An Interactive System For Fourier Analysis Of Artichoke Flower Shape.

Abstract

AbstractIn this paper we present an interactive system which allows the Fourier analysis of the artichoke flower-head profile. The system consistsof a DEC pdp 11/34 computer with both a a track-following device and Tektronix 4O1O/1 graphic and alpha numeric display on-line. Some experiments have been carried out taking into account some different parental types of artichoke flower-head samples. It is shown here that a narrow band of only eight har­ monics is sufficient to classify different artichoke flower shapes.IntroductionThis paper deals with an interactive system which allows the study of artichoke flower- head shape. In this study the use of a computer system is necessary for the wide variabil­ ity of shape which the heads present both in the same and in different parental types.This study is motivated by the connection between: shape of the heads and anti-parasitic treatment effectiveness, shape and commercial demands, shape and resistence to the atmos­ pheric agents, shape and genetic factors. To point out these connections some considerations are developed:-Shape and anti-parasitic treatments;anti-parasitic substances, scattered on the flowers, can penetrate more or less deeply and work in a span of time depending on the shape of the head. For instance, a cone-shaped head in contrast with a cylindrical one, will let an anti-parasitic substance slide away more easily, thus avoiding toxic residues [1] .-Shape and atmospheric agents; the most external bracts, of an artichoke are of ten damaged by cold, and bacterial rot is likely to cause damage. Some studies have pointed out the higher resistance of ovate heads to the damage caused by cold [2] .-Shape and industry; round heads are prefered by industries because they have got bigger receptacles and therefore a high utilizable part. As a matter of fact, the variability of the diameter influences the variability of the utilizable part of the receptacle and conse­ quently that marketability of the product [3] .This study, however, does not intend to give an evaluation of the best shape for the flower-heads in connection to the factors already mentioned, but simply proposes a model for the description of the shape.Some methods of numeric evaluation of flower-heads have been proposed in literature: one of them is based on the measurement of transversal diameters in six equidistant posi­ tions along the longitudinal section of the head; another is based on an analytic combina­ tion of the height of a head and the measurements of the diameters in a fixed position [4] .The model here proposed is founded on the Fourier analysis of the flower-head profiles. As a matter of fact, in this method, the problem of the analysis of the shapes becomes the problem of the continuous, limited plane curve analysis. It is well known that the finite dimension Fourier spaces are isomorphic to the sets of band limited plane curves, so using the Fourier spaces it is possible to describe simply a very large set of plane curves. Therefore the power of this method lies in the fact that it allows the selection of the few features sufficient to describe the shapes.The discrete Fourier analysis is here developed using the DCT (Discrete Cosine Transform) algorithm [5] and the features adopted are of the kind of Brill and Granlund [6,7] .Some experiments have been carried out taking into account the most significant parental type and pointing out the relationship between the shape of the heads and their Fourier spectra.-In the first section the model of artichoke head profile analysis is shown.-In the second one the experimental set up is described.-The third and last paraqraph report some experimental results.