# An Algorithm for Obtaining 3D Egg Models from Visual Images
## 1 Introduction  
The application of mathematical models for describing the shape of eggs is in both poultry and ornithology, as well as in industrial technology, mathematics, art, architecture, religion, and philosophy. Examples are egg-shaped sludge mills; egg-shaped water channels; compartments of cars with ovate shape; egg-shaped cell phones; and speakers; refrigerators and washing machines of this form have been developed. The mathematical models of eggs are applied to the design of buildings, the elements of infrastructure that have high energy efficiency, high aerodynamic qualities, and minimal material consumption [1, 2].  
Determining the geometric dimensions of eggs and their relationship is important for poultry and ornithology studies. The results obtained can be used in population analysis, environmental morphology, predicting the weight of chickens, and assessing the quality characteristics of eggs. Size of the egg is related to important aspects in the study of birdbehavior, such as the mass of the female, the social status of the female, the place and time of laying, the physicochemical composition of the egg, nesting, the size of the nest, and the breeding of birds.  
The following major trends are observed in the creation and analysis of egg models:  
Models based on known egg shapes without making comparisons with real eggs [3];  
Egg models and their validation with those of a small number of bird species [4];  
Models validated by a large number of bird species [5].  
Egg models have been developed both in two-dimensional [6; 7] and in three-dimensional form [8].  
Current research relating to model definition and classification of eggs has focused on the use of simplified analysis procedures. Studies and analyses are directed to the use of contactless measurement methods, including systems for image acquisition, processing and analysis, spectral, and dielectric characteristics. The mathematical description of the shape of the eggs is applied to these methods.  
Techniques for automating the inspection of products in various fields of application have been proposed by researchers in recent years. Research in this area is focused on the use of systems for obtaining, processing, and analyzing color digital images.  
One of the main applications of digital image processing is to determine the number and type of objects in them. The variety of objects creates many problems in this process as each object has its own characteristics and features. Difficulties in solving this task arise from various factors such as the contrast between objects and the background, the degree of separability and grouping of objects, their texture and variety, and size. These features are evident in organic products such as eggs, as they are too complex and the images obtained from them include all the listed factors.  
The purpose of the article is to propose a method and tool for detailed examination of the shape and peripheral contours of digital images of eggs that are suitable for grouping and sorting.  
The contributions in this paper include: image processing and analysis techniques are valuable for analysis of the external characteristics of eggs. A method of geometrical transformation of an egg contour into a three-dimensional surface was examined. Two-dimensional image processing and analysis techniques were applied for obtaining a 3D model of egg shapes. The proposed algorithm showed appropriate accuracy and low error rates.