# Assessment of Cranial Deformation Indices by Automatic Smartphone-Based Photogrammetric Modelling
###### Abstract  
This paper presents research carried out to assess the accuracy of a fully automatic smartphone-based photogrammetric solution (PhotoMeDAS) to obtain a cranial diagnostic based on the 3D head model. The rigorous propagation of the coordinate measurement uncertainty to the infant's derived cranial deformation indices is demonstrated. The cranial anthropometric parameters and cranial deformation indices that PhotoMeDAS calculates automatically were analysed based on the estimated accuracy and uncertainty. To obtain both accuracy and uncertainty, a dummy head was measured 54 times under different conditions. The same head was measured with a top-of-the-line coordinate-measuring machine (CMM), and the results were used as ground-truth data. It is demonstrated that the PhotoMeDAS 3D models are an average of 1.01 times bigger than the corresponding ground truth, and the uncertainties are around 1 mm. Even assuming uncertainties in the coordinates of up to 1.5 mm, the error in the derived deformation index uncertainties is around 1%. In conclusion, the PhotoMeDAS solution improves the uncertainty obtained in an ordinary paediatric consultation and can be recommended as a tool for doctors to establish an adequate medical diagnosis based on comprehensive cranial deformation indices, which is much more precise and complete than the information obtained by existing analogue devices (measuring tapes and callpers) and easier to use and less expensive than radiological imaging (CT and MRI).  
3D data digitisation; medicine; plagiocephay; 3D imaging; photogrammetry +
Footnote †: journal: Medical Imaging, April. 2022, 11499. [[https://doi.org/10.3390/app122211499](https://doi.org/10.3390/app122211499)]([https://doi.org/10.3390/app122211499](https://doi.org/10.3390/app122211499))  
Footnote †: journal: Medical Imaging, April. 2022, 114999. [[https://doi.org/10.3390/app122211499](https://doi.org/10.3390/app122211499)]([https://doi.org/10.3390/app122211499](https://doi.org/10.3390/app122211499))
analysed by three-dimensional photogrammetry. Photogrammetric solutions have the clear advantage of producing a 3D model, where different angles and distances can be measured without subjecting the infant to a stressful medical test, but they normally require high-end 3D (laser or structured-light) scanners or photogrammetric solutions that are rarely available at the paediatrician's office. We want to replace this instrumental requirement with the use of a standard smartphone.  
Photogrammetric Medical Deformation Assessment Solutions (PhotoMeDAS, [[https://photomedas.eu](https://photomedas.eu)]([https://photomedas.eu](https://photomedas.eu)), accessed on 9 November 2022, Universitat Politecnica de Valencia, Valencia, Spain), a low-cost tool, was developed for measuring and evaluating cranial deformation in infants [11; 12; 13]. It is composed of a coded cap fitted on the infant's head, a smartphone application used to record the overall head cap targeting its barycenter, and a cloud-based processing system that yields the head's 3D model with the automatic determination of deformational indices.  
The repeatability of the automatic smartphone-based photogrammetric solution has been analysed in previous work [11], but an assessment of the derived 3D model accuracy and its implication for determining cranial deformation indices is still lacking due to its complexity in real-life clinical consultations with fully dynamic infants. Also lacking is the assessment of the measurement uncertainty and its propagation to the final determination of deformation indices. Overcoming these limitations constitutes the purpose of the present work.