Using digital image analysis for describing fruit shape in horticultural research

Describing three-dimensional shapes mathematically is of interest for many areas of research.  Horticulturalists, for example, need to be able to systematically register shapes of fruit.  At the Institute of Agronomy and Crop Science of the University of Halle-Wittenberg, a simple, non-destructive image analysis method for describing the shapes of cherries was developed.  The image analysis used is Olympus' analySIS software.

Describing shapes objectively and simply
The objective and reproducible description of the shape of fruit is required for a wide range of purposes in horticultural research.  Fruit shape, size, colour and mass are significant properties when characterising the specific variety of fruit.  These parameters are included in the fruit descriptions as listed in variety catalogues.  Current patent protection of plant varieties is based on these variety catalogues.  For some fruit crops, the shape of the fruit influences consumer preference; this means that the fruit shape may be a decisive selection and differentiation criterion in fruit breeding.  Furthermore, some growth regulators (phyto-hormones) may affect fruit shape.  Fruit shape and especially surface curvature influence distribution of tension in the fruit skin, and the way in which tension is distributed throughout a fruit affects its tendency to split or rupture when subjected to precipitation.

Drawbacks of current methods
Currently there are various methods for describing fruit shape.  The more basic method involves simply evaluating the fruit visually and comparing it with reference drawings for classifying its shape.  This method requires no special equipment but as it is subjective, it is conducive to error.  Other methods characterise fruit shape using fruit shape indices calculated from certain fruit dimensions such as length, width and height.  The measurements are conducted using slide rules and aperture plates that are not technically complex.  Although results are objective and reproducible this method does not allow a continuous description of fruit contour as is required for some applications.  In more recent approaches, fruit shape is characterised via digitised cross-sections with Fourier descriptors or via 3-D laser scans using spherical harmonic descriptors.  The drawback of these approaches is the requirement of highly developed (and expensive) technical equipment along with substantial mathematical abilities.

fig. 3: In order to characterise fruit shape, images of many, many individual fruits are digitally acquired from three different perspectives.  The image analysis software calibrates each image automatically and converts it to a binary image to detect the fruit shape. The pedicel is removed digitally.  The middle of the yellow virtual box placed around the body of the fruit defines the origin of the coordinate system.  For subsequent evaluation, the images are automatically saved in the integrated database.

Digital image database
The method we use is based on macroscopic acquisitions that are processed and measured using image analysis with Olympus' analySIS software and a digital camera with a macro-objective.  This straightforward method provides a continuous description of fruit contour that is objective, reproducible and easy to evaluate.  The only equipment required are PCs and standard software – available in any standard lab today.
The first step in characterising fruit shape is digitally acquiring images of a large number of representative fruit of one variety via the image analysis software.  All images are immediately and systematically archived in the integrated database.  This archiving is important as image acquisition and evaluation take place at different times.  When the fruit have ripened, images of fruit specimens must be acquired in a rapid and automatic fashion.  The second step – the actual gathering of data – is where the software generates contour data based on the images acquired.  The third step involves analysing this data via a sheet calculation program.

fig. 4: The gallery view of the analySIS database shows yellow paper clips on those thumbnails that include other files.  In this case, the three views of each fruit are stored as a single record.  Evaluation sheets and other documents may also be appended to a record.

Subtracting the pedicel
Each fruit is acquired on a macro stand from three points of view: from the front (xz perspective); from the side (yz perspective); from above (xy perspective).  This procedure has been standardized and automated via an analySIS acquisition macro.  Each image series is automatically calibrated when acquired and the three views of each fruit are automatically stored in the database.  The second step involves an analySIS measurement macro extracting the x, y and z coordinates of the data points describing fruit contour from the acquired images.  To do so, images are binaries first.  One particular challenge was having the fruit pedicel automatically eliminated from the images.  The pedicel is not considered a relevant part of the contour being described. However, it cannot be physically removed from the fruit before the acquisition is made because this might alter the contour of the fruit around the pedicel cavity. Furthermore, following image analysis acquisitions of the fruit, there are some cases where this fruit is used in experiments where the pedicel has to still be attached.

1,500 points of data
Once the automatic image analysis is concluded, the measurement macro displays the x, y and z contour data of the detected fruit on a data sheet.  The point of origin is the intersection point of the diagonal lines of a virtual rectangle positioned around the fruit.  The approximately 1,500 points of data detailing the contour of each view of the fruit are transferred to a sheet-calculation program for further analysis.  In order to reduce the amount of data, every tenth point of data is used for calculation and standardized so that fruit of different sizes are easier to compare.  The common coordinate origin makes it possible to reconstruct the fruit shape three-dimensionally, based on the contour data of all three views.  The symmetry of the frontal view means that further analysis can be restricted to one half of the fruit contour.  Transforming the Cartesian coordinates (x, z) into polar coordinates (angle, length, vector) makes it feasible to describe the contour via a polynomial of the third order – even around the pedicel cavity.  We were also able to model the contour of the yz perspective via a third-order polynomial.

fig. 5: The image analysis evaluation of the three views of a body of fruit (via a specially developed analySIS measurement macro) yields a sheet with ca. 1,500 items of x, y and z contour data.  Based on this data, the fruit contour can be reconstructed three-dimensionally (A).  The calculated mathematical contour model (here: one half of the frontal view) corresponds well with the points measured (B).

Mathematical modelling
Using the method described, the way fruit shape changes during growth can be analysed.  In addition, we were able to model the shape of 24 varieties (as defined by the Bundessortenamt, Germany's Federal Office of Plant Varieties) of sweet cherry – and did so at a satisfactory quality level.  Comparing the fruit shapes with the help of a hierarchical cluster analysis and a ranking sum test resulted in 4 fruit-shape clusters.  Doing so enabled us to determine decisive parameters regarding fruit shape.

fig. 6: A dendrogram of the fruit shape of 24 sweet cherry varieties describes the systematic similarity of the various shapes.  The dendrogram is the result of a hierarchical cluster analysis of the 4 regression coefficients that were used to describe the fruit contour as seen from the frontal view (xz perspective).  The numbers 1 through 4 describe the four fruit shape clusters that we identified.

Other fields of application
The new method for describing the shape of sweet cherries was created by gathering morphological data on fruit contours using the analySIS software.  It is possible to generate objective data to describe fruit shape using relatively simple means, in an acceptable length of time, by creating software macros within the analySIS software.  Macros provide automation of digital image acquisition and analysis saving time for the user. 
The method we developed is also the basis for more advanced investigation on how environmental parameters, growth regulators and genetic factors influence fruit shape.  This method is fundamentally suitable for describing the shape of other fruits and objects as well.

Bibliography: M. Beyer, R. Hahn, S. Peschel, M. Harz and M. Knoche: Analysing fruit shape in sweet cherry (Prunus avium L.). Scientia Horticulturae 96 (2002), 139-150.

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Authors:
Dr. Stefanie Peschel, Dr. Marco Beyer and Prof. Dr. Moritz Knoche | Institute of Agronomy and Crop Science | Martin-Luther-University, Halle-Wittenberg | Ludwig-Wucherer-Strasse 2 | D-06099 Halle (Saale), Germany