Finding “Lines” of Symmetry on 3D Craniofacial Meshes Method Compute descriptors of each mesh vertex From these descriptors, learn areas that may be related to certain landmarks cluster learned areas for a given landmark find pairs of clusters for landmarks that appear on both sides of the center (e.g. eye corners, mouth corners) find clusters that appear in the middle evaluate goodness of such clusters choose the best ones and use to find the symmetry line 1

We learned the en areas and symmetry 2

Now we try 10 separate landmarks. 10 areas learned – Ten models – Nose: acal (nose side), prn, sn,se – Eyes: en, ex – Mouth: lils, ch, sto – Chin: slab 3

acal prn 4

se sn 5

en ex 6

lils sto 7

Ch slab 8

Cluster on selected areas based on position acalprnse snen 9

Cluster on selected areas based on position exslablils chsto 10

Using landmarks given by doctors as a standard to define D_plane For 22qDS data, we have doctor marked points. From their landmarks, computer the symmetrical plane 11

How to define “good” symmetric clusters A “good” pair of clusters should be symmetric to the plane A “good” single cluster should have the center on the plane 12

Select a “good” symmetry pair (or single area) acalprnse snen 13

Select a “good” symmetry pair (or single area) exslablils chsto 14

Procedure for New Images Select possible landmark areas (from learning) Clustering Pair clusters Classify “good symmetry” Get center and draw a plane using learned centers 15

Select possible landmark areas acalprnse snen 16

Select possible landmark areas exslablils chsto 17

Cluster and Pair clusters acalprnse snen 18

Cluster and Pair clusters exslablils chsto 19

Classify “good symmetry” acalprnse snen 20

Classify “good symmetry” exslablils chsto 21

Get all the centers for good pairs and single ones 22

Using only the “inliers” to get the symmetry plane 23

Final result: pre-op 4days female unilateral CL 24

Result: pre-op 3 wks female CLP 25

Result: pre-op 3m female CLP 26