Defining the Coordinate System of 3D Foot Model Using Regression Analysis

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1 Defining the Coordinate System of 3D Foot Model Using Regression Analysis Yoitsu TAKAHASHI Hiroki YAHARA Yukio FUKUI Seiichi NISHIHARA Department of Computer Science, University of Tsukuba, Japan Center for Research on International Cooperation in Educational Development University of Tsukuba, Japan Masaaki MOCHIMARU Makiko KOUCHI Digital Human Research Center, National Institute of Advanced Industrial Science and Technology, Japan {m-mochimaru Abstract In this paper, we propose a method defining the coordinate system of a human body model, in order to design products fitting well to the human body, using the data measured by a 3D scanner. We discuss a 3D foot model as an example of the human body models. The foot data measured by a 3D scanner is a simple point cloud, and the coordinate system of the data is fixed to the scanner hardware. The local coordinate system of a foot model using for designing process is defined by three points called Metatarsale Tibiale(), Metatarsale Fibulare() and Pternion. These points were measured manually by professional anthropologists with direct palpation. Thus, it is difficult to find those points automatically and accurately from the point cloud. Therefore, in this paper, we present a method of definition of the coordinate system based on the positions of and which are estimated by using regression analysis. 1. Introduction Products we wear such as clothing, shoes, and glasses are usually designed based on a rough classification of bodily form based on one size covers all. The more this form differs from the standard, the poorer the product fits, requiring costly custom-made adjustment. So it is need system for designing products fitting individual body shape easily [1]. Using anatomical points or landmarks in product design should improve fit, but such landmarks do not always correspond to geometrical features because most are based on subcutaneous anatomy. Improvements in 3-dimensional (3D) scanners have enabled the body to be measured in tens of seconds, enabling landmarks in body data to be detected automatically to develop properly fitting products. Much research has thus been done on generating models using landmarks. Detecting anatomical features or landmarks in the surface data measured by a 3D scanner is difficult. This is because they are found only by direct palpating the body surface. Research on such modeling using data measured by a 3D scanner has focused on generating models based on surface information such as curvature and/or texture, using geometrical landmarks. Other research calculates overall posture using templates and landmarks pre-scanned with a range scanner or in which facial expressions are statistically created using given landmarks. While these are suitable for animation, they are not suitable for generating human models for product design because of the need for

2 dimensional accuracy. Against the backdrop of these, a research was done to generate the model has anatomical landmarks from point cloud using the matching transformation of the standard model by Free-Form-Deformation (FFD) method.[2].the research treated foot models to design shoes. It was necessary to define the local coordinate system of the foot model to adopt FFD method. The local coordinate system of the 3D foot model is defined three important landmarks. But the positions of the points and the coordinate system of the model were treated as known information in previous researches. In this research, we propose the method to define the coordinate system based on positions of and estimated automatically. And using this to the point cloud obtained by 3D scanner, we confirm the validity of the method. 2. Keywords This section explains keywords used in this paper Foot model A foot model treated in this research is composed of three kinds of point groups; a point cloud, anatomical landmarks, and basic landmarks (Fig. 1) Point cloud The point cloud is a set of tens of thousands of points showing the body surface Landmarks Landmarks are points used to establish a correspondence between bodily form and products. They are mostly defined based on anatomical information. So they are measured manually because of the difficulty in finding automatically from a surface automatically [3]. Point Cloud Landmarks Basic landmarks Pternion Fig.1. 3D foot model 2.2. Basic landmarks Basic landmarks are points for defining 3D foot model coordinates which are subsets of landmarks 3 points that we need to define local coordinate system of foot model are defined basic landmarks. Each of them is anatomical landmarks called Pternion, and. In this paper, is point on the surface of shape which is the nearest from the most prominent point on tibial side of the 1st metatarsal head. is also the nearest point, on the surface, from the most prominent point on fibular side of the 5th metatarsal head 2.3. Coordinate system The local coordinate system of the 3D foot model is defined as follows. The intersection point of the vertical line from pternion to the foot bottom surface (or x-y plane) is defined as the origin. The direction from the origin to the intersection point of the vertical line from the midpoint between and to the foot bottom surface is defined as the x-axis. The direction perpendicular to the sole, or the bottom surface, is defined as the z-axis. The y-axis is defined to form a right-handed coordinate system. Figure 2 shows the basic landmarks and the model local coordinate system.

That is extracting several characteristic points which correlate strongly with positions of and, using them as independent variables and coordinates of and as objective variable. Y 3. Method 3.1.

3 Figure.2. shows basic landmarks and the local coordinate system of a foot model. Z Pternion Y Regression analysis is the method that estimate some value using other values, often used to predict or control In this paper, regression analysis is used to estimate positions of and. That is extracting several characteristic points which correlate strongly with positions of and, using them as independent variables and coordinates of and as objective variable. Y 3. Method 3.1. Procedure Expressed easily, our method consist of 5 steps X X shown figure 3 Z Z Y X Fig. 2 Basic landmarks and coordinate system 2.4. Sample model We prepare several foot models which were measured manually by anthropologists. They consist of point cloud, landmarks and Basic landmarks Standard model The standard model is a model in which the average position of the anatomical landmark and the average position of the reference points is defined as its reference points Target model The target model is a foot model which we try to estimated its anatomical landmarks. 2.7 Regression analysis Fig.3. Defining the coordinate system of 3D foot model 3.2 Definition of temporary coordinate system Originally, the definition of directions of x-axis and y depend on positions of and. But the point cloud which we obtain by a 3D scanner does not have information of local coordinate system of foot model. For the reason we can not treat the local coordinate system of foot model at this time. Thus to estimate positions of and, the following

4 method gives point cloud temporary coordinate system. But, in addition, the directions of the z-axes are same between local and scanned raw data. So we can regard x-y plain and z-axis as defined. Then, it is assumed that the direction of the tiptoe doesn't shift extremely because of a foot position while scanned. ( ranges + 5 degree) 1. It is assumed x -axis (this is the x-axis fixed to the scanner) on point cloud projected on x-y plane. 2. We look for the farthest point from Pternion at the x -coordinate. 3. The perpendicular bisector of the segment of a line between this point and Ptrnion. 4. We draw the line from Pternion toward the middle point between both end points of the point cloud on the perpendicular bisector above. 5. The line, drawn step 4, is defined as x -axis. 6. Y -axis is defined to form a right-handed coordinate system with x -axis, defined above step, and z-axis. Figure.4 shows parts of these steps. 4 2 X 3.3. Detection of Anatomical Landmarks on toes We detect anatomical landmarks on toes from point cloud by previous study[4] This method requires position of and as input. But, we can obtain landmarks on toes, even if the values are not so accurate. Thus we give standard model s positions of and 3.4 Estimation of x -coordinates of and We calculate regression equations, used to estimate x -coordinates, from sample data. It is necessary for explaining variables to be obtained the positions of the points accurately from shape information even if the coordinate system is not so accurate. This is why we adopt five toes as candidate of explaining variables Because the method detecting the points has already established The equation which gave the most accurate result, in the exploratory experiment, we adopt to estimate x -coordinate values of. The x -coordinate values of 1st, 4th and 5th fingers toes were used to estimate (eq.1). And about, we use the value of 5th finger s (eq.2). In equations below, the suffix const means constant term x = a1 x1 + a4 x4 + a5x5 + a const (1) 2 x = a5 x5 + a const (2) 3 About these equations, regression coefficients are calculated, from coordinates of toes of sample data. X -coordinate values of and are estimated, by assigning x -coordinates of toes of target model to independent variables. Pternion Fig.4. point cloud projected on x-y plane 3.5 Estimation of y -coordination of and Next, we estimate y -coordinates, also using the regression analysis. But, in this case, it is hard to

5 obtain positions of characteristic points which are adopted as independent variables from the surface shape.in this method, we focus on the points of bottom of a foot model. Among these bottom points, which are fulfill z < 1.5 mm, the maximum of y is defined as ymax in the estimated x -coordinate value of. Also the minimum of y -coordinate is defined ymin in the estimated x of (fig4). And each of them is used to independent variable to estimate y -coordinate values of or (eq.3, 4.). Fig.4.The positions of the points using to estimate y -coordinates y = b y + b (3) ymax ymin ymax ymin const y = b y + b (4) const These regression coefficients are calculated by values of sample data. Positions of these points are extracted from the target model. And each of them is assigned to equation 3 or 4. As above, we obtain y -coordinate values of and 3.6. Definition of coordinate system On the x-y plane, the middle point is located by and which were estimated as above. We draw a straight line from pternion to the middle point, and define the line as the local x-axis of foot model. Next, y-axis is defined to form a right-handed coordinate system with x-axis and z-axis. 4. Result Experiments were carried out in which the coordinate systems of 40 models were defined. The figure 5 shows the results. Here, we define the error as the angle between two x-axes (or y-axes) defined by this method and by the anthropologist. We can regard the errors as small considering the following. The positions of basic landmarks measured manually may have range of 1 mm. And the error is 0.66 degree if pternion of the standard model shift 1mm. Fig.5. Errors of defined X -axes Here, we define the error as the angle between two x-axes (or y-axes) defined by this method and by the anthropologist. We can regard the errors as small considering the following. The positions of basic landmarks measured manually may have range of 1 mm. And the error is 0.66 degree if

6 pternion of the standard model shift 1mm. 5. Conclusion In this paper, we proposed the method for defining the coordinate system based on positions of and which are estimated by regression analysis. As a result, we confirmed that proposal method is effective. Acknowledgment The authors are very grateful to Mr. K. Kimura, President of I Ware Laboratory, Inc., for providing the data and useful advice and discussions. References 1. Japan Leather Industry Association. Easy-order System Research Report H.Yahara, N.Higuma, Y.Fukui, S.Nishihara, M. Mochimaru, M.Kouchi, "Estimation of anatomical landmark positions from model of 3-dimensional foot by the FFD method," Systems and Computers in Japan, Vol.36, No.6, pp26-38, Apr E.Tsutsumi, M.Kouchi, Geometrical modeling of the foot, 5th ASEE International Confference ECGDG, pp , H.Yahara, S.Inou, Y.Fukui, S.Nishihara, M. Mochimaru, M.Kouchi, "Extraction of Five Anatomical Landmarks on Toes of a Foot Model by using the Surface Shape," SAE Digital Human Modeling for Design and Engineering, pp I Ware Laboratory, Inc.

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