Abstract
The capacity to process three-dimensional facial surfaces to objectively assess outcomes of craniomaxillofacial care is urgently required. Available surface registration techniques depart from conventional facial anthropometrics by not including anatomical relationship in their analysis. Current registrations rely on the manual selection of areas or points that have not moved during surgery, introducing subjectivity. An improved technique is proposed based on the concept of an anthropometric mask (AM) combined with robust superimposition. The AM is the equivalent to landmark definitions, as used in traditional anthropometrics, but described in a spatially dense way using (∼10.000) quasi-landmarks. A robust superimposition is performed to align surface images facilitating accurate measurement of spatial differences between corresponding quasi-landmarks. The assessment describes magnitude and direction of change objectively and can be displayed graphically. The technique was applied to three patients, without any modification and prior knowledge: a 4-year-old boy with Treacher–Collins syndrome in a resting and smiling pose; surgical correction for hemimandibular hypoplasia; and mandibular hypoplasia with staged orthognathic procedures. Comparisons were made with a reported closest-point (CP) strategy. Contrasting outcomes were found where the CP strategy resulted in anatomical implausibility whilst the AM technique was parsimonious to expected differences.
In the era of virtual imaging, major developments were achieved in virtual diagnosis, treatment planning, and evaluation of outcomes of craniomaxillofacial deformities . An important aspect is the capacity to assess the spatial changes in facial form at different treatment time points and/or when displaying different types of expression. This is essential for an objective audit of treatment outcomes, relapse and confirmation of predicted growth trajectories. Facial anthropometrics, needed to measure such changes in form objectively, has also evolved in the last decade from taking measurements directly on the subject to indirectly via two- or three-dimensional (3D) facial imaging . Facial form was traditionally only represented using specific points or landmarks that have developmental, functional, structural, or evolutionary significance . Today, the use of spatially dense surface representations has become possible as well.
Form is defined as size and shape independent of position and orientation . Hence, any difference in position and orientation is to be eliminated prior to analysing actual changes in form from two or more facial images. To this end, a rigid registration is required that searches for a rotation and translation to align facial images optimally according to a given similarity criterion . Typically, the criterion measures differences between one-to-one correspondences in the images. For the landmarks representing facial form, these correspondences are anatomically defined and therefore known, reducing the rigid registration to a simple superimposition. In contrast, for surfaces representing facial form, these correspondences are not defined and have to be sought. A popular registration algorithm to do this, is the iterative closest point (ICP) procedure , which is a two-step algorithm in which candidate correspondences and rotation and translation are updated until no more change in either is observed. For every point on a reference surface the candidate correspondence is defined as being the closest point on the target surface. Finally, after rigid registration of surfaces or superimposition of landmarks, remaining differences between the established or defined one-to-one correspondences are used to provide numerical and/or visual feedback as a distance map or a vector field .
In this work, two caveats in these types of assessments are noted and addressed. Firstly, whether the remaining differences reflect true structural differences in facial form depends on the definition of the one-to-one correspondences used. When using landmarks these correspondences are correctly and anatomically defined, but landmarks provide only a sparse representation and salient features of the facial form can be overlooked . In contrast, surface analyses, allow quantification and visualization of subtle changes in discrete regions of the face, but depart from conventional facial anthropometrics in not using any anatomical correspondence. Secondly, a registration is only performed on stable parts of the face , neglecting the parts that changed due to intervention, relapse, disease or expression. Current registrations rely on the manual selection of parts or landmarks that are stable, therefore introducing subjectivity to the analysis. To address these two caveats, the authors propose the application of an anthropometric mask (AM) and mapping technique followed by a robust superimposition. These techniques have been applied in previous and related work where spatially dense assessments of facial asymmetry in typical and disordered growth were obtained and where linear anthropometrics were augmented for orthodontic practice . The main idea of AM mapping is to introduce quasi-landmarks which are spatially dense one-to-one correspondences between surfaces that are anatomically plausible. First, the AM, which is a facial surface template, is mapped onto the facial surfaces of interest using a non-rigid registration. Then, rigid registrations in between the facial surfaces simply reduce to superimpositions. The use of a robust superimposition is introduced, to deal with the obvious and the more subtle changes in facial form without subjective input. Three-dimensional images of three clinical cases are used to illustrate the benefit of these techniques. The improvements will be compared with the frequently used ICP approach.
Materials and methods
All subjects had their faces scanned using a 3dMD facial scanning system (3dMD, Atlanta, Georgia). Case 1 represented facial changes associated with expression. The patient was a 4-year-old boy with Treacher–Collins syndrome who had 3D facial images captured in both a resting and smiling pose on the same day. Case 2 represented post-orthognathic surgical outcome assessment. The patient was a 19-year-old woman with right hemimandibular hypoplasia who presented with a discrepancy in the lower mandibular border and occlusal cant. This was corrected with a mandibular ostectomy in combination with a wedge Le Fort 1 osteotomy. The patient’s occlusal and skeletal discrepancies were satisfactorily resolved. Three-dimensional images were taken pre- and post-operatively after removal of fixed orthodontic appliances. Case 3 represented assessment of multi-stage orthognathic procedures. The patient was a 19-year-old woman with severe mandibular hypoplasia who was treated with a two-stage orthognathic procedure. A bilateral distraction of the mandible was performed parallel to the lower border to increase the length of the mandibular body. On completion of surgical distraction, the distractors were removed and the regenerate allowed to become consolidated whilst the mandible was supported in wedge splint and inter-maxillary fixation to reduce the occlusal plane. A Le Fort 1 osteotomy was performed after consolidation for maxillary advancement and to set the occlusion and achieve functional inculpation . A genioplasty was also performed to improve the facial appearance. Imaging was carried out prior to mandibular distraction, during Le Fort 1 osteotomy, and on removal of fixed orthodontic appliances.
AM and mapping
The idea of using an AM was to obtain spatially dense landmarks on the facial surfaces of interest. The AM is essentially a surface template covering the facial area of interest. The AM used in this work is illustrated in Fig. 1 and was the average face of 400 Western Australian healthy young individuals between the ages of 5–25 years captured with the same 3dMD facial scanning system used in the research. The mask consists of about 10,000 uniformly sampled (equally distanced at about 2 mm) points ( Fig. 1 a) connected using about 20,000 triangles ( Fig. 1 b) defining the facial surface template ( Fig. 1 c).
The surface template was mapped onto the facial images of interest, a process equivalent to the indication of traditional anthropometric landmarks. The mapping involved non-rigid surface registration of the template onto the target faces. Non-rigid registration is required because rigid registration would not account for local shape differences between the template and the facial surfaces. The non-rigid registration used here was based on the successful work of C hui and R angarajan which was further developed and validated previously on faces by C laes . As an analogue, the mapping could be compared to physically fitting an elastic mask onto a solid facial statue through the alignment and deformation of geometrically or anatomically corresponding features onto each other. By allowing iteratively more flexibility in the elasticity of the mask initially larger, but gradually more local and subtler differences, were accommodated. The resulting dense set of points in the template, mapped in a quasi-anatomical manner, provided a dense set of corresponding quasi-landmark indications over all of the facial surfaces of interest. This allowed assessments from different individuals to be standardized in a spatially dense way. Additionally, the elimination of orientation and position differences between pairs of facial surfaces reduces to simple superimpositions with known quasi-anatomical one-to-one correspondences.
Robust superimposition
For an assessment of facial change to be made, a superimposition of quasi-landmarks to eliminate orientation and position differences was required. When confronted with strong facial changes, such as surgical interventions, it was important to perform the superimposition only on quasi-landmarks that were located in stable parts of the face that were not changed. To this end, a freely available downloadable graphical user interface was developed in Matlab™ 2010 based on the robust superimposition strategy found in C laes . Essentially, instead of manually selecting stable parts, a two-step iterative, but automated, procedure was available. The procedure updates an estimate of the superimposition and an estimate of stable parts to guide the superimposition until no more change in either is observed.
Imaging and analysis
Spatial differences, both in their magnitude and direction, of the one-to-one correspondences between quasi-landmarks after superimposition were computed and visualized as a distance map onto the facial surface of the preoperative (or previous) situation. The vector field was visualized using colour-coded 3D lines by connecting the one-to-one correspondences between facial surfaces. The colours of the lines reflect the local vector magnitude similar to the distance map. The distance map was summarized into a single numerical value using the root mean squared error (RMSE). This reflected the overall or degree of difference and hence intrinsic clinical severity of facial change.
Comparing ICP technique
The first and second cases were used to compare the proposed strategy with a frequently reported ICP approach typically used and available in software from commercial 3D facial scanners. The one-to-one correspondences encoded in the quasi-landmarks after mapping the AM were substituted with correspondences defined as closest points between the quasi-landmarks. As such the definition of the landmarks in the mask was not used but the same amount of points for both analyses was guaranteed. The same robust superimposition strategy was applied but based on the different underlying one-to-one correspondences. This created a superior ICP technique compared to those already published and used in practize, but ensured that the comparison focused only on the difference in underlying one-to-one correspondence which is the key message of this work.
Results
For case 1, an illustration of the AM mapping is depicted in the top row of Fig. 2 . The capacity of the AM to fit to corresponding facial anatomy was seen in the smiling image where there were no points on the imaged dentition ( Fig. 2 top right). Dentition information was not present in the AM, hence no anatomical correspondence was anticipated and a correct result was obtained. Distance maps and vector fields after superimposition of resting and smiling poses using closest point and quasi-landmark analyses are shown in the middle and bottom row of Fig. 2 , respectively. The closest point analysis suggested that there is little to no displacement of tissues lateral to the nasolabial folds, the philtral region of the upper lip and alar base. This outcome was nonsensical however, as the contraction of obicularis oris, nasial-labial elevators, zygomaticus and platysma muscles are likely to shorten the philtrum, elevate the labial tissues, widen the alar base, and depress the chin. These hypothesized displacements were apparent in the quasi-landmark analysis. The mapped displacement between quasi-landmarks provided a more plausible illustration of the displacement of the facial soft tissue envelope associated with underlying contraction of the obicularis oris, nasolabial elevators, zygomticus and platysma muscles. Based on this quasi-landmark analysis, the relative facial change caused by the expression had RMSE 1.86 mm.
