5th Annual IEEE Conference on Automation Science and Engineering
Bangalore, India, August 22-25, 2009
Automated 3D Geometric Reasoning in Computer Assisted Joint
Reconstructive Surgery
K. Subburaj, B. Ravi, and M. G. Agarwal

Abstract—Computer Assisted Orthopedic Surgery (CAOS)
employing information and computer graphics technologies for
preoperative planning, intraoperative navigation, and for
guiding or performing surgical interventions, has received very
little attention for bone tumor surgery applications. We have
developed a CAOS system called OrthoSYS, driven by
geometric reasoning algorithms to visualize tumor size, shape,
and plan for resection according to the tumor’s spread, starting
from a 3D model reconstructed from CT images. Anatomical
landmarks on bone are automatically identified and labeled,
useful for registering patient model with virtual model during
surgery and also as a reference for tumor resection and
prosthesis positioning. The thickness of bone stock remaining
after tumor resection is automatically analyzed to choose the
best modular stem and fix the prosthesis. A method for
prosthesis components selection using fuzzy logic has been
developed to assist the surgeons. The medial axis of the long
bones and anatomical landmarks are used for positioning the
prosthesis in virtual planning and verification in the intraoperative stage. A set of anatomical metrics have been
developed to measure the effectiveness of the prosthetic
replacement of bone.
I. INTRODUCTION
C
OMPUTER Assisted Orthopedic Surgery (CAOS) uses
computer technology for preoperative planning, and for
guiding or performing surgical interventions [1]. The system
requires computed tomography (CT), magnetic resonance
(MR), or fluoroscopy images for planning and guiding a
surgery. Imageless systems use statistical shape models to
create the anatomical models based on dimensions measured
manually. Commercially available CAOS systems focus on
spine, knee arthroplasty (distal femur), and hip surfacing
(proximal femur) [2]. Surgeons have attempted to use the
above systems for tumor surgery by customizing them [3]
[4]. As per the authors‟ knowledge, there is no dedicated
system for computer aided bone tumor surgery.
Manuscript received June 9, 2009. This work was supported by the
Office of the Principal Scientific Advisor to the Govt. of India under Grant
PSA/OrthoCAD/2006.
K. Subburaj is with the Mechanical Engineering Department, Indian
Institute of Technology Bombay, Powai, Mumbai 400076 INDIA (e-mail:
[email protected]).
B. Ravi is with the Mechanical Engineering Department, Indian Institute
of Technology Bombay, Powai, Mumbai 400076 INDIA (corresponding
author phone: 91-22-25767510; fax: 91-22-25726875; e-mail:
[email protected]).
M. G. Agarwal is with the Surgical Oncology Department, Tata
Memorial Hospital, Dr. E Borges Road, Parel, Mumbai 400012 INDIA (email: [email protected]).
978-1-4244-4579-0/09/$25.00 ©2009 IEEE
A. Joint Reconstructive Surgery
Endoprosthetic reconstruction has replaced amputation as
the treatment of choice for skeletally immature individuals
(children) who have to undergo resection of juxta-articular
tumor [5]. In 80% of these patients, tumors are found in
extremities of the long bone, the knee being the commonest
[6] (Fig. 1.a & 1.b). The anatomical and physiological nature
of the human body makes the physical intervention highly
variable and complex. Each patient offers a unique challenge
in terms of the location, shape and extent of the bone tumor.
Postoperative complications such as infection, mechanical
failure, bone fracture, and aseptic loosening, lead to a high
rate of failure [7] (Fig. 1c). Inappropriate surgical
procedures following misdiagnosis affect recurrence and
survival rates [8]. Other major causes of failures include
increased fatigue loading on the bone and prosthesis. This
could be a response to unconsidered bone deformities, an
over- or under-sized prosthesis, or poor alignment in body.
The major constraints associated with joint reconstructive
surgery, which limit the usage of general CAOS systems, are:
(i) prosthesis components are smaller than bone (loss of
tissue due to biopsy contamination), (ii) most of the
reference points are lost during massive tumor excision, and
(iii) limited host bone is available for fixation (tumor spread;
patients are mostly adolescents).
B. Preoperative Planning
The goals of preoperative planning in CAOS for joint
reconstruction, which is the focus of this work, are: (i) enable
a surgeon to understand the patient anatomy, extent of spread
of the tumor, and the surgical challenges posed, (ii) help in
the development of customized prostheses, alignment of
prosthesis components, and evaluation of post-surgical
outcomes, (iii) present the data (visualization, virtual
execution of different surgical protocols before entering the
operation theatre) in a way that enables fast and accurate
decisions, (iv) assist the surgeon to execute the protocol
effectively (reference and well planned steps), and (iv) guide
medical robots or tools in computer aided surgery to perform
precision cuts, bone shaping, or positioning of the implant.
In joint reconstructive surgery, patient specific anatomical
models are required to visualize the tumor size and shape,
and plan for resection according to the spread of tumor [9].
This limits the options to adopt image based systems.
Computed tomography has a prominent role, since it is well
suited for orthopedics; the bone separates from the rest of the
367
Fig. 1. Tumor knee replacement (a) Tumor in MRI,
(b) Endoprosthetic joint replacement, (c) Failed prosthesis in body.
tissue by its intensity. Usage of a virtual 3D anatomical
model allows surgeon to visualize the extent of tumor and
regional anatomical structures during preoperative planning
[10]. This helps to improve the surgical outcome in terms of
tension-free artery and wound closure, stability, decreased
postoperative complications, and longevity of the prosthesis.
C. Need for Automation in Preoperative Planning
At present, surgeons select a prosthesis based on (i)
reasonable track record of its use (5–10 years), (ii) prior
experience of the surgeon with the prosthesis, and (iii)
suitability to the patient anatomy. A tumor knee prosthesis
typically comprises 6–12 different components, available in
a wide range (totaling 100 or more) to cater to different size,
gender, position (left/right), and condition (tumor position)
of patients. This makes it difficult to select the right set of
components in an intra operative setting. [11]. Successful
preoperative planning can prevent use of under- and oversized prosthesis components and can identify extremes of
size and bony deformity/morphology, which may require
nonstandard implant sizes.
Anatomical compatibility implies that the prosthesis has to
fit into the anatomical space, and fulfill its function without
interfering with the surrounding tissues. Anatomical
landmarks are distinct regions or points on bones, with
uniqueness in shape characteristics in their vicinity, used for
registration of virtual model with the patient bone [12].
These landmarks are also used for referencing prosthesis
components for positioning them in the body [13], and
referencing the tumor resection cut. As of now, when patientspecific surgery planning is carried out, landmarks are
identified manually and used for registration and other tasks.
Variability associated with the identification and location of
the anatomical landmarks has the potential to affect the
surgical outcome [14]. Most of the landmarks used during
the surgical procedure are manually palpable and
geometrically recognizable. Geometric characteristics of
landmarks can be explored for automatic recognition [15].
Another important factor is that the number of trained
surgeons is limited even in dedicated cancer research
hospitals (Mumbai, the commercial capital of India, a city
with a population of 13 million has fewer than 2,000
orthopedic surgeons and one cancer institute with only a few
orthopedic oncologists) [5]. The lengthy and complicated
limb salvaging procedures form a bottleneck despite their
tremendous potential. The anatomical characteristic of bones
can be described geometrically, which allow the use of
computing methods to make certain major decisions.
Integration of geometric reasoning and decision tools would
help to reduce errors, and lead to better surgical plans.
Careful patient-specific planning and evaluation should be
performed before deciding upon limb salvage surgical
treatment [8]. The above reasons have triggered a demand
for methods and tools to automate surgical guidance. This
task has been taken up for investigation and implemented as
a software program.
II. TUMOR KNEE JOINT RECONSTRUCTIVE SURGERY
PLANNING SYSTEM
A. Functional Requirements
The functional requirements of software for virtual
surgery for orthopedic applications, including tumor knee
replacement surgery, are identified as follows:
1) 3D Reconstruction and Visualization: Image (CT/MR)
import, segmentation of various tissues (semiautomated/ interactive), re-slicing, reconstruction of 3D
virtual models, basic geometric operation and tools.
2) Geometric Reasoning: Automatic anatomical landmark
identification and labeling, anatomical dimensions
extraction, automatic reference axes generation for
positioning, and remaining bone stock analysis in terms
of thickness and properties.
3) Surgery Planning: Prosthesis components selection,
resection planning, prosthesis positioning, guidance by
reference axes and anatomical landmarks, set of
anatomical metrics to evaluate the surgical outcome.
Accordingly, the architecture of a virtual surgery system
named OrthoSYS has been designed (Fig. 2).
B. System Modules
The system is divided into five modules (Fig. 3): (i) the
START module imports CT scan images in DICOM format,
orients the image set, reduces noise in the images using
filtering algorithms, analyzes distribution of density for
segmentation purpose, and maps pixel intensity into different
color patterns for visualizing tumor region, (ii) the MODEL
module segments different tissues from image data,
reconstructs 3D anatomical models from the segmented data,
automatically identifies anatomical landmarks, evaluates the
anatomical deformities (if any), and analyzes bone in terms
of thickness, (iii) the IMPLANT module allows a resection to
be planned based on oncological principles, extracts
anatomical dimensions from 3D model, and selects the best
prosthesis components suitable for the patient from database,
and (iv) the SURGERY module defines the resection plane
368
Fig. 2. Virtual implantation system modules: schematic diagram.
considering the selected prosthesis components and tumor
margin, resects the tumor affected region, positions the
prosthesis components, and verifies the alignment of the limb
after implanting the prosthesis in a virtual environment. (v)
COMMON module contains tools such as linear scale, angle
measurement, report generation by capturing output of each
step of the planning, and context sensitive help. The
algorithms are explained using a case study.
C. Reconstruction of 3D Anatomical Models
The steps of 3D anatomical model reconstruction start
with the imported axial CT images in DICOM (Digital
Imaging and Communications in Medicine) format. The ratio
of pixel resolution in the image plane (x, y), to resolution
along the normal (z) axis may not be equal (i.e. pixel size ≠
slice thickness; inter-slice gap ≠ slice thickness). A reslicing
algorithm was devised to ensure isotropic data for further
computation. These images are processed with filters to
reduce the noise while preserving the edge information in the
form of intensity gradients. Global thresholding of bony
tissue, based on a range of Hounsfield Unit (HU) values (220
to 3000 HU), is carried out in line with local adaptive
thresholding. Next, a 3D region growing algorithm groups
the bone data from the thresholded regions. Due to the
similarities (overlap) in bone and surrounding tissues,
classification based only on thresholding is not feasible. 3D
morphological operators (both manual and automatic) are
used to close the discontinuities in outer (periosteal) and
inner (endosteal) contours. These segmented data are
rendered in two modes: volume and surface rendering (Fig.
3).
D. Identification of Anatomical Landmarks
Anatomical landmarks on the body surface are either
isolated points or well defined regions exhibiting a
conspicuous shape compared to their vicinity. We have used
geometric invariant measures for identifying anatomical
landmarks on reconstructed 3D bone model automatically. A
meaningful region is defined as a set of connected facets
having certain geometrical property (e.g. curvature, surface
normal, etc.) which is similar across the region. The surface
type of a point can be classified based on the signs of
Fig. 3. 3D reconstructed bone model from CT images.
Gaussian and Mean curvature into peak, ridge, pit and
ravine. The algorithm for identification of surface region
types is as follows:
1) Identify a seed facet to grow: An internal facet which
satisfies the following criteria is identified as a seed
facet and is assigned the region type corresponding to its
vertex surface type.
i. maximum to minimum side length of triangle is
below a threshold value
ii. it has not been assigned a region yet
iii. at least one vertex is not a feature vertex
iv. all three vertices are of the same surface type
2) Grow the region: In this step, adjacent triangles (i)
whose common edge is not a feature edge, (ii) which
have not yet been assigned a region, and (iii) whose
three vertices are of the same surface type as the seed
facet are absorbed. The facets absorbed in the region are
assigned the region type of the seed facet.
3) Terminate growing: Region growing is terminated when
there are no adjacent facets of same surface type.
4) Repeat steps 1 to 3 until no seed facets are available for
growing.
These anatomical landmarks are constrained in a spatial
relationship that is the same for all of the knee models. In
order to encode these constraints in a network graph, the
edges pairs are characterized by the spatial adjacency of a
landmark relative to its neighboring landmarks. Skeletal
landmarks are automatically identified by an iterative
process using this spatial adjacency network graph (Fig. 6).
Fig. 5 shows landmarks of the femur bone and the identified
anatomical landmark regions.
E. Extraction of Anatomical Dimensions
Major anatomical dimensions of the knee include mediolateral length (ML), anterio-posterior length (AP), inner
diameter (ID), and outer diameter (OD) of femur: MLF, APF,
ODF, and IDF and similarly for tibia: MLT, APT, ODT, and
IDT. Other parameters include femur valgus angle (VAF),
femur bone curvature (CF), and resection length (RLF)
decided by the surgeon according to the spread of disease.
Bone inner diameters (ID) are measured at three different
369
Fig. 6. Landmark recognition (a) landmarks (b) landmark regions.
Fig. 6. Assembly of selected prosthesis components, suitability factors,
and verification in 3D bone model.
components and calculates the suitability factor for each one.
Rules are compiled from surgeon experience. A set of
anatomical metrics developed to evaluate the selected
prosthesis components considering their suitability with
respect to patient's anatomy, and classified with qualitative
tag (Fig. 6).
Fig. 5. Spatial adjacency network graph of distal femur landmarks.
locations at equal intervals and then the minimum of them is
taken. The APF is measured as the distance between the most
anterior and posterior points of medial condyle. The MLF is
measured between the MEF and LEF. MLT is given by the
distance between anatomical landmarks LPT and MPT.
F. Selection of Tumor Knee Prosthesis Components
A semi-automated selection methodology, driven by
extracted anatomical dimensions, has been implemented.
This segregates prosthesis components with a qualitative tag:
(1) „most suitable‟, (2) „probably suitable‟, (3) „not suitable‟.
The surgeon can select knee prosthesis components from a
limited number of possibilities without needing to select,
order, obtain and check a complete knee prosthesis set. The
standard modular tumor prosthesis components are classified
into three major categories: small (S), medium (M), and
Large (L) according to their sizes (ranges are decided by one
of our morphometric studies of the knee of Indian
individuals). The selection is performed in two steps: First,
the components that are undersized and oversized are
eliminated. The interrelationship between prosthesis
components is considered in selection. This affects the flow
of components selection. Then the geometric details of
components are mapped with the measured anatomical
parameters of the patient to form a fuzzy logic based
decision-tree. This evaluates the suitability of the
G. Bone Stock Thickness Analysis
Precise measurement of the thickness of remaining bone
stock, where the implant is to be anchored, is vital especially
in custom-designed prosthesis. Although the term thickness
is commonly used (bone thickness, cartilage thickness, etc.),
its intuitive definition (smallest dimension of a cross-section)
is ambiguous for intricate models like bones. We have
devised a definition of thickness at any point in bone and a
method for computing it automatically.
Interior thickness at a point Pi inside an object is defined
as the minimum distance of Pi from the nearest surface Sj of
the object (Fig. 7). Its value can be obtained by growing a
sphere or by firing rays from the point along all directions
towards the object surface. The shortest ray length (distance
between point and surface) gives the thickness at that point.
It can be written as Tint (Pi) = min (dist (Pi, Sj)).
Let p,s  Z , and ρ is a sequence of moves from P to S.
3
The number of moves in face, edge, and vertex is noted as f,
g, and h respectively. The weighted distance (d) can be
calculated as:
(1)
l(ρ)=fa+gb+hc
d(p)=minla,b,c (ρ)
(2)
The values a, b, and c are the weights assigned to voxels.
The actual distance of any cell from the closest boundary can
be calculated as:
(3)
l
(ρ)=V(f+ 2*g+ 3*h)
370
1, 2 , 3
Fig. 7. Internal thickness definition and visualization thickness
distribution in tibial bone
H. Tumor Resection and Prosthesis Positioning
The resection length is initially decided according to the
spread of tumor. The reconstruction length = tumor affected
region + tumor margin (≈30 mm) + tibial cut. The effective
prosthesis length is usually higher than the required
reconstruction length due to approximation of anatomical
dimensions (e.g., valgus angle) and unconsidered deformities
of tibia. Hence the resection length must be revised by
considering selected prosthesis components set. Reference
axes are generated from the identified anatomical landmarks
and medial axis of the bone. A perpendicular cut is ensured
by referencing the anatomical axis of the bone (i.e. medial
axis). The resection length (tumor + oncological margin +
extra length of the prosthesis) is measured from the distal
femur extremity (landmark: MCF or LCF). The resection
length is recalculated only if the extra length is less than 10
mm. If the extra length is greater than 10 mm, then, a
customized space filler must be used. The final resection
length = tumor affected region + margin (Fig. 8).
The positioning of prosthesis components with 3D
anatomical model is carried out with reference to anatomical
landmarks and reference axes. The medial axes of both bone
and prosthesis components are generated. Registration of
components with the corresponding bone is carried out in
two steps. Axial alignment is first ensured by registering
anatomical axes of the femur and tibia bone, and axis of
femoral and tibial stem. This step in alignment also acts as a
guide during intra-operative navigation for positioning of the
prosthesis. Rotational alignment of the prosthesis is ensured
by referencing identified anatomical landmarks before tumor
resection. The coordinate values of these landmarks are
registered along with the corresponding points in prosthesis
components. The ICP algorithm is used to minimize the error
between the bone and prosthesis. Once the prosthesis is
registered and superimposed on a patient‟s anatomical
model, radial and axial alignment of the prosthesis is visually
verified. Anatomical suitability of the prosthesis is verified
by anatomical metrics. Alignment of the lower limb is
evaluated after implantation by regenerating reference axes.
This is to ensure that deviation in alignment of the long
bones is within an acceptable range.
Fig. 8. Tumor resection and prosthesis positioning (a) resection plane,
(b) bone stock after resection, (c) prosthesis alignment verification in
bone model, and (d) virtually implanted prosthesis.
I. Anatomical Suitability Metrics
Modular prosthetic components may require a
compromise in conforming to anatomical shape and size,
which might affects the functional outcome of the joint. A set
of anatomical metrics has been developed to evaluate the
suitability of selected prosthesis for the patient anatomy.
(i) Curvature Deviation (δC): is the difference between the
measured bone curvature and the obtained curvature
after implanting a prosthesis with curved stem, with and
without osteotomy (Fig. 9a).
(ii) Geometric Deviation (δG): is the dimensional difference
between the resected bone and selected prosthesis
components (Fig. 9b).
(iii) Knee Centre Shift: is the difference between articulation
centre of the knee and the prosthesis after implantation.
If the metric‟s value is higher than an acceptable range
(in consultation with surgeons), then one may decide to
go for a custom-made prosthesis (Fig. 10a)
(iv) Reconstruction Length Deviation (δRCL): is the
difference between actual reconstruction length and
effective length of the prosthesis (Fig. 10b).
371
Fig. 9. Anatomical suitability metrics: (a) curvature deviation and
(b) geometric deviation
Using the system developed in this work, surgeons can
easily assess the difficulties and risks involved, and plan to
optimize the surgical approach and to decrease surgical
morbidity. This enables making decisions and verifying them
before entering an operation theatre. Integrating 3D
geometric reasoning algorithms for anatomical understanding
with decision methods makes the system intelligent and
fairly automatic. Although, the methods and database are
focused on knee joint reconstruction surgery, they can be
easily customized for other bone tumor surgery planning
(hip, shoulder, elbow).
Fig. 10. Anatomical suitability metrics: (a) knee centre shift and (b)
reconstruction length deviation.
REFERENCES
III. DISCUSSION
[1]
We have described a computer-aided joint reconstructive
surgery (tumor) planning system, developed to address the
gap in this area. Until now most tumor surgeries aimed at
only survival of the patient. Now due to technological and
surgical advances, it is necessary to consider the functional
outcome of the surgery in terms of quality of life. To reduce
human errors, geometry based methods were introduced in
this work to automate the planning tasks. As CAOS in
massive bone tumor resection and reconstruction is still
maturing, our work fills an important gap in this area.
Commercially available medical modeling systems, e.g.
Mimics (Materialise Inc, Belgium), 3D Doctor (Able
Software Corp., USA), Analyze (Mayo Clinic, USA), and
Amira (Mercury Systems, GMBH), are designed for CAD
engineers and not for surgeons, who actually use their
service. These systems are largely focused on visualization
capabilities rather than surgical planning and guidance of
surgical tools. Intelligence in these systems is negligible as
most of them use highly user interactive and data intensive
methods. The system developed for computer-aided joint
reconstructive surgery (tumor) planning has several unique
capabilities. All planning procedures are performed in a 3D
virtual environment (instead of a 2D method using
radiographic images) which increases the understanding of
anatomic structures of the patient and spread of the tumor. A
dedicated geometric algorithm is used to automatically
identify and label 3D anatomical landmarks, which will be
used for referencing surgical tools. A novel adaptive fuzzy
logic based decision-tree, driven by the extracted anatomical
dimensions, for categorizing and selecting prosthesis
components. The suitability metrics indicate a numerical
measure to the surgeons to give more attention to error-prone
steps during surgery and quantifying the postoperative
posture (alignment of limb) with respect to the preoperative
condition. Data generated at every stage are stored
(coordinates of anatomical landmarks, tumor region,
reference lines, anatomical dimensions, resection plane
location and orientation, and position of prosthesis) and can
be used to guide robots or execute computer assisted tools
during surgery. Once the surgical plan is developed, it
becomes a blueprint for surgical intervention.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
372
R. H. Taylor, and D. Stoianovici, “Medical robotics in computerintegrated surgery," IEEE Trans. Robot. Automat., vol. 19, no. 5, pp.
765–781, 2003.
J. Kowal, F. Langlotz, and L. -P. Nolte, “Basics of computer-assisted
orthopaedic surgery,” in Navigation and MIS in orthopaedic surgery,
J. B. Stiehl, W. H. Konermann, R. G. Haaker, and A. M. DiGioia,
Eds. Heidelberg: Springer Verlag, 2007, pp. 2–8.
K. Reijnders, M. H. Coppes, A. L. J. van Hulzen, J. P. Gravendeel, R.
J. van Ginkel, and H. J. Hoekstra, “Image guided surgery: New
technology for surgery of soft tissue and bone sarcomas,” Europ. J.
Surg. Oncol., vol. 33, pp. 390–398, 2007.
K. C. Wong, S. M. Kumta, K. H. Chiu, K. W. Cheung, K. S. Leung,
P. Unwin, and M. C. M. Wong, “Computer assisted pelvic tumour
resection and reconstruction with a custom-made prosthesis using an
innovative adaptation and its validation,” Comput. Aided Surg., vol.
12, no. 4, pp. 225–232, 2007.
M. G. Agarwal, C. Anchan, M. Shah, A. Puri, and S. Pai, “Limb
salvage surgery for osteosarcoma: effective low-cost treatment,” Clin.
Orthop. Rel. Res., vol. 459, pp. 82–91, 2007.
M. Sundaram and E. M. Rohren, “Primary bone tumours,” in Imaging
on Oncology, 2nd ed., J. Husband and R.H. Reznek, Eds., London:
Taylor and Francis, pp. 515–536, 2004.
I. W. Sim, L. F. Tse, E. T. Ek, G. J. Powell, and P. F. M. Choong,
“Salvaging the limb salvage: Management of complications following
endoprosthetic reconstruction for tumours around the knee,” Europ. J.
Surg. Oncol., vol. 33, no. 6, pp. 796–802, 2007.
D. G. Jeon, S. Y. Lee, and J. W. Kim, “Bone primary sarcomas
undergone unplanned intralesional procedures” J. Surg. Oncol., vol.
94, no. 7, pp. 592–598, 2006.
V. O. Lewis, “What‟s new in musculoskeletal oncology,” J. Bone
Joint Surg. Am., vol. 89, no. 6, pp. 1399–1407, 2007.
K. Subburaj, and B. Ravi, “High resolution medical models and
geometric reasoning starting from CT/MR images,” in Proc. 10th
IEEE Int. Conf. CAD/Graphics, Beijing, 2007, pp. 441–444.
W. D. Bugbee, D. J. Ammeen, and G. A. Engh, “Does implant
selection affect outcome of revision knee arthroplasty?,” J.
Arthroplasty, vol. 16, no. 5, pp. 581–585, 2001.
S. van Sint Jan, Colour atlas of skeletal landmark definitions:
Guidelines for reproducible manual and virtual palpations, Churchill
Livingstone/ Elsevier, 2007.
M. Viceconti, D. Testi, M. Simeoni, and C. Zannoni, “An automated
method to position prosthetic components within anatomical spaces,”
Comput. Methods Prog. Biomed, vol. 70, no. 2, pp. 127–127, 2003.
U. Della Croce, A. Cappozzo, and D. C. Kerrigan, "Pelvis and lower
limb anatomical landmark calibration precision and its propagation to
bone geometry and joint angles", Med. Biol. Eng. Comput., vol. 37,
no. 1, pp. 155–161, 1999.
K. Subburaj, B. Ravi, and M. G. Agarwal, "3D shape reasoning for
identifying anatomical landmarks," Comput. Aided Des. Applications,
vol. 5, no. 1–4, pp. 153–160, 2008.