Numerical Comparison
of 3-D Shapes:
Potential for
Application to the
Insensate Foot
Robert B. Borchers, MS
David A. Boone, CP
Aaron W. Joseph, MS
Douglas G. Smith, MD
Gayle B. Reiber, PHD
ABSTRACT
A quantitative method for comparing
external foot shapes has been developed
and evaluated for potential application
to custom shoes/orthoses and orthopedic research. The system employs a laser scanner and custom software to obtain more than 16,000 points (every 3
degrees radially, every 2 mm proximal-distal) over the entire foot (dorsal and
plantar aspects). The high-resolution
images are transferred to a computer
workstation where the foot shapes are
aligned, compared and relative differences between the shapes are graphically displayed.
The accuracy, reproducibility and
performance of the foot comparison
system are well within the tolerances required for clinical use. When comparing measurements on objects of known
size and shape to those determined by
the system, the maximum aggregate system error (both hardware and software)
was less than 1 mm. The numerical algorithm for digital alignment of
scanned feet is reproducible to I degree
and .01 mm translation. The average
computer time for comparison of
scanned images in this study was 10 seconds; the entire process, including digitizing, took less than 15 minutes.
Although this system unrealistically
treats the foot and shoe as rigid entities,
it is consistent with the goal of providing
shoes and insoles that reduce the risk of
ulceration in insensate feet during shoe
break-in or normal activity.
Introduction
Half of all diabetic individuals develop
peripheral neuropathy within 20 years
of their disease diagnosis (1). This neuropathy alters foot anatomy, resulting
in foot deformities and decreased sensation (2). The loss of protective sensation means many patients have no
mechanism to warn of lower-extremity
pain, pressure or trauma (e.g., a nail
protruding through the shoe or new
shoes blistering the skin). Footwear
with protective modifications is needed
to prevent or treat minor trauma,
which initiates half of all diabetic amputations (1).
Orthotic or pedorthic treatment of
the neuropathic foot aims to support
and accommodate the foot shape in a
manner that will avoid trauma. The
most common treatment for the neuropathic foot is accommodation of the
plantar surface through a customized
inlay. Individual orthotists may be successful in accommodating the foot geometry of individual patients, but systematic studies of foot deformity and
the relationship of foot shape to successful inlay and shoe shape are hampered by the difficulty in defining and
measuring differences in complex
three-dimensional (3-D) shapes such as
feet and shoes. Further, characterizing
both neuropathic foot geometry and
the form of structures used to treat and
protect the foot are essential in implementing computer-aided design and
manufacturing (CAD/CAM) systems
for clinical use.
The first generation of CAD/CAM
systems for orthotics and prosthetics
has been established as useful clinical
tools (3). These systems allow for efficient design and creation of custom
mobility aids for many people. In the
case of persons with a neuropathic
foot, however, the first-generation
CAD/CAM tools have two significant
limitations.
First, the current systems for insole
development (Amfit, Foot Image
Technology) work almost exclusively
with the plantar aspect of the foot while
ignoring the dorsal aspect. This limitation has arisen because full-foot digitizers are relatively rare, and orthoses are
designed to contact only the plantar
surface of the foot. This view neglects
that the internal volume of the shoe
must accommodate the entire foot-and-orthosis combination, both plantar and dorsal aspects. An insole uses
part of the available volume of the shoe
and changes the foot and shoe interface.
In the case of an insensate foot, changes
in areas of contact are potentially harmful and must be controlled (4).
Second, while systems for designing
custom shoes (CAPODC, Last-Fit) do
use the full 3-D foot shape, they do not
allow the clinician adequate control
over the shape for orthosis development. Some systems allow for shape
manipulation, but none of the systems
offers the advanced blending, template
and modification tools used in prosthetic CAD software. Again, for the
insensate foot, the ability to manipulate the shape of the insole in conjunction with the definition of the last shape
especially is critical when the orthotist
must care for a foot with, or at risk of,
ulceration.
Most limitations in the current generation of software and hardware for
use in orthotics can be overcome by
modifying existing CAD software and
using available full-foot scanners. The
piece still necessary (and the goal of
this article) is the development of a tool
for quantitatively comparing 3-D foot
shapes and insoles with the available
shoe volume. Previous work by this
group (5) applied the concept of computer-calculated rectification maps (6)
(a color or pattern display of 3-D shape
variations) to prosthetics as a means
for understanding shape change in a
prosthetic socket. These graphical displays of shape variation are exactly the
tools required for care of the insensate
foot, and with them a clinician can develop insoles that best address an individual's orthotic needs while taking
into account the available shoe volume. We describe a general algorithm
for quantitatively measuring and displaying three-dimensional shape variations as well as one possible method for
implementing such an algorithm into a
CAD/CAM system for orthotics.
Methodology
Digitizer
After scanning, the image was post-processed by the scanner system into a
series of regularly spaced planar sections. This step involves taking the independent images from the two scanning heads and "welding" them into
one image. The alignment of images
was controlled through a user-specified
calibration matrix, and the "welding"
process simply removed overlapping
points after alignment. After processing, the medial and lateral foot slices
were regularly spaced every 2 mm
along the length of the foot and consisted of approximately 250 points around
the circumference of each slice.
The scanner was very sensitive to
skin coloration, hair and levels of ambient light. Skin coloration and hair
were controlled in this project by having the subjects wear a tight-weave nylon stocking during scanning. Ambient
light was removed by scanning in a
dark room.
Software. The processed image file
from the Cyberware scanner was imported into the DVA/ShapeMaker?
(8) CAD/CAM programs where the
data set was resampled and filtered.
The Cyberware image files included
minimal artifacts due to spurious reflections from the area around the foot
being digitized (e.g., dust and
smudges). These artifacts were manifest in the foot image as drastic spikes
that were removed in ShapeMaker using a two-dimensional cubic interpolation algorithm that uses the surrounding data to remove the spike. During
importation of the data, the ShapeMaker software resampled data sets
both around the circumference and
along the length of the foot, ensuring
uniform resolution of each foot image.
After filtering and resampling, the foot
data sets were transferred to a computer workstation for alignment and comparison. All custom software was written in the C programming language
within the Explorer' development environment.
The foot image data set consisted o
"slices" spaced every 2 mm along the
length of the foot and "points" locate
every 3 degrees around the slice. For
an average size 9 foot, this data resolution resulted in approximately 16,00(
points (133 slices; 120 points/slice) de
scribing the foot's surface. The convention for these data sets was that the X
axis was aligned with the foot's proximal-distal axis, the Y-axis was along
the foot's medial-lateral axis, and the
Z-axis matched the foot's plantar-dorsal axis (see Figure 1
).
Foot position on the scanner could
not be perfectly controlled during digitizing, so the 3-D images were not
aligned and, therefore, had an inconsistent reference frame. These images
required software alignment before
comparison since misaligned images
would yield misleading results and
could potentially mask subtle, but important, shape differences.
Precisely aligning two objects by
hand is laborious and nonreproducible.
Two primary algorithms were available
for aligning a set of objects: (1) aligning
the objects according to known landmarks (fiducial points) or (2) aligning
the objects so they minimize an error
function (e.g., least mean square error). Our previous work (5) used an
error minimization principle. If two
different-sized rectangular blocks of
material were digitized and aligned using error minimization, after alignment
the smaller block would be centered
within the larger block. In this case,
this method makes no physical sense
since both blocks were digitized resting
on the same glass plate. Thus, for aligning the foot we used landmark alignment because it was more intuitive and
yielded results as accurate and reproducible as error minimization.
The key to alignment based upon
landmarks is identifying distinguishing
features that are in a repeatable location from object to object. The three
human foot landmarks we used to determine a consistent reference frame
were the center of the heel, the weightbearing plane of the foot and the centroid of the slice containing the first
metatarsal head (see Figure 1
). These
landmarks were selected for their physiological basis and for ease of location
during computation.
To align the heels, the center of the
slice 10 mm anterior from the back of
the heel was located on both feet and
used as the origin in the medial-lateral
direction. All feet compared in this
study were digitized at the same height
on the scanner (in contact with the
glass plate) and so the lowest point on
each foot was located and used as the
origin in the plantar-dorsal direction.
Finally, the slice that was widest in the
medial direction (first metatarsal head)
was located on the foot, and the center
of the slice was calculated. A line from
the center of the heel slice through the
center of this most medial slice was calculated and used as the axis in the posterior-anterior direction.
After the landmarks were identified
in each foot file, the feet were rotated into proper orientation and then translated
into final alignment (see Figure 2
).
Controls for making fine corrections to
the alignment in all directions (rotation
and translation) were incorporated into
the software to allow the user to be the
final arbiter of alignment.
When all movements of the feet
were complete, both images were
evenly resampled along the length of
the foot and around each slice using a
cubic B-spline interpolation algorithm
(9).
Foot Comparison. The foot images
were compared, and the differences
calculated, point-by-point. With each
foot regularly sampled around the slice
(every 3 degrees) and along the length
of the foot (every 2 mm), finding
matching points to compare was
straightforward. Data points on the
same radial line in the same slice were
in the same position in the data array,
so calculating alignment errors only required subtracting matching coordinates (see Figure 3
). The differences
calculated were differences in Y (medial-lateral), differences in Z (dorsalplantar) and radial differences
([Y2+Z2][1/2])
According to the magnitude of each
nodal difference (node defined as a
point on the surface of the foot), a color was assigned to that node. Shades of
red indicated regions where one foot
was larger than the other while shades
of blue indicated areas where that foot
vas smaller than the other. Thus, when
the feet were rendered, a color map
was shown on each surface, indicating
the magnitude of the shape variation
between the feet being compared (see
Figure 4a,
Figure 4b,
, Figure 4c,
and Figure 5a
), Figure 5b
) and Figure 5c
). The total sum nodal
variation in each direction also was calculated and reported as a means of assessing the quality of alignment between the feet. A lower total sum nodal
variation in shape between the feet indicated a better alignment.
For further precision in calculating
shape variations in general regions,
two options were available: the color
mapping scale could be narrowed over
a specific range of interest (e.g., -5 mm
to 5 mm) or a list of exact nodal values
could be displayed for a specific region.
In practice, we found the information
contained in the color-mapped feet was
more than sufficient.
Results
In calibration trials prior to foot scanning, the shape data obtained from the
laser scanner was compared to three
standard shapes (two with rectangular
cross sections, one circular). The calibration matrix used for "welding" the
two half-images was determined by
comparing caliper measurements from
the standard shapes to the digital image. After calibration, the digital shape
data were compared to caliper measurements at regular intervals, and the
average system error in the radial direction was determined to be less than
1 mm. The maximum error along the
length of the foot was 2 mm.
The accuracy of the custom software
was validated by taking two identical
foot images and moving one with respect to the other. The two feet were
then put into the foot comparison software for automatic alignment and
shape difference calculation. The
alignment error using landmark alignment only (no manual alignment) was
less than .1 degree rotation and .3 mm
translation.
To demonstrate the alignment process
and comparison data, we used two sets of
scans. The first set compared the shape of
a size 9 diabetic foot under weightbearing
to a typical walking shoe last.
The last, a mold used during shoe
construction, represents the internal
volume of the shoe and hence a foot/
last comparison yields information on
how a particular shoe will fit a person's
foot. Large foot and shoe volume vanations were observed between the foot
and last (see Figure 4a
, Figure 4b
and Figure 4c
).
On the medial side, the great toe
protruded 5 mm medially out of the last
volume, and the fifth metatarsal head
protruded 5 mm laterally. Clinically
these mismatches in shape correspond
with problem areas of frequent ulceration. The plantar surface view (see
Figure 4b
) shows the difference between the shape of the supporting surface beneath the metatarsal heads and
the form of the weightbearing plantar
surface, which may lead to less-than-optimal distribution of supporting
forces. Along the dorsal aspect of the
foot, larger shape differences were visible since the last was 8 to 12 mm larger
than the foot. In the heel region the
size 9 foot was 8 to 10 mm wider than
the last. Generally, the last is larger
through the toe box than the foot while
the foot was larger than the last in the
heel region.
The second set of scans aligned and
compared the shape of a subject's foot
with no weightbearing (NWB) with the
same foot under weightbearing (WB)
at a level of 95 percent of full body
weight. Comparing the foot images after landmark and manual alignment
(see Figure 5a
, Figure 5b
, and Figure 5c
) clearly shows
the expected differences between the
WB and NWB feet. The height of the
medial arch of the WB foot was decreased, and the phalanges and metatarsals were spread both medially and
laterally in the weightbearing plane
when compared to the NWB foot. Additionally, the heel of the WB foot was
widened, and the talus has rotated medially on the calcaneous as the foot adjusted to the new loading configuration. Clinically these comparisons provide quantifiable confirmation that the
shape of the foot depends greatly on
loading conditions.
Discussion
The accuracy of the laser scanner system limited the accuracy of the entire
system. Once the data were in ShapeMaker or the software written for this
study, no appreciable loss of data resolution or accuracy occurred. Within the
scanning system (hardware and software), the largest source of error was
the software used to align images from
the separate heads of the Cyberware
scanner. The calibration matrix and
"welding" process introduced seams
along the side of the foot image that
could not be completely removed, adversely affecting the scanner's accuracy. While the seam degraded the measured system's accuracy, the scanner
was accurate enough to resolve features on the foot's surface such as veins
and bony prominences.
Several alignment landmarks were
considered for use in the automatic
alignment algorithm described above.
The weightbearing plane, heel and first
metatarsal head were chosen because
they are physiologically significant and
easy to use during computation.
Choosing the weightbearing plane was
an intuitive and necessary selection because all of the feet were digitized during weightbearing on the digitizer support plate. The heel and first metatarsal slice were realistic landmarks when
considering how a foot fits into a shoe.
The heel is centered consistently and
captured by the shoe while the toe box
of the shoe constrains the widest parts
of the foot (the first and fifth metatarsal heads).
Optimally, the alignment software
would align perfectly the feet being
compared and remove the need for any
manual intervention - This scenario,
however, was not possible since a perfect set of alignment landmarks could
not be defined. Even if a "perfect" set
of alignment criteria could be calculated, in a clinical setting this would not
be advantageous. Clinicians judge
alignment differently and that definition may change from foot to foot. Incorporating tools to manually move the
feet in software removed some of the
system's reproducibility, but gave the
user more confidence in the displayed
differences and insight into the comparison process. Future versions of the
software might reach an agreeable
compromise between clinical control
and accuracy by allowing for user-defined landmarks.
This comparison process unrealistically treats the foot and shoe as rigid
constructs that do not accommodate
one another. In practice, the normal
foot adapts somewhat to the shape of
the shoe and vice versa; however, this
limitation in flexibility is reasonable for
research on the neuropathic foot since
the patient will have reduced protective sensation and increased tendency
to ulcerate from ill-fitting footwear.
Considering the foot and shoe as rigid is consistent with the goal of providing better-fitting footwear without a
period of breaking-in the shoe or
"breaking-down" the foot. Later versions of this software might be able to
incorporate some simple material
properties of the foot and shoe so as to
predict the true interference between
the two. Until such data are available,
the clinician can still interpret the results knowing where the soft tissues in
the foot will adjust to the shape of the
shoe and where the foot/shoe interference might be problematic.
For research into the neuropathic
foot, the comparison software has
proved invaluable. By comparing digital images of subjects' feet, general
morphological trends in the diabetic
foot can be determined and shoes can
be designed that adequately consider
the unique needs of diabetic subjects.
Additionally, with the ability to follow
study participants, temporal quantitative data can be gathered on the change
in foot shape during the course of the
disease. Such information and developments may eventually improve the
quality of life for persons with neuropathic feet and prevent amputations
due to poorly fitting footwear. The application of this technology to individuals with diabetes and foot insensitivity
will improve the insole/foot interface
and afford protection for the high-risk,
insensate foot.
Along with providing understanding
of the morphology of the diabetic foot,
this software also offers new insight into
the normal foot. The general observations of the nonweightbearing and
weightbearing feet match clinical and
functional observations that have been
long recognized but not quantified. Until now the exact magnitude of the
changes in foot shape during weightbearing was unavailable. The color mapping of the radial differences calculated
by the software shows this new information in a concise manner.
The general observation that the
arch of the foot dropped during weight
bearing becomes quantitative since
Figure 5c
showed that the magnitude of
the shape change in this region was 2.
to 2.5 mm. The same figure shows that
the great toe and medial malleolus
moved similar amounts in the medial
direction. The largest magnitude shape
change was observed in the heel region
(see Figure 5b
) where the heel pad widened by 7.5 to 10 mm.
In the field of orthopedic surgery,
digital preoperative image of a patient's foot can be compared to image
of the same foot at various times post
operatively. Such information would
be extremely valuable in determining
whether a particular surgery had the
desired effect on foot shape and how
that shape changed over time. Comparison of a preoperation foot to the
shapes of existing footwear could also
guide the surgeon in surgical planning.
It would also be valuable to follow the
effects of disease processes such as
Charcot Collapse or Posterior Tibialis
Tendon Rupture Syndrome on the
shape of the foot.
The cost of a full-foot digitization
and comparison as used for this investigation is prohibitive for clinical use at
this time. The software itself could easily be imported into a PC or Macintosh
computer already widely used by clinicians for CAD/CAM applications, but
less expensive full foot scanner is not
currently available.
Conclusion
The shape comparison software described here has many potential applications in the care for insensate feet
and the wider fields of orthotics and
orthopedics. Some assumptions about
the foot/shoe/insole construct have
been made during development but are
reasonable given the information available and the special case of the insensate foot. As more data are available
on foot morphology, the software will
evolve into an even more useful clinical
tool. In the present state, though, the
system described here will have a positive impact on the care for persons at
risk of limb loss and can be a useful part
of second-generation CAD/CAM tools
in orthotics.
Acknowledgements
This research was funded by the Department
of Veterans Affairs Rehabilitation Research
and Development Service. The authors
would also like to thank Nike Inc. for providing last shape information and Cyberware for
its helpful discussions on laser digitizers.
ROBERT E. BORCHERS, MS, is a research engineer at the Prosthetics Research Study (PRS), 720 Broadway, Seattle, WA 98122; (206) 328-3116.
DAVID A. BOONE, CP, is director and co-principal investigator at PRS.
AARON W. JOSEPH, MS, is a research engineer at PRS.
DOUGLAS G. SMITH, MD, is an assistant professor of orthopedic surgery at the University of Washington and is co-principal investigator at PRS.
GAYLE E. REIBER, PHD, is an assistant professor of epidemiology and health services at the University of Washington and is co-principal investigator at PRS.
References:
- Reiber GE, Pecoraro RE, Koepsell T.
Risk factors for amputation in patients with
diabetes mellitus: a case control study. Ann
Intern Med 1992; 117:2:97-105.
- Gooding GAW, Stess RM, Graf PM.
Somography of the sole of the foot: evidence for loss of foot pad thickness in diabetes and its relationship to ulceration of
the foot. Invest Radiol 1986; 21:45-8.
- Kitzmiller VG. Automation helps
O&P soar through the '90s. AOPA Almanac 1991; 40:41-2.
- Jernberger A. The neuropathic foot.
Pros and Orth Int 1993; 17:3:189-95.
- Sidles JA, Boone DA, Harlan JS,
Burgess EM. Rectification maps: a new
method for describing residual limb and
socket shapes. J of Pros and Orth 1989;
1:3:149-53.
- Dewar M, Jarman P et al. Computeraided socket design (CASD). UCL system
based on full shape sensing. Bioengineering
Center Report 1985, University College
London, 1985; 19-30.
- Cyberware Laboratory Inc., Cyberware Model 1503FF Digitizer operating
manual. Cyberware Laboratory Inc., Monterey, CA. Rev. 1991; 1-3.
- Boone DA, Harlan JS, Burgess EM.
Automated fabrication of mobility aids: review of the AFMA process and VA/Seattle
ShapeMaker Software Design. J of Rehab
Res and Dev 1994; 31:1:42-9.
- Press WH, Teukolsky SA, Vetterling
WT, Flannery BP. Numerical recipes in C. 2nd
ed. Cambridge University Press, 1992; 123ff.
|
