution. Although the average indicate averages taken over the entire row (a given

Characterization of growing lettuce from density contours variety on a given date). All heads indicated as merges by the above criterion were eliminated from the data set. [Both merge errors of Fig. 2 were detected.'] Similarly the criterion ( W D / W D ) i <_ 0.715 and (WD/WD)t+ I _< 0.715 and ( W D / W D ) i + ( W D / W D ) i + 1 <- 1.3 identified all 8 splits while identifying 3 additional heads incorrectly as splits (the split partitioning parameters were critical and may thus be less generally applicable than the merge partitioning parameters). Again, all heads identified as splits were eliminated. Using then the clustering algorithm based on the convex hull described above, followed by the merge and split criteria, we have a complete machine-driven clustering algorithm to identify a section of the strip chart with each head which is essentially error-free except that it misses roughly 2% of the viable heads (after compensation), largely at low end of the size distribution. In all that follows, when we refer to 'machine-selected heads', we have used this algorithm with the parameters given above.

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of trim level make a substantial, although consistent, change in the desired features. In future application of the present methodology the maturity of the lettuce is precisely what is desired and will not be available. One would thus need to go through the described laborious method of trimming some standing lettuce to establish the trim level experimentally. This precludes, in practice, the use of such 'trimmed' primary features to cluster or predict market parameters. SUMMARY

There is a need to develop non-destructive methods to characterize growing crops to implement nonlabor-intensive harvesting and for breeding and growth studies. An X-ray-based densitomcter system has been develope d(6) which has been applied to rows of growing lettuce yielding a strip chart presentation of leaf density vs field position. The present report describes the first stage in the conversion of such charts to a statistical representation of the parameters describing market acceptance of iceberg lettuce. The companion paper reports regression analysis while a subsequent report will describe full FEATURE EXTRACTION automation, including hardware. Following digitization (at approximately 60 points/ Five primary features wcrc selected from the selechead), individual heads appear as overlapping reted section of the chart to describe each head: the area gions of enhanced density. Although random noise is under the curve defined by {zi},(AR); area under the low (approximately 10%), non-significant signal levels convex hull, (CH); the width, x~ist-xl, (WD); the from individual leaves amount to up to 50% of the m a x i m u m intensity, max Yi, (MI); and the average sought-for density rise. Regions corresponding to intensity, (AI - AR/WD). It was feltthat A R might single heads are extracted using I-D clustering. Such correlate with.market weight (W), while C H and W D clustering is applied by using a newly developed might correlate with market volume (V) and/or algorithm for selecting convex hulls which shows market density, W/V, (D). The two height parameters similarities to one previously reported. ¢I6) Here points were chosen since currently a m a x i m u m height is used are considered in order of increasing ground position ; as a head acceptance parameter for harvesting.(6) Inspection of Fig. l(b-c) makes it clear that several the algorithm looks back from the current point to the of the primary features,in particular CH, W D and AI, last member of the hull and rejects all intermediate points which fall below the connecting chord. The are strongly dominated by the cutting algorithm, i.e.by how many wrapper leaves are included in the total number of tests required is of order ak, where n is the head. O n the other hand, the market parameters are in number of points in a head and k the number of members of the hull. Interwoven with the convex hull all cases measured on a head from which the wrapper algorithm is a valley (invagination) detector which leaves have been stripped. It thus seemed worthwhile to attempt to factor the intensityinto a part due to the serves to separate the heads. Important parameters for the algorithm are the noise level, the depth of inmarket head alone and a part due to the wrapper leaves. From geometric considerations itis found that vagination (60%) and the size of cluster to be rejected this is approximately equivalent to raising the baseline as snow (33%). As described, the algorithm misclusters about 6% of an appropriate amount before applying the cutting the heads, by either missing a head, merging two heads algorithm. The amount of baseline elevation ('trim level') required will depend on the severity of trim, or splitting a head in two. By using additional decision which was established as follows. For one of the fields, lines in the autoscaled area width space, this error rate the lettuce was scanned in the usual way, physically is reduced to 2%, virtually all of which are heads which trimmed while stillstanding, rescanned, and finally were missed as snow. Width and area refer to the width and area of the strip-chart region corresponding to a harvested. The trim level on the earlier scan was then head. In the companion paper, the area, width, maxraised until it resembled that latter one (strictly by imum and average adsorption signals are used in a watching WD). The procedure was repeated for all regression to predict the market-ready weight, volume three varieties on two dates. The optimum trim level and density of iceberg lettuce. was found to obey a relation of the form (0.032t + 0.61) _+ 0.04g cm -2, where t = days to maturity, (s) Acknowledgements - The authors would like to thank Mrs. Raglon and Miss Ullner for their aid in digitizing the data and with only a minor varietal dependence. Small changes

340

T.F.

SCHATZKI,

S. C.

WITT,

D. E. WILKINSand D. H. LENKER

Dr. E. Ryder for supplying the lettuce stands and much helpful advice.

REFERENCES

1. R. E. Garrett, M. Zahara and R. E. Griffin, Mechanical harvest of crisphead lettuce, Agric. Engng, St. Joseph, Mich. 45, 611 (1964). 2. B. L. Harriott and K. K. Barnes, Mechanical selection of crisphead lettuce for harvest, Trans. Am. Soc. Agric. Emirs 7, 195 (1965). 3. W. B. Goddard, M. Zahara, P. A. Adrian and D. H. Lenker, The relationship of physical properties to market acceptability of crisphead lettuce, Trans. Am. Soc. Agric. Engrs 15, 358 (1972). 4. R. E. Garrett, M. Zahara and R. E. Griffin, Selectorcomponent development for a head lettuce harvester, Trans. Am. Soc. Agric. Engrs 9, 56 (1966). 5. R. E. Garrett and W. K. Talley, Use of gamma ray transmission in selecting lettuce for harvest, Paper No. 69-310, The 1969 Annual Meeting of the American Society of Agricultural Engineers (1969). 6. D.H. Lenker and P. A. Adrian, Use of X-rays for selecting mature lettuce heads, Trans. Am. Soc. Agric. Engrs 14, 894 (1971). 7. P. A. Adrian, M. Zahara, D. H. Lenker, W. B. Goddard anti G. W. French, A comparative study of selectors for

maturity of crisphead lettuce. Trans. Am. Soc. Agric. Engrs 16, 253 (1973). 8. T. F. Schatzki, S. C. Witt, D. E. Wilkins and D. H. Lenker, Characterization of growing lettuce from density contours--II. Statistics, Pattern Recognition 13, 341 (1980). 9. D.H. Lenker, P. A. Adrian, G. W. French and M. Zahara, Selective mechanical lettuce harvesting system, Trans. Am. Soc. Agric. Enors 16, 858 (1973). 10. S. D. Shapiro, Detection of lines in noisy pictures using clustering, Prec. 2nd Int. Joint Conf. on Pattern Recognition, p. 317 (1974). 11. S. D. Shapiro, An extension of the transform method of curve detection for textured image data, Prec. 3rd Joint Int. Conf. on Pattern Recognition, p. 205 (1976). 12. H.B. Demuth, Feature extraction through least square fit to a simple model, Prec. 3rd Int. Joint Conf. on Pattern Recognition, p. 37 (1976). 13. G. H. Ball and D. J. Ball, A clustering technique for summarizing multivariate data, Behavl Sci. 12, 153 (1967). 14. N. J. Nillson, Learning Machines. McGraw-Hill, New York, 1965. 15. R. L. Graham, An efficient algorithm for determining the convex hull of a finite planar set, Inf. Prec. Lett. 1, 132 (1972). 16. R. A. Jarvis, On the identification ofth© convex hull of a finite set of points in the plane, Inf. Prec. Lett. 2,18 (1973).

Allollt the Autho¢ -- THOMASF. SCHATZKIobtained his B.S. in Chemistry from the University of Michigan in 1949 and his Ph.D. in Physical Chemistry from M.I.T. in 1954. He was a staffmember at Shell Development Company from 1957 to 1972, since when he has been with USDA, where he is currently Research Leader, Chemical and Structural Analysis. His interests include polymer physics, system modelling and pattern recognition, lately concentrating in image analysis. About t ~ A I I d l l O ¢ - SUE CAROLWITT obtained her degree in Chemistry from Newcomb College in New Orleans, Lousiana in 1962. She has worked at the Western Regional Research Center of the U.S. Department of Agriculture since that time. Her areas of research have included estrogenic components of forages, plant protein isolates, data processing of standing crops and, currently, nuclear magnetic resonance spectroscopy.

Ahem the Amher DALEWILKINSobtained a B.S. degreee from Purdue University, an M.S. degree from the University of Maryland and a Ph.D. from Iowa State University. He has had a research career with USDAAR of over 19 years, during which he has conducted research in a broad field including decontamination of agricultural lands subjected to radioactive fallout, crop storage, seedling emergence, cultural practice of vegetable production and equipment and systems for soil and water conservation. -

Abmlt tile Alitholr - DON LENKERreceived his B.S. degree in Mechanical Engineering from the University of California at Berkeley in 1961 and his M.S. degree in Agricultural Engineering from the University of California at Davis in 1963. For the first five years of his career he worked on developing mechanical harvesters for citrus in Florida. Since 1968 he has developed a number of machines, including a mechanical lettuce harvester and a cauliflower harvester, for the harvesting and production of leafy vegetable crops at Salinus, California.