## 1 Introduction
Recently, several methods by which to make quantitative assessments of the surgical effects of craniosynostosis have been suggested. [PERSON] [8] et al. compared the measurements for nine patients with sagittal synostosis before and after surgery in 3D scan datasets, which measures the cephalic index, head circumference length passing through glabella and occipital prominence, sagittal length over the head from the nasion in the sagittal plane, coronal width over the head from the left to the right tragion in the coronal plane, and head volume above the Frankfort horizontal plane. [PERSON] [9] et al. compared head volumes divided into six regions for 98 normal subjects and 30 patients with sagittal synostosis before and after surgery in 3D scan datasets. A skull is divided into three areas through two planes, passing through the pituitary fossa and rotating at two angles (84 degrees clockwise on the anterior axis and 31 degrees clockwise on the posterior axis), with the final six areas defined by dividing the mid-sagittal plane. [PERSON] [10] et al. compared the measurements for two patients with metopic synostosis before and after surgery in 3D scan datasets, which included head circumference length, anterior symmetry volume ratio, posterior symmetry volume ratio, and overall symmetry volume ratio. [PERSON] [11] et al. compared the measurements of 10 patients with metopic synostosis before and after surgery and 15 normal subjects in 3D scan datasets, which measures the forehead volume defined by the volume between the base plane and the posterior plane at 120\({}^{\circ}\), interfrontoparietal-interparietal ratio and frontal angle. However, these methods using 3D scan datasets can only provide information about the overall skull surface and not regional skull information. [PERSON] [12] et al. used data from 18 patients (seven with sagittal, one metopic, one bicoronal, one unilateral coronal, three multiple suture synostosis, and five with the pansynostosis types) from a dataset consisting of preoperative 3D CT images and postoperative 3D scans. In the study, two shape metrics were quantified using a shape mismatch degree, referring to a difference between a normal head shape that matches the patient's head shape and the patient's actual head shape and a curvature mismatch, which is the curvature difference between the two shapes. However, because the matched normal head shape is selected as the closest normal head shape to the patient, this method is limited with regard to its ability accurately to reflect the shape mismatch given the selection of a similar head shape. Since the previous methods only use 3D scan data sets, it is difficult to consider information about the regional cranial bones inside the head. In this paper, we propose a method to quantify the surgical effect on regional cranial bones by considering bone information using 3D CT images and comparing the shape of the skull before and after surgery. In order to estimate the shape deformation of the regional area of each cranial bone according various types of craniosynostosis, a mean normal skull surface model consisting of five cranial bones separated by open sutures is deformed into a preoperative skull, after which the deformed mean normal skull surface model is redeformed into a postoperative skull. In order to quantify the shape deformation of the expansion and reduction of the regional cranial bones between the preoperative skull and the postoperative skull, the reduction and expansion indices are calculated using positive and negative distance and area ratio indices.