Field of the Invention

The present invention is related to a method for identifying an internal parameter of an egg.

Background

In the egg production industry it is often required to test the freshness of eggs, in particular eggs intended for human consumption (i.e. unfertilized eggs, that do not contain embryos), either directly or via processing into another food product. One parameter which may be measured is the height of the air cell contained in the egg between inner and outer internal membranes. The volume of the air cell increases with time after laying and this can be used to determine the freshness or quality of an egg-

Existing methods of identifying internal quality parameters of an egg, for example candling or measuring the height of the air cell with calipers, have disadvantages such as operator dependency, lack of efficiency or requiring contact with and/or destruction of the egg.

There is thus a need for an efficient, accurate, contactless and non-destructive method for determining an internal quality parameter of one or more eggs.

JP5967766 describes an egg inspection apparatus comprising a support for supporting an egg; a temperature measurement unit for contactlessly measuring the temperature in a predetermined region of the egg supported by the support while moving relative to said egg, said temperature measurement unit comprising at least one temperature sensor for outputting temperature data relating to the temperature; and an inspection unit for inspecting the state of the egg in accordance with a change occurring, as a result of the abovementioned relative movement, in the temperature data output from the temperature measurement unit.

In JP5967766, a single temperature data point per location on an egg is used in the analysis. However, when attempting to identify an air cell within an egg, a single thermal image may not provide the required level of contrast between egg shell adjacent to the air cell and egg shell adjacent to the albumen to allow reliable separation and determination of the size of the air cell.

WO2017/137837 discloses an apparatus to identify upside-down eggs of a batch of eggs based on the presence of a heated zone in an air cell of each egg, for use in the poultry industry and especially in hatcheries.

US2008/0149033 concerns a method and apparatus for candling incubated eggs, wherein eggs are designated as live, inverted, or having a side air cell. Summary

According to a first aspect of the present invention, there is provided an active thermography method for identifying at least one internal or subsurface parameter of at least one egg, the method comprising: thermally exciting at least a surface of the at least one egg with a means for excitation such that the egg is provided in a non-equilibrium thermal condition for a non-equilibrium period having duration transient _/ obtaining a thermogram at a plurality of time intervals (N) of the at least one egg in during the non-equilibrium period, resulting in N thermograms; determining at least one parameter in dependence upon the N thermograms; identifying the at least one internal or subsurface quality parameter of the at least one egg based on the at least one parameter.

In a further embodiment, the obtaining the thermogram at a plurality of time intervals of the at least one egg can result in a temperature data cube comprising the N thermograms.

Determining at least one parameter in dependence upon the N thermograms may comprise transforming a temperature-time signal of each spatial pixel of the datacube into a corresponding phase-frequency signal, resulting in a phase data cube comprising N phase images and identifying the at least one internal or subsurface quality parameter of the at least one egg based on the at least one parameter may comprise identifying the at least one internal or subsurface quality parameter of the at least one egg based on at least one of the phase images.

The method may further comprise a segmentation step, said segmentation step comprising segmenting at least one phase image based on at least one thermogram.

The segmentation step may comprise: extracting a mask of the at least one egg, said mask extraction comprising using at least a first thermogram and a second thermogram, wherein the first thermogram is taken immediately before thermal excitation and the second thermogram is taken immediately after thermal excitation; and applying said egg mask to a selected phase image.

The method may further comprise determining a time region of interest in the phase data cube and selecting the selected phase image as a phase image within the time region of interest. The means for excitation may be hot air.

The means for excitation may be at least one source configured to thermally heat or cool the at least one egg.

The means for excitation may be an optical source, a mechanical source, or an inductive excitation means.

The method may further comprise a transforming step, said transforming step configured to transform the at least one thermogram in phase and/or amplitude data.

A plurality of thermograms may be obtained at a time interval during a period t.

The plurality of thermograms may be provided in a 3D data cube. The plurality of thermograms may be obtained at regular or irregular time intervals.

The plurality of thermograms may be obtained at a combination of regular and irregular time intervals.

The means for excitation may be configured to provide an excitation pulse for a period (tpulse).

The means for excitation may be configured to provide a periodic signal. The t _pU|Se may be maximal 5 second and preferably 3 seconds and more preferably less than 2 seconds.

An air cell size of the at least one egg may be extracted as internal quality parameter t _puise may be 1 second.

The first of the plurality of thermograms may be obtained 3 seconds after thermal excitation is ended.

The plurality of thermograms may be obtained at a sampling frequency of 60 Hz or higher.

According to a second aspect of the present invention there is provided use of active thermography to detect or monitor internal or subsurface quality parameter of at least one egg.

The active thermography may be pulsed active thermography. Also, the active thermography can be lock-in thermography using a periodical signal.

The internal or subsurface quality parameter of the at least one egg may be an air chamber. According to a third aspect of the present invention there is provided an active thermography assembly for identifying at least one internal or subsurface quality parameter of at least one egg, said assembly comprising:

- at least one means for thermally exciting at least an internal surface or subsurface of the at least one egg;

- at least one means for generating at least one thermogram of the at least one egg in the non equilibrium thermal condition;

- a processing means configured to identify the at least one internal or subsurface quality parameter of the at least one egg based on the at least one thermogram.

The assembly may further comprise at least one optical filter configured to cancel out at least a part of the reflected radiation coming from the at least one egg.

In the present invention, as will be clear to the skilled person, the at least one egg is in particular an unfertilized egg, in particular a dead egg, free from any embryos. For example, the egg can be a poultry egg. The at least one egg is preferably produced for direct or indirect human consumption. The at least one egg is preferably an uncooked egg, i.e. a raw egg. An egg shell of the egg is preferably substantially intact.

Brief Description of the Drawings

Certain embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

Figure 1 is a schematic cross-section of an egg;

Figure 2 is a schematic plan view of an apparatus for performing active thermography;

Figure 3 is a flow chart of a method of identifying the size of an air cell in an egg;

Figure 4 is a schematic representation of a data cube;

Figure 5 is an example phase image of an egg;

Figures 6a - 6d illustrate stages in the segmentation of a thermogram;

Figures 7a - 7d illustrate stages in the segmentation of a phase image;

Figure 8 is an example phase profile for an air cell pixel and an egg pixel; Figure 9 is a flow chart of a method of determining optimal parameters for determining an air cell size;

Figure 10 illustrates boxplots of F values for each of 10 Fourier frequencies for a pulse duration of 1 second and a cool down time of 7 seconds;

Figure 11 illustrates boxplots of F values for pulse duration Is, for six cool down time values, each cool down time value being associated with a Fourier frequency;

Figure 12 illustrates boxplots of F values for five pulse duration values, each pulse duration value being associated with a Fourier frequency and a cool down time value;

Figure 13 illustrates a sphere and a spherical cap thereof;

Figure 14 shows an egg and a circle which fits the contour of the egg.

Detailed Description of Certain Embodiments

Referring to Figure 1, a schematic cross-section of an egg 1 is shown. The egg 1 may be, for example, a chicken egg or a duck egg.

The egg 1 includes a yolk 2 which is surrounded by an albumen 3. The albumen 3 is enclosed by an inner shell membrane 4. The egg includes an external shell layer 5 (or "shell layer") and an outer shell membrane 6 between the external shell layer 5 and the inner shell membrane 4.

The egg 1 includes an air cell 7 between the inner shell membrane 4 and the outer shell membrane 6. The air cell 7 is formed when the egg 1 cools down after being laid, as a result of contraction of the egg contents. This causes air from outside the egg to be drawn inside the egg, forming the air cell 7.

The components of the egg 1 change in structure and composition following the laying of the egg. The air cell 7 tends to increase in size due to moisture loss, and loss of carbon dioxide through pores of the egg shell 5. The carbon dioxide can be replaced by air drawn into the egg 1 from outside the egg, which may cause the volume (or size) of the air cell 7 to increase.

Thermal properties of the air cell 7, for example thermal conductivity, may be different to thermal properties of the albumen 3. If the egg 1 is heated, the heating rate of the air cell 7 may be different to that of the albumen 3. By monitoring the surface temperature of the egg 1 during and/or after heating or cooling of the egg, for example by taking one or more thermal image(s) using a thermal camera, a thermal contrast may be observed between the air cell 7 and the albumen. In this way, the size of the air cell 7 may be determined. Referring to Figure 2, a schematic plan view of a pulsed thermography apparatus 8 for investigating an egg 1 is shown. The apparatus includes first and second excitation means in the form of first and second halogen lamps 9, 10 respectively. The first and second halogen lamps 9, 10 may be, for example, Hedler H25 available from Hedler Systemlicht GmbH, Germany. The first and second lamps 9, 10 are positioned so as to illuminate the egg 1 with excitation radiation 11 from first and second directions 12, 13 respectively. The first and second lamps 9, 10 may include reflectors (not shown) and frosted glass diffusers (not shown) which can help to provide uniform illumination of the egg 1.

The apparatus 8 includes detection means in the form of an infrared camera 14 arranged to receive radiation 15 which may be reflected, transmitted, and/or radiated by the egg 1. The detection means is capable of detecting and optionally recording thermal images, or thermograms. One suitable detection means is the FUR SC7600 available from FUR Systems Inc., USA. The apparatus 8 includes a filter 16 arranged between the egg 1 and the infrared camera 14. The filter 16 is configured to block direct reflections of excitation radiation 11 from first and second lamps 9, 10. The filter 16 may be, for example, a high pass optical filter. One suitable filter is available from Spectrogon US Inc., having a cut-off frequency of 4080 nm. However, the choice of suitable filter depends on the heat sources and camera specifications. Any suitable filter is contemplated herein. As follows from the drawings, preferably, the camera 14 and the egg 1 maintain the same mutual orientation during the obtaining of a respective N thermograms of that egg 1. In particular, the camera is not substantially moved (remains stationary) during the obtaining of the respective N thermograms of that egg 1; similarly, the egg is not substantially moved (remains stationary) during the obtaining of the respective N thermograms of that egg 1.

The apparatus 8 includes a control module 17. The first and second lamps 9, 10 and the infrared camera 14 are coupled to the control module 17. The control module 17 is configured to provide activation signals to first and second excitation means 9, 10 and to receive data from detection means 14. The control module 17 may also be configured to provide activation signals to detection means 14, for example, if it is preferred that the detection means 14 is only active (for example, detecting a thermal image) at specified times. The control module 17 is further configured to process data received from detection means 14 as will be described in further detail in the following. The control module 17 may include, for example, an optical excitation module 18 (OTvis 4000, edevis GmbH, Germany) configured to synchronise and control the first and second lamps 9, 10 and infrared camera 14. The control module 17 may include memory 19 configured to store data received from infrared camera 14 and processor 20 configured to process data received from infrared camera 14. The memory 19 may also store processed data received from processor 20. During a pulsed thermography experiment, the control module 17 provides an activation pulses to the first and second halogen lamps 9, 10, causing the lamps to emit an excitation pulse in the form of radiation 11 which has the same duration as the activation pulse. The activation pulse has an activation pulse duration (or on-time) of t _pU|Se . The activation pulse duration may be, for example, in the range of 0.5 seconds to 5 seconds. However, the activation pulse duration may be longer, for example up to 10 seconds, up to 20 seconds, up to 30 seconds, or longer than 30 seconds.

Energy provided by an excitation pulse 11 from first and second lamps 9, 10 is absorbed at the surface (or shell 5) of the egg 1, and subsequently propagates by conduction under the surface, or shell 5, of the egg 1. The presence of an air cell 7 reduces the thermal diffusion rate, so that surface or shell temperature above the air cell 7 reaches a higher temperature than the surrounding surface or shell and remains at a higher temperature during a cooling phase which follows the heating phase initiated by the radiation pulse 11. This non-equilibrum thermal condition persists for a time t _transient .

By acquiring a series of thermal images using detection means 14, time evolution of surface temperature of the egg 1 may be monitored after thermal excitation by radiation pulse 11.

Referring to Figure 3, a method of identifying size of an air cell 7 in an egg 1 will be described.

An activation pulse is applied to first and second halogen lamps 9, 10. The activation pulse causes the first and second halogen lamps 9, 10 to each emit an excitation pulse of radiation of the same duration as the activation pulse. The excitation pulses are incident on the egg 1 and cause an internal surface of the egg 1 to be thermally excited (step S301). A plurality of thermograms are obtained by the infrared camera 14 at times f, spaced apart by At (step S302), in particular without moving the egg 1 and camera 14 with respect to each other. A total number N of thermograms is obtained during the non-equilibrium period t _transient . Preferably, the N thermograms are obtained from the same side of the egg 1, in particular a side that faces respective detecting means 14.

The N thermograms are transformed into N phase images (step S303).

The transformation step S303 proceeds as follows. Referring to Figure 4, the N thermograms form a data cube having dimensions x ^c y ^c N, where x is the number of pixels along a first spatial dimension of a thermogram (for example, the horizontal dimension of the thermogram) and y is the number of pixels along a second, perpendicular spatial dimension of the thermogram (for example, the vertical dimension of the thermogram). A pixel at x, y, in the /rth thermogram may be uniquely specified by the coordinates (x,> y _s -, k).

A pixel / located at position x,> y, has a temperature value for each of the N thermograms, that is, a temperature value at each of the N times f, at which a thermogram is obtained by detecting means 14. Thus each position x„ y ) is associated with a sequence, or one-dimensional array, of N temperature values T .

A discrete Fourier transform is applied individually to each array T of temperature values, producing an array Z of complex numbers associated with each position x,> y,. The nth element of an array Zy is given by

where T _u (k) is the temperature value at x,> y, in the /rth thermogram in the sequence of N thermograms and n is the frequency increment ( n = 0, 1, 2, ... , N/2 due to symmetry of the Fourier transform).

For each element z of each Fourier-transformed array Zy, a phase value f is calculated by taking the inverse tangent of the imaginary part of the array element (lm(z)) divided by the real part of the array element (Re(z)), that is, f = arctan(lm(z) / Re(z)). Thus each position x,> y, is associated with a one-dimensional array of N phase values f„.

In this way, every position (x,> y _s -, k) in a phase data cube having dimensions x x y x W is associated with a phase value f _¾ *. The phase data cube comprises N phase images, each having dimensions x ^c y-

An amplitude data cube formed of amplitude images may additionally or alternatively be created by taking the amplitude A of the elements of each Fourier-transformed array Z _u according to A = V((\ _m (z) ² + (Re(z) ² J.

Referring to Figure 5, an example phase image of an egg 1 is shown. The phase image is at a Fourier frequency of 0.25Flz with a Is pulse duration and a cooling down phase of 3s duration. The egg 1 is supported by an egg holder 20 and is placed against a background 21 of a wooden plate. The air cell 7 can be seen as an area of high phase contrast in comparison with the rest of the egg 1 and the background 21.

The size of the air cell 7 may be determined by, for example, counting the number of pixels in the high-contrast air cell region. Other methods of determining the size of the air cell 7 are possible. For example, a contour fitting method may be performed.

A segmentation step may also be performed in order to segment the egg from the background. The segmentation step uses a first, 'cold' thermogram, taken before thermal excitation of the egg by an excitation pulse, and a second thermogram taken immediately after thermal excitation of the egg, that is, immediately after the excitation pulse finishes. The second thermogram may also be referred to as an early recorded thermogram, or ERT.

Referring to Figure 6a, a cold thermogram is shown. Referring to Figure 6b, an early recorded thermogram is shown. The temperature in Celcius is indicated by temperature scale to the right of each image. On average, the egg surface was heated by 2 to 3 degrees Celcius after a heating pulse of duration 5 seconds.

Referring to Figure 6c, the cold thermogram is subtracted from the early recorded thermogram to obtain a corrected thermal image. The position of the air cell 7 is visible in this corrected thermal image. The egg holder 20 can also be seen. Flowever, the contrast between the air cell and the egg, and between the air cell and the background, is low. Therefore, phase images are used to enhance the contrast between the air cell and the egg.

In order to segment the egg from the background in a phase image, an egg mask is obtained using the corrected thermal image (Figure 6c). Otsu's segmentation method is applied to the corrected thermal image (Figure 6c) and the result is shown in Figure 6d. Flowever, any image segmentation method is contemplated. The image is separated into three regions, namely the background 21, the egg 1, and the egg holder 20. From this image, a mask of the egg is extracted using a blob extraction method. The second largest blob of connected pixels is assigned to the egg and is used as the mask of the egg.

It may not always be the case that the background is the largest region while the egg holder is the smallest region, and the middle region is thus assigned to the egg. In such situations, an ellipse detection method can also be used. In order to remove the shadows from the egg's mask, for the pixels segmented into the second largest region, the largest blob of interconnected pixels will be assigned as the egg. Image closing techniques may additionally be used to correct for noise.

A further segmentation step may be performed to separate the air cell. Due to the low contrast between the egg and the air cell in the corrected temperature image (Figure 6c), phase images are preferably used to extract a mask of the air cell.

Referring to Figure 7a, an unprocessed phase image is shown. The egg holder 20 can be seen at the base of the egg 1. The egg mask is applied to the unprocessed image of Figure 7a and the result is shown in Figure 7b. The histogram has been rescaled to take values between 0 and 1 and the background is set to value zero.

Otsu's segmentation method is applied to the masked image of 7b. The segmentation either separates the egg 1 from both the background 21 and the air cell 7, or separates the air cell 7 from both the egg 1 and the background 21. The mask of the egg, obtained as described in the preceding, is then applied to the result of the segmentation, and the resulting image is shown in Figure 7c.

Finally the air cell 7 is extracted from the image of Figure 7c by a blob extraction method and the resulting image is shown in Figure 7d. The largest region of interconnected pixels is assigned to the egg and the second-largest region of interconnected pixels is assigned to the air cell. An air cell mask is thus provided as the region of interconnected pixels assigned to the air cell. Any noise present may be assigned to the egg region, which can be a preferred method of cancelling out noise as compared with, for example, using a median filter.

A restriction on distance of the air cell from the blunt end of the egg may be implemented in order to cancel out false positive detections of air cells. The centroid of the air cell needs to be within a specified range of distances from the blunt end of the egg in order to be recognized as an air cell. A restriction on the minimum number of pixels required to be assigned to the air cell may also be imposed. This can help to avoid noise being selected as being the air cell. A restriction on the ratio of the size of the blob to the size of the egg can also be imposed. For example, if the number of pixels assigned to the air cell is greater than 50% of the number of pixels assigned to the egg, the segmentation may be determined to be unsuccessful. An unsuccessful result does not necessarily indicate that no air cell is present in the egg; it may be the case that an air cell is present and is not visible from the side of the egg which is facing the detection means.

The size of the air cell may be determined by counting the number of pixels assigned to the air cell in the blob extraction method described in relation to Figure 7d, that is, by counting the number of pixels comprising the air cell mask. Based on a spatial calibration, this number of pixels can be translated into a measure of air cell size. For example, a spatial calibration may result in a conversion factor between a single thermogram or phase image pixel and a distance.

Analysis of phase images can have several advantages over analysis of thermograms. For example, phase images tend to be less influenced by geometrical features and less sensitive to non-uniform heating than thermal images and amplitude images. This can be of use when analyzing thermograms of objects with complex geometries, such as eggs: the directional emissivity of a patch of surface on the object will decrease with increased viewing angle (that is, the angle between the thermal camera and the normal of the surface patch). It has been shown that phase images are much less affected by the unwanted effects of shape variation than amplitude images and thermal images.

Although step S303 of the above-described method is related to transformation of thermograms into phase images, the present invention is not limited to transformation into phase images. Step S303 of the present invention comprises calculating at least one parameter based on the N thermograms. In the above-described example, the parameter is the phase, but in other embodiments of the present invention, the parameter may be different to the phase, for example in thermal signal reconstruction (TSR) methods. The parameter is preferably calculated such that undesired influences such as uneven excitation or curvature effects do not significantly disturb the result. It will be clear to the person skilled in the art that other mathematical operations can deliver the same desired properties as the phase images.

In TSR, the time-temperature profile of each individual pixel is modelled. This is typically performed using a polynomial relating log(T) to log(t).

Step S304 then comprises identifying air cell size based on one or more parameters calculated in dependence upon the acquired thermograms.

Optimal settings for air cell detection

Selection of phase image

Any phase image in the phase data cube may be selected for performing the segmentation steps to provide the air cell mask and thus estimate the size of the air cell. However, the contrast between the air cell and the rest of the egg may vary between phase images in the sequence of N phase images. Choice of the phase image to be used can thus affect the accuracy of the determination of the air cell size.

Referring to Figure 8, an example phase profile 30 of an air cell pixel and an example phase profile 31 of an egg pixel are shown. Both phase profiles 30 and 31 take a negative value at lower frequencies and a positive value at higher frequencies. The Fourier frequency at which each phase profile 30, 31 changes from negative to positive is different and may depend on parameter settings such as the excitation pulse duration t _pu/se , the sampling frequency at which the N thermograms are obtained, and the cooling down time. The cooling down time is the time period during which thermal images are acquired after the end of the excitation pulse.

In Figure 8, the phase profile 30 of the air cell pixel changes sign at a Fourier frequency f ₁ that is smaller than the Fourier frequency f ₂ at which the phase profile 31 of the egg pixel changes sign. The frequency range between fa and f ₂ is the frequency range in which the largest contrast is seen between the air cell 7 and the egg 1. Successful segmentation may be more likely when performed on a phase image selected from within this optimal frequency range.

Thus, the method of identifying the size of an air cell contained in an egg may include a step of selecting a phase image within a Fourier frequency range specified by a first frequency at which the phase profile of an air cell pixel changes sign, and a second frequency at which the phase profile of an egg pixel changes sign.

Determining parameter combination

Other parameters may affect the contrast between the egg and the air cell. Examples of such parameters are the excitation pulse duration, the sampling frequency, and the cooling down time. A preferred or optimal parameter combination may be determined in order to provide phase images with an increased contrast between the egg and the air cell.

A method of determining an optimal parameter combination will now be described. In this example, five different pulse durations (PD) and seven different cooling down times (CDT) are considered and twelve eggs are used as test objects for obtaining thermograms. The pulse durations are 0.5s, Is, 2s, 3s, 5s. The cool down times are 0, 0.5, 1, 2, 3, 7, 10. However, different numbers and/or combinations and/or values of parameters may be compared in a similar manner. The number of test objects is not limited to twelve.

For example, for each combination of a PD value and a CDT value, a range of sampling frequency values may be assessed. In the example described herein, the sampling frequency is set to 60Hz. A high sampling frequency, for example 60Hz or higher, is preferable if the available computing power is adequate for processing the resulting larger datacube (for higher sampling frequencies, the number N of thermograms will be higher). This is because datasets taken at higher sampling frequencies tend to exhibit less noise. However, in applications wherein data processing speed may be limited, it may be desirable to determine a sampling frequency which provides a good balance between noise reduction and processing speed. In these cases, and in other cases where further parameters may be varied, the following method of determining an optimal parameter combination may be easily modified to account for a different and/or more parameters.

Referring to Figure 9, the Fourier frequency at which the best possible segmentation of the air cell occurs is determined for all parameter combinations, that is, for each of the five possible PD values and the seven possible CDT values (step S901). Thus 5x7=35 possible parameter combinations are tested. The optimal Fourier frequency is determined as follows. For each parameter combination, 12 data cubes are acquired by taking thermograms of 12 eggs following excitation at a specified PD value and cooling time at a specified CDT value. Thus 5x7x12 = 420 data cubes in total are acquired. The air cell segmentation process described hereinbefore is performed for each Fourier frequency within each of the 12 data cubes for each of the 35 parameter combinations.

The segmentation method described hereinbefore results in two groups of pixels within the mask of the egg: pixels that belong to the air cell and pixels that do not belong to the air cell. Each pixel within each group has an associated phase value. It is important for successful segmentation that there is a clear distinction between the two groups. The groups may be compared with each other by using a one-way ANOVA F test. The phase value of each pixel within a group is considered a sample of that group. The F test compares the variance between each group with the variance within each group for one phase image which has been segmented. The F test results in an F value for each Fourier frequency within each of the 12 data cubes for each of the 35 parameter combinations. The F value quantifies the contrast between the air cell and egg in phase images. Thus, a high F value is preferred.

The outliers in each group of F values (a group of F values being the set of 12 F values at a particular Fourier frequency, PD value, and CDT value) are removed, resulting in a modified group of F values. For example, an implementation of Grubb's test may be used. Then, a boxplot is constructed for each modified group of F values. This can help to enable comparison between modified groups of F values in order to determine the Fourier frequency, for each combination of PD and CDT, at which the segmentation is most successful. The comparison can include comparing the median and the interquartile range of each modified group of F values. A high median and a small interquartile range is preferred.

As an example, Figure 10 shows F value boxplots for each of 10 Fourier frequencies for a pulse duration of 1 second and a cool down time of 7 seconds. The boxplot at 0.25Flz has both a high median F value and a small interquartile range in comparison with the boxplots at other Fourier frequencies. The 0.25Flz frequency may thus be determined to be the optimal Fourier frequency for this parameter combination.

Thus, for every combination of PD and CDT, one boxplot at a specific Fourier frequency is chosen for use in further analysis. In general, the Fourier frequency of the chosen boxplot for one combination of PD and CDT will not be the same as the Fourier frequency of the chosen boxplot for a different combination of PD and CDT. In the example described herein, within every pulse duration group, there is a significantly increased contrast between the air cell and the egg if the cooling down phase was monitored for more than one second. It was also determined that the boxplots shift to lower frequencies if a longer heating pulse was applied.

In summary, at the end of step S901, a specific Fourier frequency is determined for each combination of PD and CDT.

For each PD value, the CDT value with the optimal segmentation is determined (step S902). For each PD value, the seven boxplots having specific Fourier frequency values are compared, each boxplot being associated with a different CDT value. The median and interquartile range are compared within each PD value and the CDT value showing the highest median and smallest interquartile range is selected for further analysis.

As an example, Figure 11 shows boxplots of the ANOVA F test for pulse duration Is, for six CDT values, each CDT value being associated with a Fourier frequency as selected in step S901. The tick labels on the x axis are in the format: cool down time (Fourier frequency). The CDT is given in seconds and the Fourier frequencies are given in Hz. Figure 11 does not show a boxplot for a CDT of 0 seconds. This is because it was not possible to detect the air cell at this value of cool down time. The cool down time of 3 seconds and corresponding Fourier frequency of 0.25 Hz were determined to be optimal for the pulse duration of 1 second.

Thus, at the end of step S902, an optimal CDT value is determined for each PD value.

The final step is to compare the PD value boxplots (step S903). The median and interquartile range are compared between the five PD values and the PD value showing the highest median and smallest interquartile range is selected. This combination of PD value, CDT value, and Fourier frequency is then determined to be the optimal combination for successful segmentation of the air cell.

As an example, Figure 12 shows boxplots of the ANOVA F test for five PD values, where each PD value is associated with a Fourier frequency and a CDT value as selected in steps S901 and S902 respectively. The tick labels on the x axis are in the format: pulse duration (cool down time, Fourier frequency). The PD and CDT are given in seconds and the Fourier frequencies are given in Hz.

Based on the boxplots in Figure 12 it can be seen that it is advantageous to increase the pulse duration from 0.5s to Is. The boxplots of pulse durations Is, 2s, 3s, and 5s, do however partially overlap. Fast data acquisition is preferred. The total recording time of the pulse groups in Figure 12 are from left to right 3.5s, 4s, 12s, 10s and 12s. The total recording time thus increases substantially for the three highest tested pulse durations. Therefore, it may be preferred to select the pulse duration of Is.

Further analysis may be performed once the optimal combination of PD, CDT, and Fourier frequency has been determined.

For example, the boxplots of the five parameter combinations shown in Figure 12 may be analyzed in more detail as a function of the Fourier frequencies. Parameter combinations in which the two intersection points f f ₂ are very close to each other should be avoided. The physical attributes of an egg depend on various parameters which cannot be controlled, and the optimal parameters in this example were determined for a group of 12 eggs. It cannot be guaranteed that the optimal frequency will be the same for a second, different group of eggs. A slight shift of the optimal frequency is possible if a different group of eggs is being tested. Therefore, a broad peak or a platform of optimal frequencies is preferred, so that when moving between groups of eggs the pulse duration and cool down time do not need to be adjusted.

In this example, the Is pulse duration time is chosen as the ideal setting for pulse duration since it gives a slightly higher overall F-value, and since the total recording time is only increased by 0.5s in comparison to the pulse duration of 0.5s. The ideal Fourier frequency is taken at 0.225 Hz instead of 0.25Flz as the 0.225 Hz is surrounded by two frequencies for which the F-value is not significantly different. Thus in this example the optimal parameter settings were determined to be Is pulse duration, 3s cooling time, 60 Hz sampling rate, and the phase images at 0.225 Hz were used for the extraction of the air cell.

Determining an optimal parameter combination can be useful in applications wherein continual monitoring of air cell size is required. Continued reliable segmentation of air cells of eggs without requiring adjustment of parameters can provide an efficient and effective method of monitoring quality parameters, for example the air cell size, of a plurality of eggs.

One example of an egg storage monitoring experiment is described in the following.

Sixty brown eggs were collected from a local farmer one day after the eggs were laid. The eggs were visually inspected and cracked, dirty or irregularly shaped eggs were discarded. An assembly of thirty eggs from different weight classes (50g - 70g) was eventually selected to be used in the experiment. The air cell size and the weight of these eggs were monitored during fourteen days. The eggs were stored under controlled conditions at 20 °C and a relative humidity of 20% in a climate room (WKL 100, Weiss Technik Belgium Bvba, Belgium) during the experiment. On day 1, 2, 3, 4, 7, 10 and 14 the eggs were each taken out of the climate room and monitored with the optimal settings as described hereinbefore, namely Is pulse duration, 3s cooling time, 60 Hz sampling rate, and the phase images at 0.225 Hz. The air cell was segmented according to the segmentation method described hereinbefore.

Each egg was manually turned and monitored on four sides of the egg at angles of 0°, 90°, 180° and 270° relative to the initial orientation of the egg. Each egg was rotated around its axis of rotational symmetry. At the same time, the eggs were weighed on a O.lmg precision digital scale (FR-300 MK2, A&D Company, Ltd., Japan). The increase in volume of the air cell corresponds with a moisture loss and thus with a weight loss. The weight loss was used as the 'gold standard' in this experiment. On the basis of the water density, the weight loss can be converted to a volume increase. On the last day of the experiment the dimensions (i.e. length and width) of the eggs were measured with a digital caliper (Digimatic caliper 150mm, Mitutoyo Inc., USA) on a 0.01mm precision scale; the dynamic stiffness of the eggshell was being measured using a crack detector as described in Dunn et al. (2005); and at last, the eggshell thickness was measured with a 0.001mm precision digital micrometer (Mitutoyo 395-541-30, Mitutoyo Inc., USA).

The air cell size was monitored during storage in two different ways.

In a first method, the number of pixels of the air cell was determined for each of the four views of the egg, and these values were summed to obtain an overall air cell size. The cumulative increase in a number of pixels can then be linked to the cumulative weight loss of each egg.

In a second method, the volume and height of the air cell are estimated using geometry considerations. These two variables can be estimated if we assume that the blunt end of an egg approaches a spherical shape and that the air cell can be approached as a spherical cap of this sphere. Approximating the air cell as a spherical cap implicitly assumes that the inner shell membrane by which the air cell is formed has no curvature. Referring to Figure 13, the dimensions of a spherical cap 40 can be described by the parameters a, r and h for which a is the base of the spherical cap, r is the radius of the sphere, and h is the height of the spherical cap.

The parameters a, r, and h can be used to estimate the volume V of the air cell according to the following equation: nh

V =—(3a ² + h ² )

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where the height h is approximated as: h = r— jr ² — a ² The parameters a, r, h are expressed in units of pixels.

The a parameter is extracted from the mask of the air cell. The longest length of this mask was set to equal 2a. The length of the mask was measured by the function "regionprops.m" within Matlab. To estimate the volume of the air cell as accurately as possible, it is important to estimate carefully the radius of the sphere that surrounds the air cell. A simple estimation of the curvature of the blunt end of the egg would not be sufficiently accurate as the air cell is not always centered at the blunt end.

One method of estimating r is to first extract the contour of the egg mask, and calculate the centroid coordinates of the air cell. The contour of a mask is extracted by Matlab Function "bwboundaries.m" while the centroid of a mask can also be calculated by using "regionprops.m". The nearest point (xl,yl) of the egg contour to the centroid of the air cell was calculated with the Euclidian distance. This point was extracted from the contour, together with a segment of the contour around this point. The two ends of this contour segment supplied two further points (x2,y2) and (x3,y3). An example of this is illustrated in Figure 14 where the 3 points 41, 42, 43 are indicated with three red crosses. These three points belong to the circle 44 of which the radius is to be estimated. A system of three equations may be formed and solved to estimate the radius r of the circle and to calculate the center (x0,y0) of the circle:

Oi - x ₀ ) ² + (yi - y ₀ ) ² = r ²

(x ₂ - x ₀ ) ² + (y ₂ - y ₀ ) ² =

(x ₃ - x ₀ ) ² + (y ₃ - y ₀ ) ² = r ²

The volume V of the air cell can now be estimated by using parameters r and a as described in the above equations. The final step is the conversion of dimensions. Dimensions of the egg, for example the width and/or the length of the egg as measured with a caliper, may be used to convert the parameters V, r, a, h from units of pixels to SI units. Estimated volume increase of an air cell may be correlated with weight loss of the egg.

Modifications

It will be appreciated that many modifications may be made to the embodiments hereinbefore described. Where examples of models of apparatus components are provided, it will be understood that these are provided as examples only and any suitable components are contemplated.

The excitation means may be any means configured to provide the egg in a non-equilibrium thermal condition for a period of time. For example, an optical excitation source may be used such as a photographic flash, IR lamp, or laser excitation by point or line scanning. A mechanical excitation source may be used such as sound or ultrasound excitation, preferably causing internal stresses and thus heat (vibrothermography). An inductive excitation source may be used such as one which causes eddy currents (eddy current thermography). Any appropriate means is contemplated including hot air or microwave heating. An excitation means can be a heating or cooling source which can create a temperature difference or provide the egg in a non-equilibrium thermal condition for a period of time.

The thermograms are described as being acquired at equally, or regularly, spaced points in time. However, the thermograms may be acquired at points in time which are not equally spaced. For example, the time spacing may be relatively shorter in the initial, fast part of cooling following excitation and the time space may be relatively longer as the cooling rate decreases. The time spacing may increase or decrease monotonically as time elapsed since the excitation increases.

Although the methods hereinbefore described are described in relation to an egg which is thermally excited and undergoes an increase in temperature as a result of that excitation, it is also contemplated that an egg may undergo a decrease in temperature as a result of excitation. For example, if the excitation means is a source of cool air at a first temperature T ₁ and the egg is initially in thermal equilibrium with surroundings at a second temperature T ₂ , where T ₂ is greater than T _lt then the excitation may result in the temperature of the egg being decreased.

The at least one egg may comprise a plurality of eggs, in which case the active thermography method comprises obtaining a thermogram at a plurality of time intervals (N) of each egg of the plurality of eggs, resulting in N respective thermograms for each egg of the plurality of eggs. A single thermogram may relate to, e.g. show, a single egg or a plurality of eggs, as long as at least one respective thermogram is obtained at a plurality of time intervals for each egg.

Definitions

Where in embodiments reference is made to "internal or subsurface", reference is made to existing or occurring within a body under its surface. For example, in embodiments where the biological sample is an egg, reference is made to a body under its surface, for example under its shell, and thus not incorporating the surface or shell itself.

Where in embodiments reference is made to "pulsed thermography", reference is made to pulsed or flash thermography, whereby there is no restriction on the length of the pulse or flash; the duration of the pulse can be very short (flash) or longer. For example, the duration of the pulse can be at least 1 second, at least 5 seconds, at least 10 seconds, at least 20 seconds, or at least 30 seconds. The duration of the pulse may be no more than 2 second, no more than 3 seconds, or no more than 5 seconds.

Where in embodiments reference is made to "active thermography", reference is made to using a means for excitation (e.g. an energy source) to produce a thermal contrast between different features of interest/areas of interest within the sample (e.g. egg). In the active approach the inspected eggs are usually in thermal equilibrium with the surroundings before excitation; the excitation disturbs the thermal equilibrium with the surroundings.

Where in embodiments reference is made to "hot air", reference is made to using air which has been heated and which is configured to heat up at least the internal or subsurface of the egg. However, the heating of at least the internal of the egg is preferably kept to a minimum to avoid quality loss. Therefore, in preferred embodiments, a maximum heating of 2°C, preferably of 1°C is provided for the internal or subsurface of the egg.

Where in embodiments reference is made to "thermogram" reference is made to an image (2D) of the temperature calculated or determined based on the radiation emitted by an object.