DET MORPH-a new method for an accurate acquisition of fine-morpholoqical data-Exemplified on the Achillea millefolium group ( Asteraceae )

Det-Morph is a new approach for a detailed morphological analysis of primary segments of leafs and ray florets from some species of the Achillea millefolium group (Asteraceae). 56 features of primary segments and 21 features of ray florets both in two different transformation types are yielded by the new software. The usefulness of these features is shown on data of 616 specimens of Achillea setacea, A. collina, A.ceretanica, Adistans s.l., A. millefolium s.1. and A.pannonica.


Introduction
One of the major goals of pharmacognostical research is a precise description of medicinal plants and herbal drugs.Within the scope of our studies on Herba Millefolii (derived from species of the genus Achillea (Asteraceae)) we indicated that the shape and to a lesser extent the size of primary segments (called leaflet) of upper stem leafs and of the ray florets are important characteristics for each taxon [1,2].Traditionally used features, e.g.breadth and length of leaflets or of ligule (ray florets) are not sufficient for the description of the respective parts.In [3] the product from breadth and length was used as an approximate value for the area of leaflets etc.The first reason for the development of a special software was the striving for the proper evaluation of the area and the perimeter of leaflets and of rayflorets (or parts of them).A first report was given in [4], and test applications are given in [5 -91.A further advantage is the electronic availability of detailed drawings of interesting parts of the plants, particularly with regard to the large number of investigated material.

Functional principle
The software was written in GFA-BasicB for Atari-computer@ and is also running under Windows 98, 2000, XP@ and higher with the software emulation Magic-PCB.
In the following only those parts of the DET-MORPH algorithm are described in detail which are necessary to yield the new features: l a ) The creation of sample drawings using a microscope with drawing apparatus, after this the use of a scanner or a digital camera to get a bitmap.
I b) The use of a digital camera for a shoot from the microscope.
Both methods supply a bitmap (rgb).The pictures must be transformed into a two color bitmap.Only this can be processed by the algorithm.

2)
Conversion from the bitmap into a vector graph which can be resized (extraction of the outline, cp.fig.I .).
3) Input a standard (length or breadth) for the pictured object.4) Resize the vector to a proper dimension (so all details can be seen on the screen).5) Define characteristic points onto the vector (e.g.begin and end of the ultimate segment of a leaflet, see fig.3.).6) Automatic measurement of the vector and outputlsave of the computed values.A list of the new features in tab. 1. and 2.. Ad 1) The method of choice is l a .It takes more time than I b , however, the editor has the possibility to make corrections on deleted or folded parts of the object.Furthermore the degree of accuracy is much higher than in I b.Using I b the precision of the vector depends on the homogenous illumination of the microscope slide and on the transparency of the objects.In addition, no software is available which has the capability to trace the outline of an object with overlapping areas (cp.

Fig. 1. bottom fication
Screenshot of the conversion from a bitmap into a vector graph.In the left corner you can see a part of a leaflet; on the right a square magniof an overlapping area and on the top left there is a software magnifier.
Ad 2) The conversion of a bitmap into vector graphs is the crucial point of the method.There are some algorithms, which are used for line tracing [lo].But these algorithms are not suitable for overlapping areas of e.g.secondary segments (cp.fig.I. and 2.).For this purpose it was necessary to develop a new and interactive algorithm.
For the further processing (e.g.excision of secondary segments or of the ultimate segments (US) of leaflets, cp.fig.7.-9.) it is essential that all points of the vector form an incessant ascending index series.The editor has to fix the starting point (always in the bottom left side of the vector).The algorithm trace the outline throughout time so that there is a white pixel on the left and a black pixel on the right.Fig. 2. Vector graph of a leaflet from Achillea pratensis.A-overlapping areas are black.Vector graph with plotted vector points A-with more than 3000 points, Bafter a thinning with only 1000 points.
Crossings will be detected by a polygonal testfield (cp.fig.1.).If the software recognizes a possible crossing then an alert box appears.If the editor accepts this region as a crossing then he has the possibility to mark the correct following point with the mouse and lead the line tracing algorithm over the cross.Possible gaps in the lines are also detected and can be overbridged.After the conversion the software asks if every or every other point should be used.The editor has to make a compromise between accuracy and available memory.In the standard screen the points are invisible since only the lines between the points are plotted.The pictures of both types of resized vectors are stored as a compressed bitmap for a quick usage on the screen.Ad 5) An automatical recognition of the structure of the leaflets or of the rayflorets by the use of an algorithm is not possible.Therefore it is necessary to ask the editor for characteristic points of the object (cp.fig.3., 4.).This input is separated from the measuring procedure, and the information about those points is stored in a separate file.Therefore it is possible to control the position of these points at any time.).This kind of processing ensures that all marked segments of the object can be cut out and stored as separate vector or can be rotated or can be resized (cp.fig.8., 9.).Ad 6: Before measurement each vector will be resized to a maximum size.This procedure guarantees a maximum precision.After that all high-order segments (cp.fig.4.) will be cut out.The area of each segment are computed according formula l..The perimeter of segments is the sum of Euclidian distances between the vector points.A = I C ( x ( i ) * ( y ( i + 1 ) -y ( i -1 ) ) ) ( I 2 for i=l ... number of points Formula 1. Computation of the determinant of the x-and y-coordinates from the vector points leads to the area of the polygon.

Results and Discussion
The new software fullfills two major tasks.On the one hand exactly measured values of new features from leaflets and rayflorets are available for taxonomic purpose now.On the other hand the yielded graphs (leaflets -fig.5., rayfloretsfig.6., ultimate segmentfig.8. and ultimate lobefig.9.) can be sorted with arbitrary data, e.g.results of the M o e c ~~~~-a l g o r i t h m [I I] and combined e.g. with a dendrogramm of a cluster analysis (fig. 11.).On the basis of such possibilities it is easy to get a clear sight of the data.This leads quickly to a precise interpretation.
For the application of the newly available features in a biosystematic study some important questions should be discussed.Shape and size: With the great number of newly available features there is a serious question about the importance of these features [13,14].Which ones are essential for the description of shape, which are hidden behind the correlation with the size?The now available vector graphs make it possible to compare a plot of original-sized with equal-sized data from leaflets (cp. fig. 5., 6.).It is obvious that the human recognition favored the size for grouping, but in a biosystematic study, size and shape, both are necessary purviews.
We would like to point out that many features show a low correlation between the equal-sized and original-sized computations.Within the features of original-sized data of leaflets strong correlations are visible between the features from the entire leaflet (perimeter, breadth, length and area) and the mean values of leaflet of second order (perimeter, breadth, length and area) and the values of the greatest segement of second order (perimeter, breadth, length and area).A second group of correlations is visible between features of ultimate lobe, and in a weaker manner against the features of ultimate segments and ultimate lobe of leaflet of second order.The third group of strong correlations is within features of ultimate segments.
At a first glance on features of equal-sized data of leaflets there are similar groups of stronger correlations but there are also some remarkable differences.
The perimeter of the entire leaflet (LL-P) is correlated with NRLOB, ML2-P and MLZNRLO only.The ultimate lobes'values and the ulitmate segments'values show negative correlations against NRLOB and NRLLZO.
Between features of rayflorets there are also strong correlations visible.Three groups of features can be distinguished.First the correlations between original-sized features are strong for all features of entire rayfloret, the ligula and the area beside corrolatube (CTBA).Second all features of ligula, and third all features of central lobe show a strong correlation.In the case of equal-sized data there are similar groups visible.
These observations lead to the following conclusion: The shape of leaflets is controlled at least by three groups of genes A) leaflet's rhachis and segements of second order B) ultimate segment C) ultimate lobe.

Figure 3 .
Figure 3.  shows the position of the characteristic points.Each point must be a point of the vector (cp.fig.2.).This kind of processing ensures that all marked

Fig. 6 .
Fig. 6.Rayflorets of Achillea speciesa, A-A.collina; b, B-A.pannonica; c, C-A.sudetica (type SUD-W1, [3]); d, D-A.sudetica (type SUD-W2, [3]); e, E-A.distans; f, F-A.pratensis.Vectorgraphs signed with lower case letters are resized to the same length, signed with upper case letters are correctly sized to each other.As one can see in fig.3., 4. the baseline of the ultimate segment (US) and ultimate lobe (UL), is in most cases oblique.For a better comparison the
Definition of the ultimate segment (US) of a leaflet of the leafs: A first clue to the use of the ultimate segments is given in[IZ], however no appropriate definition can defined.One usefull rule is that most species of the A.millefolium group show an ultimate segment with at least 2 to 3 lobes.Fig.7.shows leaflets from different species with various possibilities for the definition of ultimate segments.It is evident that the ultimate segment of e is 3-lobed but the definition given under f may be accepted too.In contrast in h we cannot determine exactly which definition is correct.A similar situation is given in a to d.In most cases (a to d and g, h) a clear decision is only possible if one can look on a greater sample of a population!The shape and size of US are very important features for the definition of taxa[I 21.