Computerized girth determination for custom footwear manufacture

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Abstract

Good fitting footwear requires matching not just the linear dimensions of feet but their girths as well. Footwear fitters have been using manual measurements for a long time, but the development of computerized techniques and scanner technologies have now made automatic determination of different foot dimensions feasible. The resistance to using such computer measurements has been the lack of trust in the accuracy of the data. This paper proposes an approach to obtain the necessary girths of feet in order to customize footwear. The proposed approach attempts to simulate the manual measurement procedures, and its effectiveness is assessed through an experiment with 15 foot castings. The results show that the simulated measurements can be within 5 mm of the manual measurements if the measuring locations can be correctly identified. Linear regressions show that the differences between the manual measurements and the simulated measurements can be modeled with the addition of a systematic error term of less than 4 mm. The computerized acquisition of foot dimensions is a useful way forward for custom shoe manufacturers.

Introduction

Anthropometers and plastic tapes are commonly used for obtaining measurements on people (Hu et al., 2007). Traditionally, foot dimensions, such as length, width, and girth, are measured using a ruler, tape, caliper, and other special devices, such as the Brannock device (Brannock, 2006), the Ritz Stick (Ritz, 2006), the Scholl device etc. (Hawes and Sovak, 1994, Rossi, 1983). These linear and girth measurements are then used to evaluate the degree of fit between feet and footwear (Witana, Goonetilleke, & Feng, 2004) and they have also been used to generate the three-dimensional (3D) shapes of feet (Luximon and Goonetilleke, 2004, Luximon et al., 2005). Anatomical points or landmarks on the foot are used for the measurements (Au and Goonetilleke, 2007, Luximon et al., 2003, Witana et al., 2006), but, unfortunately, the measurement definitions tend to differ among different footwear standard organizations (SATRA Footwear Technology Center, 1982, Venkatappaiah, 1997).

With the development of 3D digitalization technologies (Treleaven, 2004), there is now an opportunity to determine such dimensions automatically from scans of feet (Witana et al., 2006). However, footwear fitters still rely on manual measurements due to their distrust of computerized systems (National Research Council, 1997), especially for measuring foot dimensions, and also due to the inability of such systems to locate the exact anatomical locations in order to obtain the necessary measurements.

Bunch (1988) used a 3D digitizer to collect the coordinates of 34 landmarks on the foot surface from which the foot dimensions were determined with a computer program. In another study, Liu, Miller, Stefanyshyn, and Nigg (1999) used an electromagnetic digitizing device to get the coordinates of 26 points on the surface of the foot and leg, from which 23 variables that included heights, lengths, widths and angles were computed. Tsung, Zhang, Fan, and Boone (2003) used an optical 3D digitizing system to obtain dimensions such as foot length, foot width, rearfoot width, contact area, arch height, and arch angle. The reported accuracy of each measure in each of the studies differs among these studies. All such studies have mostly reported linear dimensions and have seldom dealt with foot girth due to the complexity of calculating the girths from a foot scan.

Foot girths are known to be important for fitting a foot to footwear (Rossi, 1988), especially custom-made shoes such as ski-boots (Butdee, 2002, Chang et al., 1988). Generally, a cloth or plastic tape is laid around the foot surface to determine the girth measurements, as shown in Fig. 1. Due to the non-uniform contours on the foot, the tape is generally not in contact all along the surface of the foot. Yet, footwear manufacturers have perfected the manufacture of shoes from such manual foot measurements.

If the girth measures are to be obtained from scanned data, the computer-generated data have to simulate the manual measurements obtained with a simple tape. Therefore, girths computed along the surface using geodesic distances (Kimmel and Sethian, 1998, Novotni and Klein, 2002, Polthier and Schmies, 1998) or other types may not be suitable as they may not simulate the manual tape measurements where the tape is wrapped around the foot in a certain way. The approach proposed in this paper is a means to simulate the manual measurements so that foot girths can be obtained reliably and relatively quickly so that footwear customization can become more widespread.

Section snippets

Equipment

The YETI™ I laser foot scanner (Vorum Research Corporation, 2000) was used to obtain the surface data of the foot. Four lasers shine a line of light on the surface. Eight cameras then capture images of the reflected laser light as the laser light advances along the scanned surface. The captured information is then used to create the 3D coordinates of 360 points in each section, spaced 1.0 mm apart, along the length of the foot.

Types of girths

Ball girth, instep girth, waist girth, long heel girth, short heel girth and ankle girth are important dimensions for designing personalized footwear (Miller, 1976). This paper thus focuses on determining these six girths from 3D point clouds of scanned data. The definitions of these dimensions are given in Table 1. Depending on the relative positions in the 3D coordinate system, girths can be divided into three types: (1) those that have the normal of the girth plane parallel to one and

Experimental evaluation

To test the proposed method and algorithms, 15 models (or castings) of the feet of real people, made of plaster of Paris were used. The foot models were manually measured, with a tape, by an experienced operator twice (two repetitions) in order to obtain six sets of traditional manual measurements (MM) of girth.

The foot castings were scanned thereafter with 5 mm diameter black stickers placed at nine anatomical landmarks so that the ball of the foot and the ankle bones could be identified. The

Discussion

Determining foot girths using computerized procedures so that the measures thus generated are not different from manual measurements is a non-trivial activity. The simplest approach is to determine the points within a certain bandwidth and then to calculate the total point-to-point distance along the required perimeter. Such an approach, however, produces a jagged line along the perimeter, which is different from the measuring tape used in manual measurements, which follows a continuous curve

Conclusions

Overall, obtaining computerized measurements from scanned data is viable as long as accuracies of around 5 mm are acceptable for footwear manufacture. It is understandable that there is some level of distrust in computerized measurements. The algorithms proposed in this paper could potentially be improved to increase the accuracy so that they can then be integrated into footwear CAD/CAM systems (Bao et al., 1994, Chen, 1988) as there is a trend towards footwear customization (Viavor, 2006),

Acknowledgements

The authors thank the Research Grants Council of Hong Kong for funding this study under Grant HKUST 6162/02E. The first author was supported by the National Natural Science Foundation of China (NSFC) No. 60603079.

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