A 2-D imaging-assisted geometrical transformation method for non-destructive evaluation of the volume and surface area of avian eggs

Shell temperature: How shall we tell if a still gosling is under the eggshell?

The present investigation was aimed at predicting a still (i.e., dead) vs. live embryo within a hatching goose egg by measuring the eggshell cooling rate. For this, we daily measured the temperature (T) values on the shell surface of goose eggs after they were removed from the incubator and during further natural cooling. T was recorded every 0.5 h for further 1.5 h of cooling. It was possible to recognize eggs with dead embryos using the combination of T, egg weight (W), and surface area (S). The resultant indicator (TS/W) was called specific temperature index (STI). The mathematical relationship using STI measurements between Days 8-13 facilitated 80 % correct identification of the eggs with dead embryos. Additionally, we derived mathematical dependencies for shell weight (Ws) and thickness (t) by utilizing the values of W, egg volume (V), S, the average T of all measurements taken, as well as the drop in T during 1.5 h of natural cooling. The key advantage of these parameters was their measurement and/or calculation by applying non-destructive methods. The integrated application of these parameters resulted in achieving high calculation accuracy as judged by correlation coefficients of 0.908 for Ws and 0.593 for t. These novel mathematical models have the potential to decrease hatching waste by predicting embryo viability. Our research will add to a toolkit for non-invasive egg assessment that is useful in the poultry industry, research on eggs, and engineering.

Metabolic Rate and Egg Production in Japanese Quails Can Be Predicted by Assessing Growth Parameters of Laying Hens

The aim of the current study was to assess the female metabolic rate and test the hypothesis that there is a relationship between the egg productivity of Japanese quails from eight breeds and their morphometric, or growth, parameters. Parameters measured were body weight (B), volume (V), and surface area (S), as well as the metabolism level expressed by the ratio S/V. The collected egg performance traits were as follows: the number of eggs produced (N), the average egg weight (W), and the total egg mass (M) (i.e., N multiplied by W). To measure the S and V values, a novel technique was developed that takes into account the similarity of the quail's body to an ellipsoid. An analysis of the relationships between productivity indicators allowed us to introduce a new index called the metabolic index, B·S/V, based on all three main growth parameters in quails. Using the values of this index, we were then able to judge indirectly the level of quails' egg productivity. We went on to assess the N, W, and M values, not only depending on the size of the bird's growth parameters but also according to the degree of their changes during quail growth. These changes were expressed as the slope angles of trend lines describing the growth process data. This approach produced more accurate results for predicting the egg productivity in terms of W and M.

Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio

Avian eggs represent a striking evolutionary adaptation for which shell thickness is crucial. An understudied eggshell property includes the neutral axis, a line that is drawn through any bent structure and whose precise location is characterized by the k-factor. Previous studies have established that, for chicken eggs, mean k corresponds to the golden ratio (Φ = 1.618, or 0.618 in its reciprocal form). We hypothesized whether such an arrangement of the neutral axis conforms to the eggshell of any bird or only to eggshells with a certain set of geometric parameters. Implementing a suite of innovative methodological approaches, we investigated variations in k of 435 avian species, exploring which correspond to Φ. We found that mean k is highly variable among birds and does not always conform to Φ, being much lower in spherical and ellipsoid eggs and higher in pyriform eggs. While 21 species had k values within 0.618 ± 0.02 (including four falcon species) and the Falconinae subfamily (six species) revealed a mean of 0.618, it is predominantly domesticated species (chicken, ducks, and geese) that lay eggs whose neutral axis corresponds to the golden ratio. Thus, the study of the mathematical secrets of the eggshell related to the golden ratio of its neutral axis suggests its species-specific signatures in birds.

Equation for Egg Volume Calculation Based on Smart’s Model

In the egg industry, it is necessary to estimate the egg volume accurately when estimating egg quality or freshness in a non-destructive method. Egg volume and weight could obtain egg density and could be used to determine egg freshness. Therefore, the egg geometric must be obtained first to establish a volume equation with a geometric shape. This research proposes an innovative idea to derive the mathematical model and volume equation of egg shape, calculate its volume, and verify the accuracy of the mathematical equation proposed using the volume displacement method. Using the proposed equation, the minimum error between the calculated egg volume) and actual egg volume is 0.01%. The maximum volume error does not exceed 2%. The egg shape equation can accurately draw the outer contour curve of the egg by the half-length of the maximum long axis and maximum breadth of the short axis, and the distance from the center point of the egg to the maximum breadth (xm).

An Algorithm for Obtaining 3D Egg Models from Visual Images

Mathematical models for describing the shape of eggs find application in various fields of practice. The article proposes a method and tools for a detailed study of the shape and peripheral contours of digital images of eggs that are suitable for grouping and sorting. A scheme has been adapted to determine the morphological characteristics of eggs, on the basis of which an algorithm has been created for obtaining their 3D models, based on data from color digital images. The deviation from the dimensions of the major and minor axes measured with a caliper and the proposed algorithm is 0.5–1.5 mm. A model of a correction factor has been established by which the three-dimensional shape of eggs can be determined with sufficient accuracy. The results obtained in this work improve the assumption that the use of algorithms to determine the shape of eggs strongly depends on those of the bird species studied. It is approved with data for Mallard eggs which have a more elliptical shape and correspondingly lower values of correction coefficient ‘c’ (c = 1.55–4.96). In sparrow (c = 9.55–11.19) and quail (c = 11.71–13.11) eggs, the form tends to be ovoid. After testing the obtained model for eggs from three bird species, sparrow, mallard, and quail, the coefficient of the determination of proposed model was R2 = 0.96. The standard error was SE = 0.08. All of the results show a p-value of the model less than α = 0.05. The proposed algorithm was applied to create 3D egg shapes that were not used in the previous calculations. The resulting error was up to 9%. This shows that in the test, the algorithm had an accuracy of 91%. An advantage of the algorithm proposed here is that the human operator does not need to select points in the image, as is the case with some of the algorithms developed by other authors. The proposed methods and tools for three-dimensional transformation of egg images would be applicable not only for the needs of poultry farming, but also in ornithological research when working with different shaped varieties of eggs. Experimental results show that the proposed algorithm has sufficient accuracy.

Egg and math: introducing a universal formula for egg shape

The egg, as one of the most traditional food products, has long attracted the attention of mathematicians, engineers, and biologists from an analytical point of view. As a main parameter in oomorphology, the shape of a bird's egg has, to date, escaped a universally applicable mathematical formulation. Analysis of all egg shapes can be done using four geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped). The first three have a clear mathematical definition, each derived from the expression of the previous, but a formula for the pyriform profile has yet to be derived. To rectify this, we introduce an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere-ellipsoid-Hügelschäffer's ovoid transformation, and it is applicable to any egg geometry. The required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical analysis and description represents the sought-for universal formula and is a significant step in understanding not only the egg shape itself, but also how and why it evolved, thus making widespread biological and technological applications theoretically possible.

The grades and freshness assessment of eggs based on density detection using machine vision and weighing sensor

The water displacement and flotation are two of the most accurate and rapid methods for grading and assessing freshness of agricultural products based on density determination. However, these techniques are still not suitable for use in agricultural inspections of products such as eggs that absorb water which can be considered intrusive or destructive and can affect the result of measurements. Here we present a novel proposal for a method of non-destructive, non-invasive, low cost, simple and real-time monitoring of the grading and freshness assessment of eggs based on density detection using machine vision and a weighing sensor. This is the first proposal that divides egg freshness into intervals through density measurements. The machine vision system was developed for the measurement of external physical characteristics (length and breadth) of eggs for evaluating their volume. The weighing system was developed for the measurement of the weight of the egg. Egg weight and volume were used to calculate density for grading and egg freshness assessment. The proposed system could measure the weight, volume and density with an accuracy of 99.88%, 98.26% and 99.02%, respectively. The results showed that the weight and freshness of eggs stored at room temperature decreased with storage time. The relationship between density and percentage of freshness was linear for the all sizes of eggs, the coefficient of determination (R2) of 0.9982, 0.9999, 0.9996, 0.9996 and 0.9994 for classified egg size classified 0, 1, 2, 3 and 4, respectively. This study shows that egg freshness can be determined through density without using water to test for water displacement or egg flotation which has future potential as a measuring system important for the poultry industry.

Shifts in eggshell thickness are related to changes in locomotor ecology in dinosaurs

Birds share an array of unique characteristics among extant land vertebrates. Among these, external and microstructural characteristics of extant bird eggs have been linked to changes in reproductive strategy that arose among non-avian theropod dinosaurs. More recently, differences in egg proportions recovered in crown birds relative to other dinosaurs were suggested as possibly linked to avian flight, but dense sampling close to its proposed origin was lacking. Here we assess the evolution of eggshell thickness in a targeted sample of 114 dinosaurs including birds, and test the relationship of eggshell thickness with potential life history correlates and locomotor mode using phylogenetic comparative methods. Only egg mass and flight are identified as significant predictors of eggshell thickness. While a high correlation between egg mass and eggshell thickness is expected, that relationship is much stronger in flying taxa, which show a significantly higher slope and lower residual variance than flightless species. This suggests stabilizing selection of eggshell thickness among theropods, as recovered for other traits in extant birds (e.g. genome size, metabolic rate). Within living birds, Eufalconimorphae present an apomorphic increase in relative eggshell thickness which remains unexplained, as few morphological synapomorphies of this clade have been identified.