# Three-Dimensional (3D) Model-Based Lower Limb Stump Automatic Orientation
## 1 Introduction  
According to World Health Organization (WHO) statistics, up to one billion people in the world constituting about 15% of the total population live with certain form of disability, including approximately 200 million experiencing considerable difficulties in functioning that limit their participation in family and society life, with the domination of cases in the upper age group of \(\geq\)60 years old, where nearly every second a person experiences moderate and about 10% severe disabilities [1]. Severe disabilities are often associated with lower limb amputations, with approximately 30,000 to 40,000 amputations performed each year, and more than 1.5 million people living with a lost limb in the U.S. alone, with the majority requiring access to lower limb prosthetics [2]. The total number of lower limb prostheses provided annually in Russia increased from around 60,000 in 2012-2014 to above 80,000 in 2016-2018 [3]. Although reasons for amputation vary considerably between regions and age groups, ranging from severe trauma, wounds and burns caused by road traffic and occupational injuries as well as violence and humanitarian crises to tumors and inflammatory diseases potentially leading to thedevelopment of sepsis and multiple organ failure, on average around one half of amputation cases can be attributed to either trauma or disease, respectively [1; 4]. Modern prosthetics largely rely upon technological support to improve the accuracy of design and finally to enhance the quality of rehabilitation taking into account the individual characteristics of the patient. Current technologies allow for a highly automated prosthetic design procedures based on the geometry and properties of human organs obtained by 3D scanning [5] or computed tomography (CT) scanning [6] followed by prosthetic model reconstruction. In addition to the design itself, adequate 3D models allow for running biomechanical simulations, leading to certain optimization strategies based on objective visual data sources and numerical mathematics [7]. In some cases, appropriate model design requires a combination of different technologies. In contrast to 3D scanning, CT and magnetic resonance imaging (MRI) are also capable of visualization of soft tissues [8; 9]. Thus, modern scanners with the usage of digital models and mathematical simulations can predict the behavior of patient's organs at both micro [10] and macro scales [11] as well as over different time spans [12]. Modern approach to the design of receiving sockets for lower limb prostheses typically consists of the following stages:  
1. 3D scanning of the lower limb stump;
2. Design and analysis of a digital geometric model;
3. Printing the prosthetic socket using a 3D printer. The 3D scanning involves recording of the surface points coordinates [13] using a 3D scanner or recording device followed by the reconstruction procedure used to obtain a 3D-model of a limb segment. One of the key stages in 3D-model processing is the orientation of the model in 3D Cartesian coordinates. Among recent approaches to the automation of the 3D-model orientation problem, using various mathematical filters for reconstructions of the 3D-model from 2D X-ray images can be mentioned [14]. The rotation matrix used for the automatic orientation of the model is in 3D space. However, this approach is limited to certain specific 3D-model rotation angles. Another approach is based on the virtual environment that is used to automatically select the position of the 3D-model in three-dimensional space is considered in [15]. The key disadvantage of this particular method is that it limits possible 3D-model orientations to a set of specified templates. In another recent work [16] orientation of the 3D image of the scapula is based on the preliminarily fixed markers that are being further compared against the control model. The disadvantage of this method is that the expert needs to place markers in the 3D-model manually.