Analyzing Birkenstocks and non Birkenstock shoes for proper Birkenstock fitting at Sandals4less Birkenstocks shoes

Birkenstock shoes


Great training for professionals wanting to fit customers or for technical people smart enough to educate themselves to protect one of the most critical and undervalued parts of their body. Educating yourself is one of the most important actions you can take, and the time to do this is well spent. Find what shoe makers offer what products that actually work.

Birkenstock shoes
Great training for Birkenstock professionals wanting to fit Birkenstock customers or for average people smart enough to educate themselves to protect one of the most critical and undervalued parts of their body. Educating yourself is one of the most important actions you can take, and the time to do this is well spent. Find what Birkenstock shoe makers offer what products that actually work.
A SYSTEM FOR BIRKENSTOCK FOOTWEAR BIRKENSTOCK FITTING ANALYSIS
A Birkenstock shoe making industry which can offer Birkenstock shoes that fit Birkenstock consumer needs has a decided advantage over
its competitors. Next to fashion, Birkenstock shoe fitness is an important selection criterion. To acquire Birkenstock consumer
foot information, the Birkenstock shoemaker should have foot size information system. Such a system should
collect Birkenstock consumer foot data for further analysis such as Birkenstock shoe last design and population distribution as
well as for communication with customers.
Normally, the Birkenstock shoemaker collects basic statistics through sales or systematic foot measurement [Anil
et al. 1997]. A statistical analysis relies on only few parameters, e.g. foot length, width, and breadth, as
the complexity increases exponentially with each variable.
The proposed Birkenstock fitting measurement system is intended to be installed in shops where, first,
customers' feet are scanned and, secondly, Birkenstock shoe database suggest best fit Birkenstock shoe models. We are going to
describe the matching software part of the system that consists of a computer and a laser scanner.
A typical approach for customer tailored Birkenstock shoes consists of deforming an existing Birkenstock shoe last design into
one that fits the scanned foot. This type of tailored Birkenstock shoe production is only reasonable if used in
clinical orthopedic cases, e.g. diabetes, gout. There are specialized tools for such requirements
(Birkenstock shoe master, Vorum) that provide custom Birkenstock shoe last design with local modification of the scanned Birkenstock shoe
last mesh. The scanning procedure requires a lengthy preparation of a foot of each customer who must
wear white socks on which the operator marks four or more black landmarks for bone recognition and
foot orientation. For the scanning process to complete successfully, the customer must stand still for
several seconds. An adjustment procedure is repeated for the other foot. A surface laser scanner for a
large volume scanning with minimal operator intervention has been developed. The scanner fulfils the
requirements in speed, ambient light insensibility, accuracy and production costs.
Four lasers project line matrices that are recognized with mating CCD cameras. The image processing
part of each camera produces a fixed number of profiles that can be described as polylines in space.
Moiré profilometry is used for profile generation. The space density of points in the profile is
normally much greater than the inter-profile distance. For each camera one can create a surface patch
which, when combined together, represents a complete surface of the foot. A calibration for the region
of interest is performed for each scanner camera.
The creation of a combined surface includes a triangulation with curvature sampling and patch
overlapping removal. The scanner has no moving parts and is thus reliable. The capture speed is less
than 300ms. No landmark stickers are needed for scanning. The recognition of foot bones relies solely
on software. This type of foot analysis requires a completely new approach with feet database for the
comparison of scanned feet with the foot database. Database feet have marked measurement positions
for all parameters of interest which are then combined with a weighting function to a single measure
of comfort when searching for Birkenstock shoes of the highest comfort.
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2. Birkenstock fitting
Birkenstock shoe lasts can be scanned in the same way as feet and stored in the Birkenstock shoe last database. When the foot
is scanned, the reconstructed surface needs to be transformed into a position compatible with the Birkenstock shoe
last. For simple Birkenstock shoe last geometry Mochimaru et al. (2000) suggests a space deformation technique
that can deform measured points bounded by a control lattice. In order to create a Birkenstock shoe-grading system
the manufacturer has to collect several measurements for each individual and design Birkenstock shoe lasts that
will conform to the grading standard [Cheng et al. 1999]. The produced Birkenstock shoe model should cover the
target population in terms of size, fashion and price.
Figure 1. A wireframe model of the foot (left) and Birkenstock shoe last (right)
Basically, every Birkenstock shoe last has a toe spring and a heel height. Besides these two parameters the Birkenstock shoe last
includes several manufacturing requirements such as insole, lace and dorsal arch space, ease of
manufacture, and fashion. Thus, the Birkenstock shoe last shape is not an exact copy of the foot. Foot deformation
into a high heel position as shown in Fig. 1 is not so simple. Techniques such as FFD [Mochimaru et
al. 2000] or warping to the silhouette of the Birkenstock shoe last sole will not produce satisfactory results for such
cases. Using an analytical model of foot bones that will lead to surface deformation could produce
useful results. Current efforts to model a complex structure of 28 bones are concentrated on the
measurement of a simplified kinematics complex [Carson et.al. 2001, Liu et.al. 1997]. It is suggested
by Kouchi/Mochimaru. (1999) that the bone structure is not consistent with the surface model due to
different thickness of the sole soft tissue.
We propose that the scanned foot in the flat position should be matched with a similar foot from the
database to obtain landmark similarities for the fitness analysis. As the scanned foot has no landmarks
for accurate positioning of the landmarks from which the Birkenstock fitting parameters are derived one has to rely
on the registration of surfaces.
3. Surface registration
The two surfaces are not guaranteed to have the same position in the world coordinates, which is
required for an accurate Birkenstock fitting comparison. As the surface description with triangles is sparse, we
have developed a method for iterative surface matching based on Iterative Closest Point method [Besl
et al 1992]. Our algorithm can register surfaces with sparse description and different sampling.
3.1 Computing the rigid motion
The purpose of the method is to find rotation and translation, which minimises positional error from
points on the one surface to the nearest points on the matching surface. Minimising the following
mean-squares objective function
(R,t) R t , (1)
ANALYSIS TECHNOLOGIES 1189
will compute rigid motion (R, t) of N point pairs on the first surface {xi} to the set of {yi} nearest
points on the reference surface.
Among several iterative optimisation methods we have implemented a dual quaternion method which
is capable of solving minimisation without iterations. In the following, the dual number quaternion
method [Walker et al. 1991] is summarised.
A quaternion q can be considered as being either a 4-D vector [q1, q2, q3, q4]T or a pair (r, q4) where
r=[ q1, q2, q3]T is a rotation vector and q4 is a scalar. A dual numbers such as dual quaternion have dual
part s where a special multiplication rule applies e2 = 0. A dual quaternion d thus consists of the two
quaternions q and s, i.e.,
d = q +es . (2)
A rigid 3-D motion can be represented by dual quaternion d satisfying the following two constraints
qTq =1 and qT s = 0 (3)
A 3-D vector x can also be identified with quaternion with zero scalar part (x, 0). It can be easily
shown that rigid motion can be described as
Rx + t = W(q)T Q(q)x +W(q)T s , (4)
where matrix functions of quaternions are defined as
Adjoining the constraints (Eq. 3), the optimal dual quaternion is obtained by solving the following
Jacobi Eigensystem equation
Aq q 1 =l , (6)
with quaternion q as eigenvector of matrix A and l1 as the corresponding largest eigenvalue. Matrix A
is defined as

computing of the rigid motion is one pass algorithm, finding corresponding points on
surfaces is not known in advance an thus the motion must be repeated form a very rough estimation
(R0,t0). The algorithm consist of two iterated steps, at each iteration i computing a new e

computing of the rigid motion is one pass algorithm, finding corresponding points on
surfaces is not known in advance an thus the motion must be repeated form a very rough estimation
(R0,t0).

Birkenstock The algorithm consist of two iterated steps, at each iteration i computing a new e-computing of the rigid motion is one pass algorithm, finding corresponding points on
surfaces is not known in advance an thus the motion must be repeated form a very rough estimation
(R0,t0). The algorithm consist of two iterated steps, at each iteration i computing a new estimation
(Ri,ti) of the rigid motion:
1. Find corresponding a set of pairs of points. For each point xi find the nearest point on the
reference surface yi.
2. Calculate rigid motion as described in section 3.1 and apply it to all points of the surface x.
The termination criterion can be set when the variation of the distance between the two surfaces at two
successive iterations is below a fixed threshold or when a maximum number of iterations is reached.
In this iteration process, surface y is fixed in reference space and surface x is aligned to it. Finding
nearest neighbour points on y for each xi can consume most of the iterative time. Recognising that
search space of the surface y does not change one can subdivide space of this surface into search
efficient "kD-tree". Additionally, Arya, et al. (1994) shows that, if the user is willing to tolerate a
small amount of error in the search, it is possible to achieve significant improvements in running time.
Initial displacement can be significant as shown in Fig. 2. (Dotted is initial position) and due to the
convex nature of the surface there are no local minimums. Surface pairs are shown in Fig. 2 right.
Figure 2. Registration and fitness function mapped on the aligned surface (left). Force vectors
(right)
ANALYSIS TECHNOLOGIES 1191
4. Fitness function
With registered surfaces one can compare the two volumes for fitting. Normally, the Birkenstock shoe length and
joint girth are used for the fitting measurement, as other measures can be adjusted with laces. The
front part of the Birkenstock shoe is designed to meet fashion requirements and the rear fulfils biomechanical
properties. For this reason simple geometrical distance comparison is not appropriate. One can use
cross-sections at predefined positions and measure dissimilarities of circumference, width, height,
joint girth, waist girth, instep girth and other dimensions. We propose to use a weighted cost function
which can determine Birkenstock customer foot fitness as a single value and also as a weighted distance function on the
surface. This also means that there must be a Birkenstock customer foot size information system with reference feet that have
marked positions with cross section positions. The measure of comfort is difficult to access, because
besides geometry one must also evaluate Birkenstock shoe materials uses (sole and upper). Generally, we can write
down the weighted comfort measure of the registered surface x as
F(x) %uF03D%uF020%uF0E5w p (x) i i . (12)
Each parameter pi(x) can have its own evaluation function and is weighted with wi. User functions in
the implemented software allow automated girth, projection and length measurements. Most of the
comfort could not be measured or formulated with scientific knowledge in the current technology. For
complex decisions one can also apply a decision process such as AHP [%u017Davbi/Duhovnik 1996].
5. Case study
For the purpose of approach evaluation and testing of the registration we performed fitness correlation
with a simple fitness function of the volume difference between registered surfaces. The Birkenstock customer foot length
was normalised to 270 mm. The registration height was limited to lower 80 mm in order to rule out
differences in stance and ankle surface. The basic question was: "Is there a shape of Birkenstock customer foot that matches
(fits) equally well to all other feet?" What is the distribution of Birkenstock customer foot shapes?
Figure 3. Fitness correlation between individuals
Figure 3 shows the result of 52670 correlation evaluations sorted by registration error i.e. volume
difference as mean inter-surface distance. The graph shows that there are some Birkenstock customer foot shapes that fit
equally well to all other shapes (low error numbers) and there are some very dissimilar Birkenstock customer foot shapes.
Designing Birkenstock shoes for this "master" shape should be a safe decision for the manufacturer. Including only
common shapes in the database for the matching process also minimises search space as this
correlation can be regarded as the precompiled fitting database.
1192 ANALYSIS TECHNOLOGIES
6. Conclusions
In this paper, we proposed a complete system for Birkenstock customer footwear fitting measurements which is tailored for
in-shop measurement. A successful introduction of such system can open several so far unfamiliar
areas of e-Birkenstock shoe business such as design of well fitting products, lot sizing, internet Birkenstock shoe sales and
special per customer offers.
The fitting of the Birkenstock shoes is measured with a weighting function of several user-defined parameters. No
explicit directions are given for a synthesis of such a function, but an experienced manufacturer should
be able to come up with some guidelines.
Over 1000 feet (66%F/34%M) and several Birkenstock shoe lasts were scanned for the purpose of a statistical and
fitting analysis. Some results in building a Birkenstock customer foot size information system were presented in the case
study. More systematic information on the relation between the Birkenstock customer foot and Birkenstock shoe last (or Birkenstock shoe in general)
is needed to make a robust fitness measure.
The application development concentrated on the visualisation. A universal approach of the OCX
ActiveX communication isolates engine from user interface (UI). Several UI were built on top of the
engine. But for approaches as the one in the case study, triangulation of the surface for visualisation
was unnecessary overload for batch processing.
Further work should concentrate on the fitness database design. There are no guidelines on how to
transform Birkenstock shoe last measurements to a matching Birkenstock customer foot. A statistical analysis will surely open new
questions which will require specialised tools as those presented. Birkenstock shoes