## Introduction

Cone-beam computed tomography (CBCT) is commonly used for 3-dimensional (3D) evaluation and treatment planning of patients in orthodontics, where precision and reproducibility of landmark annotation are required. Manual landmarking is a time- and effort-consuming task regardless of the practitioner’s experience. We introduce a hybrid algorithm for automatic cephalometric landmark annotation on CBCT volumes.

## Methods

This algorithm is based on a 2-dimensional holistic search using active shape models in coronal and sagittal related projections followed by a 3D knowledge-based searching algorithm on subvolumes for local landmark adjustment. Eighteen landmarks were located on 24 CBCT head scans from a public dataset.

## Results

A 2.51-mm mean localization error (SD, 1.60 mm) was achieved when comparing automatic annotations with ground truth.

## Conclusions

The proposed hybrid algorithm shows that a fast initial 2-dimensional landmark search can be useful for a more accurate 3D annotation and could save computational time compared with a full-volume analysis. Furthermore, this study shows that full bone structures from CBCT are manageable in a personal computer for 3D modern cephalometry.

## Highlights

- •
A hybrid algorithm for automatic cephalometric landmark annotation on CBCT volumes is suggested.

- •
We scored a 2.51 mm mean error for 3D landmark localization.

- •
We investigated a state-of-the-art cephalometric landmarking system for CBCT cephalometry.

A cephalometric analysis has diagnostic value that depends on the accuracy and reproducibility in identification of cephalometric landmarks on head radiographs or cone-beam computed tomography (CBCT) volumes. Manual cephalometric landmarking and tracing are monotonous, difficult, and time-consuming processes. Many orthodontists choose not to trace cephalograms because of the tedium. For example, a recent study reported that less than 40% of orthodontists perform a cephalometric analysis on pretreatment cephalograms. Specially, experienced orthodontists may believe that there is no need to trace lateral cephalometric radiographs because their judgment may be perceived to be as accurate as a cephalometric analysis. Contrarily, in the same study, over 70% of orthodontists reported using computer-aided digital-tracing software. Therefore, a fast, affordable and automatic 3-dimenional (3D) cephalometric landmarking system for cephalometric analysis can help in diagnosis by avoiding the conventional disadvantages of cephalograms such as overlapped bone structures and facial asymmetries while increasing the impact on orthodontic practice and maintaining diagnostic protocols. CBCT scans have been introduced in orthodontics as a diagnostic tool and are becoming a standard imaging technique, because they provide accurate 3D information about the patient’s size and position. We believe that automatic landmark annotation not only could considerably increase a practitioner’s efficiency, but also could reduce the associated subjectivity of the annotation, thus saving valuable clinical time.

Recently, several approaches for automatic landmark detection on CBCT volumes have been proposed. From that literature, we describe 4 outstanding contributions. First, Gupta et al proposed an algorithm to locate 20 cephalometric landmarks on 30 CBCT volumes by grouping head-searching sections. Although they reported a 2.01-mm mean localization error, but only 64.67% of the landmarks had accuacy less than 2 mm. Second, Codari et al presented a method for automatic cephalometric landmark location on CBCT volumes. In this approach, after automatic hard tissue segmentation, a nonrigid holistic registration between objective and reference volumes is done. Then, cephalometric landmarks on a reference volume are registered onto the objective volume. They reported a 1.99-mm mean localization error for 21 landmarks on 18 CBCT volumes. Third, Sahidi et al introduced a software for cephalometric landmark localization on CBCT. They reported 14 landmarks localizations with less than a 4-mm mean localization error and 63.57% of landmarks with a mean localization error less than 3 mm using their manual localization (ground truth). Fourth, Makram and Kamel proposed a system for automatic localization of 20 hard tissue cephalometric landmarks using reeb graphs on 3D patient meshes where some nodes were considered as cephalometric landmarks. Ninety percent of their landmarks had a localization error less than 2 mm.

Cephalometric landmarks have been traditionally studied in 2 dimensions in orthodontics. However, because the head is a 3D structure, it is necessary to locate its position in 3D space. In this article, we introduce a hybrid technique based on the active shape models (ASM) of Cootes et al for a holistic automatic 2-dimensional (2D) landmark approximation in related digitally reconstructed radiograph projections. After that, we applied the knowledge-based approach of Gupta et al for landmark localization improvement and adjustment in cropped subvolumes. Our approach has been tested on 24 CBCT volumes for automatic localization of cephalometric landmarks.

## Material and methods

The sample for this experiment consisted of 24 large field-of-view CBCT head volume scans from the Virtual Skeleton Database from the Medical Image Repository of the Swiss Institute for Computer Assisted Surgery; they are 0.4-mm isometric voxel DICOM volumes with about 320 slices. No demographic data were available, and volumes were not identified by age, sex, or ethnicity. As indicated in Table I 18 cephalometric landmarks were selected and manually annotated on sagittal and coronal projections from each volume for ASM training. To establish true positions of selected cephalometric landmarks, manual annotation was independently made twice by 2 observers (R.S.V., J.M.T.) with varying landmarking experience on rendered volumes in 3DSlicer. The mean localization from manual annotation for each landmark was taken as our ground truth.

Landmark | Definition |
---|---|

Sella (S) | Midpoint of rim between anterior clinoid process in median plane |

Nasion (N) | Midsagittal point at junction of frontal and nasal bones at nasofrontal suture |

Basion (Ba) | Most inferior point on anterior margin of foramen magnum, at base of clivus |

Orbitale (O _{R }and O _{L }) |
Most inferior point on right and left infraorbital rims |

Anterior nasal spine (ANS) | Most anterior limit of floor of nose, at tip of ANS |

Posterior nasal spine (PNS) | Point along palate immediately inferior to pterygomaxillary fossa |

A-point (subspinale) | Most concave point of anterior maxilla |

B -point (supramentale) | Most concave point on mandibular symphysis |

Gonion (GoR and GoL) | Points in the middle of the curvature on angles of the mandible |

Pogonion (Pg) | Most anterior point along curvature of chin |

Menton (M) | Most inferior point along curvature of chin |

Porion (PoR and PoL) | Most superior point in left and right anatomic external auditory meatus. |

Gnathion (Gn) | Perpendicular on mandibular symphysis midway between Pg and M |

Incisor inferior (Ii) | Incisal edge of the most prominent mandibular incisor |

Incisor superior (Is) | Incisal edge of the most prominent maxillary incisor |

Our proposed approach for automatic 3D landmarking on CBCT consists of 3 main steps described in Table II and illustrated in Figure 1 . DICOM volumes were loaded into MATLAB (MathWorks, Natick, Mass) without previous preprocessing. In the first step, a holistic ASM cephalometric landmark search is performed on corresponding coronal and sagittal digitally reconstructed radiograph projections. In the second step, based on first-step approximation, a subvolume cropping for each 3D landmark is performed. In the third step, for each cropped subvolume, 3D contours are described by individual mathematical entities based on each landmark’s definition to locate 3D landmarks. Finally, automatically annotated landmarks can be visualized on the 3D multiplanar reconstruction representation of the volume.

Automatic 3D cephalometric landmark annotation | ||
---|---|---|

Start | Loading volume DICOM data | Automated |

Step 1 | Model-based holistic landmark search | Automated |

Step 2 | Subvolume cropping | Automated |

Step 3 | Knowledge-based local landmark search | Automated |

End | 3D landmark annotation on CBCT volume voxels | Automated |

For the model-based holistic landmark search, we use a holistic approach for a fast 3D approximation of cephalometric landmarks on CBCT volumes by shape adjustment (ASM) on 2 related digitally reconstructed radiograph projections. An ASM is a simple and robust tool for statistical shape analysis. The principle of the digitally reconstructed radiograph as an intensity projection is to project all slices within a volume into a single 2D image based on the attenuation absorption law.

We generate coronal and sagittal digitally reconstructed radiograph computed projections with no magnification, and they were used as conventional cephalograms as in the study of Kumar et al. The projections were manually traced using 48 digitally reconstructed radiograph projections to train 2 separate ASMs, a 70-point coronal model and a 95-point sagittal model.

Shape and gray-intensity appearance models were created as in the study of Hutton et al, and localization results were validated by the leaving-one-out approach. Mean localization errors of 3.89 mm for coronal landmarks and 4.01 mm for sagittal landmarks were achieved. Figure 2 shows the ASM adjustment on coronal and sagittal digitally reconstructed radiographs. Because of the high localization errors, a new training for the gray-intensity model by k-means bone segmentation was done. Image fusion was performed on mean intensity projections, standard deviation projections, and maximum intensity projections to increase the digitally reconstructed radiograph imaging quality, demonstrating a better performance in ASM adjustment; this achieved a mean localization error of 3.31. An approach for tridimensional landmark estimation from 2 related projections was presented by Brown and Abbott ; they mentioned a basic algorithmic plane relationship for future implementation. We use individual projection ASM search results to obtain approximated 3D cephalometric landmark locations.

By related projections search, we find a single 3D point for each landmark by relating coronal and sagittal localization landmark coordinates in the sagittal plane (Πs)

( Πs )

were denoted as PΠs=(0,yi,zi),

P Πs = ( 0 , y i , z i ) ,

and the same landmark coordinates in the coronal plane (Πc)

( Πc )

were denoted as PΠC=(xi,0,zi).

P ΠC = ( x i , 0 , z i ) .

To represent every cephalometric landmark on R3

R 3

, PΠs,

P Πs ,

and PΠC

P ΠC

coordinates were merged as P=(xi,yi,zi)

P = ( x i , y i , z i )

, being P our approximation of the 3D cephalometric landmark locations by related Πs

Πs

and Πc

Πc

landmark coordinates associated with a CBCT volume. In this way, this holistic approximation of 3D cephalometric landmarks allows us to crop subvolumes based on localization errors in our whole dataset to be used for local search. Figure 3 shows how subvolume cropping on CBCT is performed based on related ASM results by forming individual landmark clusters.

We use a knowledge-based local landmark search. Our approach for cephalometric landmark localization on CBCT volumes can be seen as an improvement of the study of Gupta et al, because we are performing a faster initialization. As a result, we are achieving a quantitatively more efficient, fully automatic landmark search. This unique method complements the standard clinical assessment used to qualify and quantify malformations affecting head bone structures by simplifying the search for 3D cephalometric landmarks in specific subvolumes ( Fig 3 ).

Eighteen subvolumes (1 for each cephalometric landmark) were segmented from 24 CBCT scans on cluster size based on those locations from the related projections. After we determined the volume of interest, 3D contours were detected, and an individual landmark search starts based on mathematical entities. Each contour (C) is defined as a succession of voxel coordinates:

A preprocessing operation can be performed to smooth the contour values, depending on cephalometric landmarks. Subsequently, by means of a mathematical entity, a particular target point (cephalometric landmark) is selected from the rest of the points in the contour. For different landmarks, mathematical entities are associated with the knowledge of landmark locations according to their definitions (eg, highest point, farthest point, lowest point) evaluating their proximity on each contour. Twelve landmarks in our set have been located as prescribed by Gupta et al —nasion, ANS, PNS, A-point, B-point, pogonion, gnathion, menton, orbital right, orbital left, gonion right, and gonion left. The remaining 6 points (sella, basion, incisor superior, incisor inferior, porion left, and porion right) were localized according to the knowledge approach included in the individual mathematical entities that represent each. Next, subsections describe the process to find those 6 landmarks that have not been studied before on 3D volumes.

For sella, a 3D contour was not generated on the skull structure because sella is a reference point in the center of a cavity, according to its cephalometric landmark definition.

To generate the contour of the anatomic geometry in the sella subvolume, each sagittal slice on the y-z plane was sequentially traversed in the x-axis direction to fit a circle on bone structures by using the Hough transformation. According to the normal limits for length and height of sella on radiographic projections, the centroid of a theoretic cylinder with a radius of 4 to 5 mm and a length of 13 to 17 mm must contain this cephalometric point. Thus, a search radius on slices in this subvolume can generate a succession of circles to approximate a virtual cylinder. Then, the center of this cylinder can be taken as sella’s 3D location. This location can be expressed as a mathematical entity:

C S ( x i , y i , z i ) = ( a r g max 1 ≤ k ≤ l R k ( s l i ) , R k ( s l i ) , i )

where *R *_{k }is the values of the largest radius found and associated with the coordinates of the center in each slice of the i-th circle found on yz (sli)

( s l i )

of the volume of interest and i = {1,2, …, N}. Subvolume and landmark searches are shown in Figure 4 , and an adjustment of a circle on clear edges of the expected size of sella can be visualized. By collecting the position of the detected circle centers on each sagittal section, a succession of those circles approximates a cylinder, forming a virtual anatomic structure of sella; then cephalometric landmark location can be estimated by: