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Classification of cereal grains, namely; barley, oat, rye and wheat (Canada Western Amber Durum (CWAD) and Canada Western Red Spring (CWRS)) was performed using morphological and color features. Grain image boundary contours were extracted from the digital images of kernels, expressed as chain-coded points and then approximated by 13 elliptic Fourier coefficients. After normalization of the rotation and starting point of the contours, symmetrical standard coefficients were determined. The symmetrical Fourier index (S"F"X) of individual kernels was calculated from the product of the sum of absolute symmetrical coefficients and the circularity (roundness) index. Three geometric features, namely; aspect ratio (AR), major diameter (M"D) and roundness (C"e"q) were determined using ellipse fitting and Green's transformation of curve integrals, respectively. The morphological classification model was defined using S"F"X, AR, M"D, and C"e"q. The color classification model was defined using color indices of individual kernels, which were calculated from the RGB color values of their images. The classification accuracies of different models were evaluated and compared. The combined model defined by morphological and color features achieved a classification accuracy of 98.5% for barley, 99.97% for CWRS, 99.93% for oat, and 100% for rye and CWAD.

An algorithm to classify cereal grains, namely: barley, oats, rye and wheat (Canada Western Amber Durum (CWAD) and Canada Western Red Spring (CWRS)) based on grain kernel shapes using invariant elliptic Fourier descriptors (IEFDs) was developed. Boundary contours were extracted from the digital images of kernels, expressed as chain-coded points and then approximated by 13 Fourier harmonics. After normalisation of the size, rotation and starting point of the contours, the IEFDs were determined. Based on the first three IEFDs, perfect classification was achieved for barley, CWAD, CWRS and rye. The classification accuracies of oats were 99.7% and 100% for the first three and five IEFDs, respectively.

The variation in the shape of cereal grains, namely; barley, oat, rye and wheat (Canada Western Amber Durum and Canada Western Red Spring), were quantitatively evaluated using principal components analysis (PCA) based on elliptic Fourier descriptors. Grain image boundary contours were extracted from the digital images of kernels, expressed as chain-coded points and then approximated by 13 elliptic Fourier coefficients. After normalization of the size, rotation and starting point of the contours, four groups of coefficients namely; invariant, symmetrical, asymmetric and standardized Fourier coefficients were analyzed separately using PCA. The PCA based on the symmetric Fourier coefficients captured the shape variability of different grains with fewer principal components (PCs) than the rest. Results suggest that the major shape variations of grains can be summarized by the first two, five, eight and seventeen PCs of the symmetric, standardized, invariant and asymmetric Fourier coefficients, respectively, capturing about 99% of shape variations. The effect of growing regions on kernel shapes was also studied and results revealed that the shape variability is well captured by the PCA of the symmetric coefficients of the standardized Fourier descriptors.

A finite element model was developed to simulate compression experiments on single tomato cells from suspension cultures. The cell was modelled as a thin-walled liquid-filled sphere with a permeable wall allowing flow of fluid out in response to internal turgor increases due to the compression. The permeability of the cell wall/plasma lemma was considered to be constant throughout compression. The contact between cell and compression probe was modelled using a soft contact boundary condition. The cytoplast was represented as an internal pressure acting on the plasma lemma and cell wall. Assuming linear elastic constitutive behaviour for the cell wall, and using previously determined cell wall material parameters, the model was found to be remarkably capable of reproducing the force–deformation behaviour of a single cell in compression, as well as its deformed shape, even for large strains. The model might be used as a building block to construct more comprehensive tissue deformation models.

A novel modeling procedure for semi-symmetrical plant organs using longitudinal and transverse organ profiles was developed to simplify and improve virtual organ representation. Fruits were used as model organs. The fruits were divided into halves to capture the fruit profile. Using a regular photo camera (Nikon-Coolpix 4500), and an in-house image acquisition setup, the half fruit images were captured. In-house Matlab (The Mathworks, Natick, MA) based program was used to determine the boundaries of the digitized images. Based on the boundary points, and using Fourier series approximation, the image boundaries were defined mathematically. Fourier series approximation defines boundary shapes using the sum of sine and cosine terms. Based on the Fourier descriptors, which are coefficients of the Fourier series approximation, fruit contours were extracted. Surface construction algorithms based on smoothed contour boundaries were developed. Because of non-axis symmetricity of most fruits, and the presence of surface perturbations, for example, carpels in tomato fruits, models based on only longitudinal cross sections were not satisfactory. A complete fruit model was finally developed by combining the longitudinal cross section of half fruits and the transverse cross section of whole fruits. To our knowledge, this is the first realistic geometrical fruit model that captures the fruit shape complexities. Such a model may be useful to analyze the genetic and environmental controls of fruit morphological and biochemical properties. Our modeling approach has limitation in producing geometric models for unusual curved shape plant organs such as banana, cucumbers, cassava and Jerusalem artichoke that are not quasi-symmetrical along the longitudinal axis. (C) 2010 Elsevier B.V. All rights reserved.

An algorithm to separate touching grain kernels using an elliptic Fourier series approximation, based on boundary curvature values, is presented. The Fourier approximation smoothes the boundary contours of the images avoiding local pseudo-corners caused by the presence of rough boundaries and image acquisition inefficiencies. Once the curvature values along the boundary of the kernels are calculated, nodal points separate the touching instances. Evaluating the curvature along the boundary of the image and selecting those points at which the curvature falls below a threshold determines nodal points. With multiple nodal points, a nearest-neighbour and a radian critical (cumulative) distance difference [rad] of chain-coded boundary point criteria are used to draw the segmentation lines. The algorithm was tested for different grain types under different touching scenarios and was successful in separating more than 98% of the touching grains. The algorithm appears to be robust enough to separate most of the multiple touching scenarios with few exceptions where the kernels are broken or have rough boundaries.

A multiscale gas exchange model was developed to perform in silico experiments to evaluate the effect of external storage conditions, fruit size and maturity on the intra-cellular respiration and risks of occurrence of physiological disorders. Pear fruit was chosen as a model system. The approach consists of interconnected models that describe the transport phenomena at the macro- and the microscale. First, macroscale model simulations of the respiratory gas concentrations in the critical fruit region (region of the lowest and highest O 2 and CO 2 concentration of intact fruits) were performed. This region was considered to be more susceptible to physiological disorders caused by anoxia and high CO 2 partial pressure. Next, the microscale model was applied to compute the corresponding intra-cellular metabolic gas concentration. The in silico study revealed that O 2 concentration of optimally picked pear stored at typical controlled atmosphere condition (2.5 kPa O 2 , 0.7 kPa CO 2 at -1°C) were higher than the Michaelis-Menten constant for cytochrome c oxidase K m,c , the rate limiting enzyme of the respiration pathway. In contrast to small pears, large pears and extreme low O 2 storage conditions lead to O 2 concentrations well below the K m,c . This most probably leads to fermentation and physiological disorders that have been observed under such conditions. Ripening of the fruit increased the risk of physiological disorders since increased respiration resulted in anoxia in the fruit center even at the typical storage conditions.

The design of controlled and modified atmosphere storage systems for fruit and vegetables requires knowledge about gas and moisture transport processes in the storage facility or the package. Mathematical models based on reaction-diffusion kinetics have been used successfully for this purpose. However, they involve apparent material parameters which have to be measured again for every product and which cannot be considered as physical parameters. Further, they do not explain small scale phenomena which are at the basis of storage atmosphere related disorders. Multiscale modelling is a new modelling paradigm to describe phenomena for which different spatial scales are relevant. In this paper the multiscale modelling paradigm is introduced in postharvest technology. The concept is illustrated by means of some examples.

The traditional approach to study fruit from a macroscopic perspective is being redirected to the microscopic level as our understanding of the lower scale increases. The microstructural components (cells, cell walls and air voids) of fruits determine the fruit's mechanical and transport properties. However, this relationship is unclear to date. Microscale models offer a means to compute the mechanical material behaviour and transport properties in the true microscopic geometry of the fruit. This calls for the 3-D characterization and representation of fruit tissue components. Cells, cell walls and air voids of cortex tissue of pear (cv. 'Conference') fruit were defined based on imaging at submicron resolution by means of transmission electron microscopy (TEM) and synchrotron radiation X-ray computed microtomography. The cell wall thickness was determined from TEM images using digitization procedures. An ellipsoid tessellation algorithm was developed to cut individual cells from the microtomography images. The air voids were a result of the natural stacking of the ellipsoids in the 3-D microstructural domain. Validation of the structures was achieved by means of conventional segmentation of the original microtomographs into air voids and cells, and calculating the geometric characteristics of the, resulting networks. The resulting geometric solid model comprising the three principal components was modelled in ANSYS (ANSYS, Inc., Canonsburg, USA) working environment. The model geometry will be used in finite element or finite volume in silico simulations of gas and water transport and mechanical deformation of the microstructures. The advantages of the novel method are that individual cells are segmented and the tool provides a framework for in silico generation of fruit structures.

Fruit microstructure determines mechanical and transport properties of tissues. This calls for geometric characterization and representation of fruit tissue components. In this paper, three important components of fruit cortex tissue, cell wall, pore network and cells were modeled in 3-D. These components were explicitly defined based on the information gathered from synchrotron X-ray computed tomography and transmission electron microscopy. The cells were modeled based on a novel ellipsoid tessellation algorithm, producing also 3-D void structures in small fruit cortex sample volumes. The cell wall thickness was determined from TEM images using digitization procedures. The resulting geometry models compared well to the tomographic images. The method has the significant advantages of, one, producing models that are easy to use in computer aided design software for multiscale mechanics and mass transfer, and two, providing a framework for virtual tissue generation, including cell growth modeling. Furthermore, the solid modeling approach avoids many problems of finite element meshing existing today.

Our understanding of the gas exchange mechanisms in plant organs critically depends on insights in the three-dimensional (3-D) structural arrangement of cells and voids. Using synchrotron radiation x-ray tomography, we obtained for the first time high-contrast 3-D absorption images of in vivo fruit tissues of high moisture content at 1.4-μm resolution and 3-D phase contrast images of cell assemblies at a resolution as low as 0.7 μm, enabling visualization of individual cell morphology, cell walls, and entire void networks that were previously unknown. Intercellular spaces were always clear of water. The apple (Malus domestica) cortex contains considerably larger parenchyma cells and voids than pear (Pyrus communis) parenchyma. Voids in apple often are larger than the surrounding cells and some cells are not connected to void spaces. The main voids in apple stretch hundreds of micrometers but are disconnected. Voids in pear cortex tissue are always smaller than parenchyma cells, but each cell is surrounded by a tight and continuous network of voids, except near brachyssclereid groups. Vascular and dermal tissues were also measured. The visualized network architecture was consistent over different picking dates and shelf life. The differences in void fraction (5.1% for pear cortex and 23.0% for apple cortex) and in gas network architecture helps explain the ability of tissues to facilitate or impede gas exchange. Structural changes and anisotropy of tissues may eventually lead to physiological disorders. A combined tomography and internal gas analysis during growth are needed to make progress on the understanding of void formation in fruit.

The relationships between fruit structure and the material properties affecting fruit quality are not well understood to date. One reason is that the effect of fruit structure is difficult to investigate due to the presence of important structural features at all spatial scales. Multiscale modelling offers a framework in which the relevant transport processes are studied at microscopic scale and the resulting information is transferred to the global scale by homogenization procedures. In this respect, modelling the geometry at the smaller and larger scales is an essential aspect of study. This paper presents the advances that have been made on geometrical modelling of fruit at different scales.

The microstructure and the connectivity of the pore space are important variables for better understanding of the complex gas transport phenomena that occur in plant tissues. In this study, we present an experimental procedure for image acquisition and image processing to quantitatively characterize in 3D the pore space of apple tissues (Malus domestica Borkh.) for two cultivars (Jonagold and Braeburn) taken from the fleshy part of the cortex using X-ray computer microtomography. Preliminary sensitivity analyses were performed to determine the effect of the resolution and the volume size (REV, representative elementary volume analysis) on the computed porosity of apple samples. For comparison among cultivars, geometrical properties such as porosity, specific surface area, number of disconnected pore volumes and their distribution parameters were extracted and analyzed in triplicate based on the 3D skeletonization of the pore space (medial axis analysis). The results showed that microtomography provides a resolution at the micrometer level to quantitatively analyze and characterize the 3D topology of the pore space in apple tissue. The computed porosity was confirmed to be highly dependent of the resolution used, and the minimum REV of the cortical flesh of apple fruit was estimated to be 1.3 mm(3). Comparisons among the two cultivars using a resolution of 8.5 mum with a minimum REV cube showed that in spite of the complexity and variability of the pore space network observed in Jonagold and Braeburn apples, the extracted parameters from the medial axis were significantly different (P-value0.05). Medial axis parameters showed potential to differentiate the microstructure between the two evaluated apple cultivars.

Microstructural properties are the core in defining and modelling macroscopic properties of fruits. In this regard, realistic microstructures that could be validated against microscopic images of fruit tissues were generated. Microscopic images of tissues of different apple cultivars (Greenstar, Kanzi, Pinova and Cameo) were digitized using an image analysis software program. The geometrical cell structure was described by means of statistical distributions of the cell area, cell aspect ratio and cell orientation. The cell orientation and cell aspect ratio were calculated based on the moments of inertia (area moments) and least-square ellipse fitting, respectively. The statistical geometrical properties of different cultivars were compared. These quantitative descriptors were then used in conjunction with a Poisson Voronoi tessellation algorithm to produce virtual cell tissue with the same statistical properties as the real tissue. The geometrical models will be used in a multiscale modelling approach to investigate water and gas transport in fruits.

Apple and pear are stored under controlled atmosphere conditions. Too low internal oxygen (O2) or too high carbon dioxide (CO2) concentrations may lead to storage disorders such as browning. The internal gas concentration is mainly determined by the fruit’s gas exchange properties, which depend on the structural arrangement of fruit cells and tissues. We used (for the first time) submicron synchrotron X-ray computed tomography (CT) to investigate how pome fruit tissues are spatially organized to facilitate or impede gas exchange. The experiments were conducted on beamline ID19 at the European Synchrotron Radiation Facility (ESRF, Grenoble, France), i.e., on a long (150 m) imaging beamline where the spatial coherence of the beam is particularly large (transverse coherence length in the order of 100 μm). The method allows for imaging in phase contrast, which, as opposed to absorption contrast, is a powerful method to distinguish, in absorbing materials, phases with very similar X-ray attenuation but different electron densities. In this study, it is efficiently used for edge detection at cell-cell interfaces where absorption images have insufficient contrast. We visualized 3-D networks of gas-filled intercellular spaces in two fruits, apple (cv. Jonagold) and pear (cv. Conference), that provide the main routes for exchange of O2 and CO2 with the environment, using absorption as well as phase contrast synchrotron X-ray CT at a pixel resolution ranging from 0.7 to 5.0 μm. The differences in void dimensions and connectivity between tissues and fruits helped explain imbalances in gas exchange that may result in internal disorders and structural degradation. We also showed that tomography with synchrotron radiation operated in phase-contrast mode and is able to visualize the 3-D geometry of voids, cells, and cell walls of biological tissues with high water content at submicron voxel resolution. In terms of facilitating gas exchange, the network pattern of the voids indicated a large size and volume fraction difference with the unconnected void structure found in apple. The partial breakdown of such networks would quickly lead to an internal gas imbalance leading to internal disorders. The achievement of high-resolution 3-D microstructural properties of cells and tissues is an important breakthrough for the study of gas exchange mechanisms in fruits stored under controlled atmosphere conditions. In addition to gas exchange, the results will benefit the study of water relations and mechanics of foods.

* Gas-filled intercellular spaces are considered the predominant pathways for gas transport through bulky plant organs such as fruit. Here, we introduce a methodology that combines a geometrical model of the tissue microstructure with mathematical equations to describe gas exchange mechanisms involved in fruit respiration. * Pear (Pyrus communis) was chosen as a model system. The two-dimensional microstructure of cortex tissue was modelled based on light microscopy images. The transport of O(2) and CO(2) in the intercellular space, cell wall network and cytoplasm was modelled using diffusion laws, irreversible thermodynamics and enzyme kinetics. * In silico analysis showed that O(2) transport mainly occurred through intercellular spaces and less through the intracellular liquid, while CO(2) was transported at equal rates in both phases. Simulations indicated that biological variation of the apparent diffusivity appears to be caused by the random distribution of cells and intercellular spaces in tissue. Temperature does not affect modelled gas exchange properties; it rather acts on the respiration metabolism. * This modelling approach provides, for the first time, detailed information about gas exchange mechanisms at the microscopic scale in bulky plant organs, such as fruit, and can be used to study conditions of anoxia.

Pome fruit such as pear and apple are often stored under controlled atmosphere conditions with reduced oxygen and increased carbon dioxide levels to extend their commercial storage life. When the gas conditions are too severe, fermentation may occur in some fruit, eventually leading to physiological disorders such as brown discoloration in pear circumference. Knowledge of gas exchange mechanisms would be very valuable to guide commercial storage practices for stored fruits such as apple and pear, since disorders related to fermentation are a prime cause of concern. In the past, mathematical models have been by us to predict the internal gas concentrations including permeation, diffusion and respiration and fermentation kinetics. However, these models are essentially based on the continuum hypothesis which is not likely to hold for cellular tissue such as that of fruit.

Gas filled intercellular spaces are considered the predominant pathways for gas transport through plant organs and, as such, are greatly related to the characteristics of gas exchange. To understand the transport mechanisms of gas diffusion of fruit tissue, a microscale model for the transport of O2 in the intercellular spaces, the cell wall network and the intracellular liquid phase was introduced. The objective of this study was (1) to verify the applicability of the microscale model of the gas transport at tissue level and (2) to quantify the pathways of gas transport in relation to the microstructure of fruit tissue. The 2D microstructure of pear tissue was modelled from light microscopy images using the ellipse tessellation method. Gas transport properties of the gas and liquid phases and the cell membrane were determined from available literature data. The O2 transfer in each of intercellular space, cell wall and cytoplasm was applied using diffusion laws and irreversible thermodynamics. The model was solved using the finite element method. The results showed that the microscale model can be applied to study the gas transport in fruit tissue. The model quantified the pathways of gas transport in fruit tissue. The O2 transport was mainly by means of the intercellular space, the cell wall network and less through the intracellular liquid. The results have important consequences for respiration–related disorders of fruits. ispartof: 13th World Congress of Food Sciences & Technology location:Nantes, France date:17 Sep - 21 Sep 2006 status: published

Modeling plant microstructure is of great interest to food engineers to simulate the behavior of the physical properties (e.g., concerning mass transfer, mechanics) of plant tissues at the cellular level. The generation of geometrical models of microscopic structures is considered a prime requirement to develop microscale models to study and describe these properties. For this end, this paper presents a novel ellipse tessellation algorithm to generate a 2D geometrical model of apple tissue. Ellipses are used to quantify the orientation and aspect ratio of cells on a microscopic image. The cell areas and centroids of each cell are also determined by means of a numerical procedure. These characteristic quantities are then described by means of probability density functions. The model tissue geometry is generated from the ellipses which are truncated when neighboring areas overlap. As a result, a virtual microstructure consisting of truncated ellipses fills up the entire space with the same number of cells as that of microscopic images and with similar area, orientation and aspect ratio distribution. The spatial variability of the geometric characteristics (cell area size, cell shape, cell orientation and tissue porosity) of the virtual cellular structure was also evaluated and compared to that of the microscopic images. Statistical analysis showed that the virtual geometry generated with this approach yields spatially equivalent geometries to that of real fruit microstructures. Compared to the more common algorithm of Voronoi diagrams, ellipse tesselation is superior for generating the microstructure of tissue. The extension of the algorithm to 3D is straightforward. These representative tissues will be exported into a finite element environment via interfacing codes to perform in silico experiments for estimating gas and moisture diffusivities and investigating their relation with fruit microstructure.