Abstract
A geometrical model generator for biological products is presented, which uses X-ray computed tomography images of quasi-axisymmetric biological products as input. It was tested with a dataset of 73 scanned Braeburn apples. For each sample, the generator constructed different cross sections. From these sections, contours were extracted and selected. The contours were expressed as a series of shape descriptors. For this purpose, elliptical Fourier descriptors were used. The obtained frequency distributions were transformed to standard normal distributions. On these transformed distributions, the covariance decomposition algorithm was applied. This algorithm generated new sets of descriptors, which opened up a large range of possibilities for generation of representative shape contours. After reverse transformation of the (generated) descriptor distributions, new contours were obtained from the new descriptors. These new contours were converted to 3D geometrical models of biological products by interpolation and revolving. By comparing the volumes of the generated models with those of the scanned fruit, it was shown that the resulting geometrical models have the same variability as the biological variability in the original dataset. This generator is a fast method, which requires minimal user intervention, and creates 3D models including the biological variability as observed in the scanned fruit. Because these 3D geometrical models are directly available as CAD models, they are useful for numerical modelling of transport phenomena in and around biological products.
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Abera, M. K., Fanta, S. W., Verboven, P., Ho, Q. T., Carmeliet, J., & Nicolai, B. M. (2012). Virtual fruit tissue generation based on cell growth modelling. Food and Bioprocess Technology. doi:10.1007/s11947-011-0775-4.
Ambaw, A., Verboven, P., Delele, M. A., Defraeye, T., Tijskens, E., Schenk, A., et al. (2012). CFD modelling of the 3D spatial and temporal distribution of 1-methylcyclopropene in a fruit storage container. Food and Bioprocess Technology. doi:10.1007/s11947-012-0913-7.
Costa, C., Antonucci, F., Pallottino, F., Aguzzi, J., Sun, D. W., & Menesatti, P. (2011). Shape analysis of agricultural products: a review of recent research advances and potential application to computer vision. Food and Bioprocess Technology, 4(5), 673–692.
Dehghannya, J., Ngadi, M., & Vigneault, C. (2010). Mathematical modelling procedures for airflow, heat and mass transfer during forced convection cooling of produce: a review. Food Engineering Reviews, 2(4), 227–243.
Delele, M. A., Tijskens, E., Atalay, Y. T., Ho, Q. T., Ramon, H., Nicolai, B. M., et al. (2008). Combined discrete element and CFD modelling of airflow through random stacking of horticultural products in vented boxes. Journal of Food Engineering, 89(1), 33–41.
Delele, M. A., Schenk, A., Tijskens, E., Ramon, H., Nicolai, B. M., & Verboven, P. (2009). Optimization of the humidification of cold stores by pressurised water atomizers based on a multiscale CFD model. Journal of Food Engineering, 91(2), 228–239.
Fernández, L., Castillero, C., & Aguilera, J. M. (2005). An application of image analysis to dehydration of apple discs. Journal of Food Engineering, 67(1), 185–193.
Goñi, S. M., Purlis, E., & Salvadori, V. O. (2007). Three-dimensional reconstruction of irregular foodstuffs. Journal of Food Engineering, 82(4), 536–547.
Goñi, S. M., Purlis, E., & Salvadori, V. O. (2008). Geometry modelling of food materials from magnetic resonance imaging. Journal of Food Engineering, 88(4), 561–567.
Goñi, S. M., & Purlis, E. (2010). Geometric modelling of heterogeneous and complex foods. Journal of Food Engineering, 97(4), 547–554.
Herremans, E., Verboven, P., Bongaers, E., Estrade, P., Verlinden, B. E., Wevers, M., et al. (2013). Characterisation of ‘Braeburn’ browning disorder by means of X-ray micro-CT. Postharvest Biology and Technology, 75, 114–124.
Hertog, M. L., Scheerlinck, N., & Nicolai, B. M. (2009). Monte Carlo evaluation of biological variation: random generation of correlated non-Gaussian model parameters. Journal of Computational and Applied Mathematics, 223(1), 1–14.
Ho, Q. T., Verboven, P., Verlinden, B. E., Herremans, E., Wevers, M., Carmeliet, J., et al. (2011). A three-dimensional multiscale model for gas exchange in fruit. Plant Physiology, 155(3), 1158–1168.
Ho, Q. T., Verboven, P., Yin, X., Struik, P. C., & Nicolai, B. M. (2012). A microscale model for combined CO2 diffusion and photosynthesis in leaves. PloS One, 7(11), e48376.
Ho, Q. T., Carmeliet, J., Datta, A. K., Defraeye, T., Delele, M. A., Herremans, E., et al. (2013). Multi-scale modelling in food engineering. Journal of Food Engineering, 114(3), 279–291.
Imou, K., Kaizu, Y., Morita, M., & Yokoyama, S. (2006). Three-dimensional shape measurement of strawberries by volume intersection method. Transactions of the ASAE, 49(2), 449–456.
Iwata, H., Ebana, K., Uga, Y., Hayashi, T., & Jannink, J. L. (2010). Genome-wide association study of grain shape variation among Oryza sativa L. germplasms based on elliptic Fourier analysis. Molecular Breeding, 25(2), 203–215.
Jancsók, P.T., Nicolai, B.M., Coucke, P. & Baerdemaeker, J.D. (1997). 3D finite element model generation of fruits based on image processing. Mathematical and control applications in agriculture and horticulture, 131–135.
Jancsók, P. T., Clijmans, L., Nicolai, B. M., & De Baerdemaeker, J. D. (2001). Investigation of the effect of shape on the acoustic response of ‘conference’ pears by finite element modelling. Postharvest Biology and Technology, 23(1), 1–12.
Kawabata, S., Yokoo, M., & Nii, K. (2009). Quantitative analysis of corolla shapes and petal contours in single-flower cultivars of lisianthus. Scientia Horticulturae, 121(2), 206–212.
Kaya, A., Aydın, O., & Dincer, I. (2006). Numerical modelling of heat and mass transfer during forced convection drying of rectangular moist objects. International Journal of Heat and Mass Transfer, 49(17), 3094–3103.
Kuhl, F. P., & Giardina, C. R. (1982). Elliptic Fourier features of a closed contour. Computer Graphics and Image Processing, 18(3), 236–258.
Lammertyn, J., Dresselaers, T., Van Hecke, P., Jancsók, P., Wevers, M., & Nicolaı, B. M. (2003). Analysis of the time course of core breakdown in ‘conference’ pears by means of MRI and X-ray CT. Postharvest Biology and Technology, 29(1), 19–28.
Lestrel, P. E. (1989). Method for analysing complex two-dimensional forms: elliptical Fourier functions. American Journal of Human Biology, 1, 149–164.
Lilliefors, H. W. (1967). On the Kolmogorov–Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62(318), 399–402.
Liming, X., & Yanchao, Z. (2010). Automated strawberry grading system based on image processing. Computers and Electronics in Agriculture, 71, S32–S39.
Lu, L., Xu, H., Song, W., & Liu, G. (2007). Research on visualisation of fruits based on deformation. New Zealand Journal of Agricultural Research, 50(5), 593–600.
Lu, L., Song, W.L. & Wang, L. (2009). A simulation method for the fruitage body. In: Society of Photo-Optical Instrumentation Engineers Conference Series, PIAGENG 2009, China.
Massey, F. J. (1951). The Kolmogorov–Smirnov test for goodness of fit. Journal of the American Statistical Association, 46(253), 68–78.
Mebatsion, H. K., Boudon, F., Godin, C., Pradal, C., Génard, M., Goz-Bac, C., et al. (2011). A novel profile based model for virtual representation of quasi-symmetric plant organs. Computers and Electronics in Agriculture, 75(1), 113–124.
Moreda, G. P., Muñoz, M. A., Ruiz-Altisent, M., & Perdigones, A. (2012). Shape determination of horticultural produce using two-dimensional computer vision: a review. Journal of Food Engineering, 108(2), 245–261.
Moustakides, G., Briassoulis, D., Psarakis, E., & Dimas, E. (2000). 3D image acquisition and NURBS based geometry modelling of natural objects. Advances in Engineering Software, 31(12), 955–969.
Nguyen, T. A., Dresselaers, T., Verboven, P., D’hallewin, G., Culeddu, N., Van Hecke, P., et al. (2006). Finite element modelling and MRI validation of 3D transient water profiles in pears during postharvest storage. Journal of the Science of Food and Agriculture, 86(5), 745–756.
Nicolai, B. M., Verlinden, B., Beuselinck, A., Jancsok, P., Quenon, V., Scheerlinck, N., et al. (1999). Propagation of stochastic temperature fluctuations in refrigerated fruits: propagation des fluctuations de température stochastiques dans des fruits réfrigérés. International Journal of Refrigeration, 22(2), 81–90.
Peralta, J. M., Rubiolo, A. C., & Zorrilla, S. E. (2010). Mathematical modelling of the heat transfer and flow field of liquid refrigerants in a hydrofluidization system with a stationary sphere. Journal of Food Engineering, 99(3), 303–313.
Pradal, C., Boudon, F., Nouguier, C., Chopard, J., & Godin, C. (2009). PlantGL: a python-based geometric library for 3D plant modelling at different scales. Graphical Models, 71(1), 1–21.
Prusinkiewicz, P., & Runions, A. (2012). Computational models of plant development and form. New Phytologist, 193(3), 549–569.
Rashidi, M., & Gholami, M. (2008). Determination of kiwifruit volume using ellipsoid approximation and image-processing methods. International Journal of Agriculture and Biology, 10, 375–380.
Rubinstein, R. Y. (1981). Simulation and the Monte Carlo method. New York: John Wiley and Sons.
Saad, M., Sadoudi, A., Rondet, E., & Cuq, B. (2011). Morphological characterisation of wheat powders, how to characterise the shape of particles? Journal of Food Engineering, 102(4), 293–301.
Severa, L., Máchal, L., Švábová, L., & Mamica, O. (2010). Evaluation of shape variability of stallion sperm heads by means of image analysis and Fourier descriptors. Animal Reproduction Science, 119(1), 50–55.
Tanabata, T., Shibaya, T., Hori, K., Ebana, K., & Yano, M. (2012). SmartGrain: high-throughput phenotyping software for measuring seed shape through image analysis. Plant Physiology, 160(4), 1871–1880.
Veraverbeke, E. A., Verboven, P., Van Oostveldt, P., & Nicolai, B. M. (2003a). Prediction of moisture loss across the cuticle of apple (Malus sylvestris subsp. mitis (Wallr.)) during storage: Part 1. Model development and determination of diffusion coefficients. Postharvest Biology and Technology, 30(1), 75–88.
Veraverbeke, E. A., Verboven, P., Van Oostveldt, P., & Nicolai, B. M. (2003b). Prediction of moisture loss across the cuticle of apple (Malus sylvestris subsp. mitis (Wallr.)) during storage: part 2. Model simulations and practical applications. Postharvest Biology and Technology, 30(1), 89–97.
Verboven, P., Nicolai, B. M., Scheerlinck, N., & De Baerdemaeker, J. (1997). The local surface heat transfer coefficient in thermal food process calculations: a CFD approach. Journal of Food Engineering, 33(1), 15–35.
Verboven, P., Flick, D., Nicolai, B. M., & Alvarez, G. (2006). Modelling transport phenomena in refrigerated food bulks, packages and stacks: basics and advances. International Journal of Refrigeration, 29(6), 985–997.
Zhang, D., & Lu, G. (2004). Review of shape representation and description techniques. Pattern Recognition, 37(1), 1–19.
Zhang, D., & Lu, G. (2005). Study and evaluation of different Fourier methods for image retrieval. Image and Vision Computing, 23(1), 33–49.
Acknowledgements
Financial support of FWO Vlaanderen (project G.0645.13) and the University of Leuven (project OT 12/055) is gratefully acknowledged. Thijs Defraeye is postdoctoral fellow of FWO and acknowledges its support.
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Rogge, S., Beyene, S.D., Herremans, E. et al. A Geometrical Model Generator for Quasi-Axisymmetric Biological Products. Food Bioprocess Technol 7, 1783–1792 (2014). https://doi.org/10.1007/s11947-013-1169-6
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DOI: https://doi.org/10.1007/s11947-013-1169-6