## 1 Introduction  
Osteoarthritis has a negative impact on daily activities for millions of elderly people around the world [1, 2]. In relation to the aging of articular cartilage or rotator cuff dysfunction, glenohumeral joint osteoarthritis prohibits smooth motion between the humeral head and glenoid [3]. Previous epidemiology studies show that 32.8% of people with over sixty years old are affected by glenohumeral joint osteoarthritis and debilitated joint function due to the age-related change [1]. The breakdown of cartilage causes the humeral head and glenoid to rub and grind against each other [3]. It induces acute pain and loss of function, i.e., mobility of the arm [2]. To compensate for the cartilage breakdown, excess cells are produced in the humeral head in the form of bone spurs. This leads to even more friction, pain, and limiting of function. Thus, one of the most popular treatments of this disease is to surgically remove the humeral head and replace it with an artificial one [3]. The design of an artificial humeral head is likely to alter the surgical outcome for glenohumeral joint osteoarthritis. Research studies showed that artificial humeral head design with some kind approximation (e.g., spherical or elliptical) did not bring an adequate outcome [4]. It also limited the range of motion (ROM) of the shoulder [5]. Some studies showed that increasing the similarity between the artificial humeral head and the actual one could increase the ROM of the shoulder [4,6]. Therefore, the focus of this research was to discuss a method that can provide patient-specific design of artificial humeral heads. From the previous study in humeral head morphology, the humeral head was composed of different curvatures [7,8]. In addition, [PERSON] et al. [9] clarified that use of elliptical heads resulted in improved replication of the normal humeral head shape in comparison with use of spherical prosthetic heads. Furthermore, the cadaveric study by [PERSON] et al. [4] revealed that the custom, non-spherical prosthetic head more accurately replicated the head shape, rotational range of motion, and glenohumeral joint kinematics than the commercially available, spherical prosthetic heads when compared with the native humeral head. However, humeral head size, including interindividual variation, has not been well investigated. The statistical shape model (SSM) [7] is one of the methods that expresses the interindividual variation of the shape statistically, and is basically used as prior knowledge of various algorithms. SSMs were used in number of medical applications, especially related to bones and joints. To assess the potential risk factors associated with bone fracture, an SSM was used by [PERSON] et al. [10] in their study. They concluded that SSMs might be useful in identifying the individuals at risk of possible femoral fracture. To aid detecting vertebral fractures, SSMs of vertebrae were used by [PERSON] et al. in [11]. SSM was used successfully for early identification of developing radiographic osteoarthritis of hips by [PERSON] et al. [12]. Apart from that, SSMs were used to automate implant design and screw placement in shoulder arthroplasty [13], surgical planning [14], medical image segmentation [7], and implant design [15,16]. SSMs avoid arbitrary assumptions by trying to capture the actual patterns of variability in a set of objects of same class. It is usually constructed by applying principal component analysis (PCA) [17] to feature vectors of multiple individual shapes [18]. PCA is used in other statistical modeling as well [19]. Feature vectors can be classified into two categories: point-based or distance-based feature vectors [7]. The point-based feature vector is calculated from 2-D or 3-D coordinate values of feature points. The feature points between individuals should be associated. Thus, it requires a feature point extraction method, which limits the application. The distance-based method segments the target organ first, and then makes distance map from the extracted organ contour.