# Three-Dimensional Human Head Reconstruction Using Smartphone-Based Close-Range Video Photogrammetry
## 2 Materials and Methods
### Reconstruction Quality Evaluation  
Three-dimensional head reconstruction algorithms were evaluated and compared by several tests. The most important results were gathered by comparing the created test models (sparse point clouds) to the reference model (mesh). Details on the model construction procedures can be found in Section 2.2. The comparison of the models was organized in two different setups: by comparing the distances between all closest points of the aligned models and by comparing the distances between the closest points of aligned models only in the facial area of the head. The rationale of comparing all points--it evaluates the overall quality of the model (incorporates the influence of the non-model parts to the model's evaluation results)--includes semantic noise (objects from the background) and assesses the need for additional processing of the model in order to clean it. The rationale of comparing only the facial points of the models shows the algorithm's ability to reconstruct fine details of the head that are relatively stable, i.e., excluding parts that may be changing during separate imaging runs. The hair region shape can be easily distorted (distortions may be larger than face details but smaller than variations in the whole reconstructed scene), so only model points from the facial region are used in the model comparison. Additionally, head shape, not necessarily including hair, will be the right source of head size information for applications, such as for size selection of hat, helmet, glasses, or similar wearables. Points of the reference model were manually classified into facial and non-facial regions. During the model comparison, when the distances between the closest points of two models are computed, non-facial points of the reference model and the closest points of the test model are discarded. Figure 5: Construction of the mannequin’s reference 3D head model. (**a**) Visualized reconstructed point cloud with camera poses. Some pictures that correspond to various camera poses are shown alongside. (**b**) Is the final rendered result of the reconstruction. In this research, the absolute scale of the models was not calculated. This is the consequence of using uncalibrated 2D images. Additional information is needed in order to estimate absolute scale [85]. Scale differences are eliminated during the alignment of test models to the reference model; therefore, comparative evaluation of the automatic reconstruction algorithms does not require scale information. The comparison procedure of the test and reference models when all closest points of both models are used (Evaluation Case 1) and only points in the facial area of the head are used (Evaluation Case 2) (all steps are common for both cases unless otherwise noted) is as follows:  
1. Three-dimensional facial feature points are detected in the test and reference models (explained below in this Section and in Figure 6): 1. detection of facial feature points in individual frames; 2. transfer of points from images to the 3D model;
2. Estimation of parameters of the 3D geometric transformation between two sets of 3D facial feature points. Applying the geometric transform to the test model to align it to the reference model;
3. Finding of the closest test and reference model points and distances between them using the \(k\)-nearest neighbors algorithm;
4. (Only in Evaluation Case 2) Remove distances that include points from the facial region of the reference head;
5. Evaluate the distances (as residual errors of model alignment) by applying statistical methods to find the mean and confidence intervals. Anatomical landmarks, in this research, facial feature points, provide the means to perform various manipulations with the target object [21; 86; 87; 88; 89]. In this research, facial feature points were used to align the test and reference 3D models. The approach to use facial feature points for model alignment is selected due to the variety of the created test models.