Investigation of random walks knee cartilage segmentation model using inter-observer reproducibility: Data from the osteoarthritis initiative

Abstract

Background:

Existing knee cartilage segmentation methods have reported several technical drawbacks. In essence, graph cuts remains highly susceptible to image noise despite extended research interest; active shape model is often constraint by the selection of training data while shortest path have demonstrated shortcut problem in the presence of weak boundary, which is a common problem in medical images.

Objectives:

The aims of this study is to investigate the capability of random walks as knee cartilage segmentation method.

Methods:

Experts would scribble on knee cartilage image to initialize random walks segmentation. Then, reproducibility of the method is assessed against manual segmentation by using Dice Similarity Index. The evaluation consists of normal cartilage and diseased cartilage sections which is divided into whole and single cartilage categories.

Results:

A total of 15 normal images and 10 osteoarthritic images were included. The results showed that random walks method has demonstrated high reproducibility in both normal cartilage (observer 1: $0.83 \pm 0.028$ and observer 2: $0.82 \pm 0.026$ ) and osteoarthritic cartilage (observer 1: $0.80 \pm 0.069$ and observer 2: $0.83 \pm 0.029$ ). Besides, results from both experts were found to be consistent with each other, suggesting the inter-observer variation is insignificant (Normal: $P = 0.21$ ; Diseased: $P = 0.15$ ).

Conclusion:

The proposed segmentation model has overcame technical problems reported by existing semi-automated techniques and demonstrated highly reproducible and consistent results against manual segmentation method.

Keywords

Knee cartilage random walks segmentation semi-automated osteoarthritis

1. Introduction

Osteoarthritis (OA) is the most prevalent joint disease [1] and the second most debilitating global disease after cardiovascular disease in western society [2,3]. In absence of effective cure for OA, Total Knee Arthroplasty (TKA) is often viewed as painful alternative for chronic OA patients by replacing damaged cartilage with knee joint implant. Hence, imaging biomarker [4] has been proposed to quantify the pathogenesis of OA in order to produce potent Disease Modifying OA Drug (DMOAD). Initially, ruler, callipers or computer software have been used to measure the joint space width (JSW) derived from X-ray images [5]. Nevertheless, the technique’s reliability fell under close scrutiny after several studies suggested that JSW may not solely reflect cartilage loss because the narrowing was ascribable to meniscal extrusion [6,7] instead of cartilage thinning. Besides, frequent use of radiography will inevitably expose the subjects to radiation hazard.

Subsequently, imaging biomarker based on magnetic resonance imaging (MRI) was proposed. MRI is a 3D medical imaging technology which grants whole view of knee cartilage, which contributes to the direct monitor of OA progression [8]. Moreover, it is non-invasive and radiation free; guaranteeing the safety of patients. Currently, substantial amount of morphological variables derived from MR imaging biomarker have been studied extensively. Among these variables, cartilage thickness, cartilage volume, surface area and curvature [9,10] are considered as crucial to signify the development of OA.

The process to obtain these morphological variables starts with the segmentation of knee cartilage. Existing studies have used manual segmentation to separate knee cartilage from image background [11] because it is extremely useful to tackle great anatomical variation demonstrated by knee cartilage. The disadvantage, however, is the expert will spend great amount of time and effort to complete the segmentation process [12], rendering the technique unsuitable to cope with huge dataset. To mitigate the manual intervention problem while maintaining the incorporation of expert knowledge, semi-automated segmentation methods have been broadly applied.

Graph cuts [13,14], growcut [15], region grow [16] and shortest path [17–19] are among the most common segmentation methods used for knee cartilage segmentation. Although the intention to preserve direct expert knowledge fusion has been achieved, these segmentation methods have exhibited severe limitations. For example, graph cuts method is infamous for shortcut problem, sensitive to image noise and demands heavy computation [20]. Besides, the method is limited to binary segmentation and does not guarantee global optimality. Meanwhile, shortest path method suffers from constant boundary deviation in the presence of weak boundary, which occurs commonly in medical images processing. While the problem can be minimized by inserting more free points along curvature and vague boundary, this implies the method is highly sensitive to free point position [20,21]. Lastly, region grow method is easy to implement but requires manual threshold setting and high computation power [22].

These shortcomings suggest the need for more intuitive segmentation method in order to process great amount of image data acquired from longitudinal OA studies. In this works, we propose a new semi-automated segmentation method known as random walks [23]. The proposed method is a probabilistic based segmentation approach which measures the likelihood of each unlabelled pixel belongs to every label using system of linear equations. Comparatively, random walks have demonstrated superior technical features. It is not sensitive to image noise, supports multi-label segmentation and demonstrates fast computation. In the following section, we discuss the implementation of random walks for knee cartilage segmentation.

2. Materials and methods

2.1. Image dataset

The study involved 15 normal dual echo steady state (DESS) MR knee images with water excitation (we). Two radiologists (A.H.A.K. and K.A.S.) were involved and both experts were blinded throughout the study. All MR images of knee were acquired by using 3.0T MRI scanner (Siemens Magnetom Trio, Erlangen, Germany) with quadrature transmit-receive knee coil (USA Instruments, Aurora, OH) [24]. The DESS images have section thickness of 0.7 mm and an in-plane resolution $0.365 \times 0.456 {mm}^{2}$ ( $field of view = 140 \times 140 mm$ , $flip angle = 25 °$ , $TR / TE = 16.3 / 4.7 msec$ , $matrix size = 384 \times 384 mm$ , $bandwidth = 185 Hz/pixel$ ) [25]. More information related to the Osteoarthritis Initiative (OAI) dataset can be found at http://oai.epi-ucsf.org/datarelease/About.asp.

2.2. Overview of segmentation procedures

Two methods, manual segmentation and random walks segmentation were implemented on 2D images by using MATLAB R2014a (Mathworks, Natick, MA) on a laptop equipped with Core i7-4700HQ @2.50 GHz processor and 8.00 GB RAM. Figure 1 shows the execution of manual segmentation and semi-automated segmentation.

Fig. 1.

Overview of knee cartilage segmentation process using manual and semi-automated approaches.

2.3. Manual segmentation

Manual segmentation is the most common segmentation method in medical imaging; being implemented as validation atlas [12,26,27] and segmentation tool in clinical study [28,29]. In this context, experts are required to delineate the cartilage boundary manually. The procedures are outlined below:

1)
Load the MR image into image processing software [30].
2)
Expert will interpret the image.
3)
Select the manual delineation function and outline knee cartilage boundary using mouse cursor.
4)
Continue to outline the boundary until an initial shape enclosing the knee cartilage is obtained.
5)
Adjust initial boundary until expert is satisfied with the refinement.
6)
Proceed to the next knee cartilage and repeat step (1) to (5).

2.4. Random walks segmentation

Random walks method obeys the uniqueness principal for harmonic functions. Implementation of the random walk is summarized as follows:

1.
Insert seeds on non-cartilage, femoral cartilage, tibial cartilage and patella cartilage.
2.
All information is translated into edge weight and stored in Laplacian matrix.
3.
Minimize the Dirichlet integral by solving the Dirichlet problem. The Dirichlet problem is regarded as an attempt in searching for a suitable harmonic function that solves a specified partial differential equation in the interior of a given region. The PDE takes into account the prescribed values of the boundary of the region.
4.
Assign unseeded pixels to the most likely labels (seeded pixels) according the probability of the pixel.

2.4.1. Placement of seeds

In this study, we have developed cartilage label and non-cartilage label. The cartilage label consists of three selections namely femoral cartilage, tibial cartilage and patella cartilage. Meanwhile, non-cartilage label comprises of all background tissues such as menisci, bone, fat tissues and other knee tissues. Experts first interpret the MR image of knee and then place suitable seeds on different cartilage and non-cartilage regions [31].

2.4.2. Graph structure of random walks

Random walk algorithm treats an image with size $m \times n$ as a graph with fixed number of vertices and edges. Intuitively, a graph is defined as $G = (V, E)$ where $v \in V$ represents the vertices (node) and $e \in E \subseteq V \times V$ represents the edge. An edge spanning two vertices, $v_{i}$ and $v_{j}$ is denoted by $e_{i j}$ is characterized by weight denoted as $w (e_{i j})$ or $w_{i j}$ . Meanwhile, the degree of a vertex is defined as $d_{i} = \sum w (e_{i j})$ for all edges $e_{i j}$ incident on $v_{i}$ . To interpret $w_{i j}$ as the bias affecting a random walker’s choice, we require that $w_{i j} > 0$ .

In this context, the image pixels are treated as vertices. Then, we use a Gaussian weighting function that maps the changes in image intensities (intensity gradient) to maximize the entropy. The weighting function is defined in $\begin{matrix} (1) & w_{i j} = e^{- β {(g_{i} - g_{j})}^{2}} \end{matrix}$ where $g_{i}$ and $g_{j}$ represent the image intensities at pixel i and pixel j respectively. β is a free parameter controlling the strength of the edge weight. The value of β is fixed at 100 in this works.

To construct an image graph structure, we store weights and degree information inside a combinatorial Laplacian matrix with size $m \times n$ . The Laplacian matrix is given in $\begin{matrix} (2) & L_{i j} = \{\begin{matrix} d_{i}, & i = j \\ - w_{i j}, & v_{i} and v_{j} are adjacent vertices \\ 0, & otherwise \end{matrix} \end{matrix}$

2.4.3. Discrete Dirichlet problem

Random walks method generates the probability that each random walker will reach every labelled seed and assign the unlabelled pixel to the label with highest probability. The probability that each random walker will reach a labelled seed is equivalent to the solution to Dirichlet problem, which is defined as a problem of finding a harmonic function under the constraint of boundary values. Intuitively, harmonic function that obeys the boundary condition will minimize the Dirichlet integral for field u and region Ω. The Dirichlet integral is defined as $\begin{matrix} (3) & D | u | = \frac{1}{2} \int_{Ω} | \nabla u |^{2} d \nabla \end{matrix}$

In this work, the boundary condition of labelled seed point is fixed to unity and all unlabelled points are set to zero. The label vector for labelled seeds is defined as a function $Q (v_{i}) = s_{j}$ , where $v_{j} \in V_{M}$ . Then, the $| V_{M} | \times 1$ vector for each label, s, at node $v_{j} \in V_{M}$ is defined as $\begin{matrix} (4) & m_{i}^{s} = \{\begin{matrix} 1 & if Q (v_{i}) = s_{j}, \\ 0 & if Q (v_{i}) \neq s_{j} . \end{matrix} \end{matrix}$

The motivation, for instance, is to derive a combinatorial harmonic function x that minimizes the combinatorial Dirichlet integral $D [x]$ by decomposing $D [x]$ into seeded part, $L_{M}$ and unseeded part, $L_{U}$ . $\begin{matrix} (5) & \begin{matrix} D [x_{U}] & = \frac{1}{2} [\begin{matrix} x_{M}^{T} & x_{U}^{T} \end{matrix}] [\begin{matrix} L_{m} & B \\ B^{T} & L_{U} \end{matrix}] [\begin{matrix} x_{M} \\ x_{U} \end{matrix}] \\ = \frac{1}{2} (x_{M}^{T} L_{m} x_{M} + 2 x_{U}^{T} B^{T} x_{M} + x_{U}^{T} L_{U} x_{U}) \end{matrix} \end{matrix}$ where $x_{M}$ and $x_{U}$ correspond to the probabilities of the seeded and unseeded pixels respectively. To identify critical point, $D [x_{U}]$ is differentiated with respect to $x_{U}$ and yields a sparse, symmetric, positive-definite, system of linear equation with $| V_{U} |$ number of equations and $2 | E |$ nonzero entries as shown in $\begin{matrix} (6) & L_{U} x_{u} = - B^{T} x_{M} \end{matrix}$

Since $L_{U}$ is guarantee to exist and be unique, we can model Eq. (6) into a linear equation and solve the system for its potentials. Equation (7) illustrates the system model where X has column taken by each $x^{s}$ and M has columns given by each $m^{s}$ . Thus, there are $K - 1$ sparse linear system to solve with K indicating the total number of labels. $\begin{matrix} (7) & L_{U} X = - B M \end{matrix}$

Figure 2 demonstrates the probability map of each label for knee cartilage created during the execution of random walks method.

Fig. 2.

Segmentation procedures using random walks algorithm. (a) An original MR image of knee. (b) Segmentation result. Probability map for (c) femoral cartilage label, (d) tibial cartilage label, (e) patellar cartilage label, and (f) non-cartilage label.

2.5. Evaluation metric

In this works, 15 normal images and 10 diseased images from the OAI dataset were used. Two experts performed the segmentation of knee cartilage using semi-automated methods and manual method independently. Both experts were blinded throughout the experiment. Then, Dice similarity coefficient (DSC) was used to verify the performance of the proposed method against manual segmentation result, which is the common practice in knee cartilage segmentation studies in the absence of groundtruth [32,33]. Accuracy of the model was tested by using DSC, sensitivity and specificity. DSC evaluates the degree of agreement between two set of results, sensitivity measures the correct classification of cartilage pixels and specificity measures the correct classification of non-cartilage pixels. $\begin{array}{l} (8) & Dice = \frac{2 TP}{(FP + TP) + (TP + FN)} \\ (9) & Sensitivity = \frac{TP}{TP + FN} \\ (10) & Specificity = \frac{TN}{TN + FP} \end{array}$ where $TP$ is true positive, $TN$ is true negative, $FP$ is false positive and $FN$ is false negative. A $Dice$ value of 0 indicates no overlap while a Dice value of 1 indicates perfect agreement. $Sensitivity$ and $Specificity$ have maximum value of 1 and minimum value of 0.

2.6. Statistical analysis

All statistical analyses were performed by using SPSS (version 21; SAS Institute, Cary, NC). DSCs were obtained by superimposing manual segmentation results on semi-automated segmentation results. The experiment consisted of whole cartilage and single cartilage analyses. Whole cartilage was defined as the combination of femoral, tibial and patella cartilage while single cartilage was defined as separated femoral, tibial and patella cartilage compartments. In both analyses, we further categorised the results into normal ( $KL = 0$ ) and diseased ( $KL = 1 – 4$ ). Then, Pair t test was performed to examine the consistency between two sets of results where $α < 0.05$ indicated results inconsistency. Figure 3 shows the MR images of normal, mild and severe osteoarthritic cartilage.

Fig. 3.

Comparison between normal and osteoarthritic cartilages. (a) normal cartilage. (b) mild osteoarthritic cartilage (c) severe osteoarthritic cartilage.

3. Results and discussion

3.1. Segmentation reproducibility

Table 1 summarized the inter-method reproducibility generated by using whole cartilage. By referring to normal cartilage section ( $KL = 0$ ), random walks method have reported high reproducibility against manual method. For instance, random walks method has exhibited Dice similarity index of $0.83 \pm 0.028$ for observer 1 and $0.80 \pm 0.069$ for observer 2. Besides, the method has yielded sensitivity of $0.82 \pm 0.040$ for observer 1 and $0.86 \pm 0.032$ for observer 2. By referring to diseased cartilage section ( $KL = 1 – 4$ ), random walks method has reported reproducibility of $0.80 \pm 0.069$ for observer 1 and $0.83 \pm 0.029$ for observer 2. Meanwhile, the random walks method has yielded sensitivity of $0.84 \pm 0.033$ for observer 1 and $0.86 \pm 0.027$ for observer 2.

Table 1
Reproducibility results generated by whole cartilage

KL Observer 1 Observer 2

Dice Sens Spec Dice Sens Spec

0 0.83 0.82 0.996 0.82 0.86 0.995

(0.028) (0.040) (0.0012) (0.026) (0.032) (0.0099)

1–4 0.80 0.84 0.994 0.83 0.86 0.994

(0.069) (0.033) (0.0021) (0.029) (0.027) (0.0011)

KL	Observer 1	Observer 2
0	0.83	0.82	0.996	0.82	0.86	0.995
(0.028)	(0.040)	(0.0012)	(0.026)	(0.032)	(0.0099)
1–4	0.80	0.84	0.994	0.83	0.86	0.994
(0.069)	(0.033)	(0.0021)	(0.029)	(0.027)	(0.0011)

Table 2

Reproducibility results generated by single cartilage

KL	Label	Observer 1			Observer 2

		Dice	Sens	Spec	Dice	Sens	Spec
0	$i = 1$	0.82	0.82	0.997	0.82	0.86	0.996
	$i = 1$	(0.049)	(0.063)	(0.00010)	(0.040)	(0.058)	(0.00033)
	$i = 2$	0.80	0.80	0.999	0.76	0.75	0.998
	$i = 2$	(0.074)	(0.078)	(0.00039)	(0.054)	(0.071)	(0.00042)
	$i = 3$	0.80	0.83	0.999	0.79	0.81	0.999
	$i = 3$	(0.050)	(0.096)	(0.00033)	(0.047)	(0.023)	(0.0012)
1–4	$i = 1$	0.80	0.85	0.995	0.82	0.82	0.996
	$i = 1$	(0.082)	(0.056)	(0.0023)	(0.040)	(0.053)	(0.00099)
	$i = 2$	0.76	0.80	0.998	0.73	0.86	0.998
	$i = 2$	(0.072)	(0.11)	(0.00089)	(0.065)	(0.051)	(0.00053)
	$i = 3$	0.77	0.77	0.999	0.82	0.86	0.999
	$i = 3$	(0.051)	(0.072)	(0.0071)	(0.037)	(0.059)	(0.00037)

Table 2 summarized the inter-method reproducibility generated by using single cartilage i.e. femoral data ( $i = 1$ ), tibial data ( $i = 2$ ) and patellar data ( $i = 3$ ). By referring to normal cartilage section ( $KL = 0$ ), observer 1 generated reproducibility of $0.82 \pm 0.049$ for femoral, $0.80 \pm 0.074$ for tibial and $0.80 \pm 0.050$ for patellar cartilage. Observer 2 generated reproducibility of $0.82 \pm 0.040$ for femoral, $0.76 \pm 0.054$ for tibial and $0.79 \pm 0.047$ for patellar. By referring to diseased cartilage section ( $KL = 1 – 4$ ), observer 1 generated reproducibility of $0.80 \pm 0.082$ for femoral, $0.76 \pm 0.072$ for tibial and $0.77 \pm 0.051$ for patellar and observer 2 generated reproducibility of $0.82 \pm 0.040$ for femoral, $0.73 \pm 0.065$ for tibial and $0.82 \pm 0.037$ for patellar.

3.2. Discussion

To our best knowledge, this is the first extended attempt to evaluate the performance of random walks for knee cartilage segmentation. Retrospectively, the proposed semi-automated segmentation method has exhibited several technical properties which establish itself as better alternative to existing methods. First, random walks have high robustness to image noise and shortcut problem compared to graph cuts and shortest path. Second, random walks support arbitrary segmentation with global solution in differ from graph cuts, another graph based method that can only produce approximated solution for multi-label segmentation. This property is very important given cartilage segmentation involves bone, non-cartilage and different types of cartilage tissues. Lastly, random walks do not require heavy computation in order to obtain desirable results; making it more applicable to process large amount of image [23]. These desirable properties contribute to the coveted intuitive knee cartilage segmentation.

In the works, we found out the inter-method reproducibility for normal whole cartilage produced by both observer 1 and 2 are consistent (Observer 1: $0.83 \pm 0.028$ and Observer 2: $0.82 \pm 0.026$ ; $P = 0.21$ ). Similar consistency was achieved in reproducibility for diseased whole cartilage (Observer 1: $0.80 \pm 0.069$ and Observer 2: $0.83 \pm 0.029$ ; $P = 0.15$ ). Besides, random walks segmentation method also achieved high sensitivity and specificity in both normal and diseased cartilage. These findings suggest that the semi-automated random walks method is not subjected to inter-observer variation.

In single cartilage analysis, we have observed similar results except normal tibial cartilage data and diseased patellar cartilage data. Normal tibial cartilage has yielded DSC of $0.80 \pm 0.074$ for observer 1 and $0.76 \pm 0.071$ for observer 2 ( $P = 0.018$ ). Diseased patella cartilage has yielded DSC of $0.77 \pm 0.051$ for observer 1 and $0.82 \pm 0.037$ for observer 2 ( $P = 0.0040$ ). Both sets of results have demonstrated significant difference. While the extent of result inconsistency is limited, we attribute the segmentation geometric disagreement to greater ambiguity due to irregular shape when segmenting smaller cartilage and inferior tissue contrast [34]. Hence, it is common that experts cannot find consensus among themselves.

Both sets of findings suggest random walks offer great potential as betterment for existing methods. Nonetheless, the study is limited by relatively small number of images used, which implies the need to expand the size of dataset in order to strengthen the reliability of future studies. Besides, current study uses 2D images since this is the novel attempt to validate the model performance. Therefore, future study will be carried out by using 3D based clinical morphological variables to explain the significance of random walks from clinical perspective.

4. Conclusions

In this works, random walks method was proposed to segment knee cartilage on MR DESS image of knee. The proposed method avoids major technical problems reported by current semi-automated segmentation techniques and was found to be highly accurate in order to be tested with clinical morphological variables in future studies.

Footnotes

Acknowledgements

The authors gratefully acknowledge the Short Term Research Grant (STRG) provided by Universiti Kuala Lumpur British Malaysian Institute (UniKL BMI) in supporting the study.

Conflict of interest

The authors have no conflict of interest to report.

References

Brooks

, The burden of musculoskeletal disease – a global perspective, Clin Rheumatol 25(6) (2006), 778–781. doi:10.1007/s10067-006-0240-3.

McCauley

T.R.

and Disler

D.G.

, MR imaging of articular cartilage, Radiology 209(3) (1998), 629–640. doi:10.1148/radiology.209.3.9844653.

Haq

Murphy

and Dacre

, Osteoarthritis, Postgrad Med J 79(933) (2003), 377–383.

Kraus

V.B.

Burnett

Coindreau

Cottrell

Eyre

Gendreau

et al., Application of biomarkers in the development of drugs intended for the treatment of osteoarthritis, Osteoarthritis Cartilage 19(5) (2011), 515–542. doi:10.1016/j.joca.2010.08.019.

Wright

, Quantitative radiography of osteoarthritis, Ann Rheum Dis 53(4) (1994), 268–275. doi:10.1136/ard.53.4.268.

Adams

J.G.

McALindon

Dimasi

Carey

and Eustace

, Contribution of meniscal extrusion and cartilage loss to joint space narrowing in osteoarthritis, Clin Radiol 54(8) (1999), 502–506. doi:10.1016/S0009-9260(99)90846-2.

Sharma

Eckstein

Song

Guermazi

Prasad

Kapoor

et al., Relationship of meniscal damage, meniscal extrusion, malalignment, and joint laxity to subsequent cartilage loss in osteoarthritic knees, Arthritis Rheum 58(6) (2008), 1716–1726. doi:10.1002/art.23462.

Augat

and Eckstein

, Quantitative imaging of musculoskeletal tissue, Annu Rev Biomed Eng 10(1) (2008), 369–390. doi:10.1146/annurev.bioeng.10.061807.160533.

Hayashi

Roemer

F.W.

and Guermazi

, Osteoarthritis year 2011 in review: Imaging in OA – a radiologists’ perspective, Osteoarthritis Cartilage 20(3) (2012), 207–214. doi:10.1016/j.joca.2011.12.016.

10.

Eckstein

Kwoh

C.K.

Boudreau

R.M.

Wang

Hannon

M.J.

Cotofana

et al., Quantitative MRI measures of cartilage predict knee replacement: A case–control study from the osteoarthritis initiative, Ann Rheum Dis 72(5) (2013), 707–714. doi:10.1136/annrheumdis-2011-201164.

11.

Tameem

H.Z.

Ardekani

Seeger

Thompson

and Sinha

U.S.

, Initial results on development and application of statistical atlas of femoral cartilage in osteoarthritis to determine sex differences in structure: Data from the osteoarthritis initiative, J Magn Reson Imaging 34(2) (2011), 372–383. doi:10.1002/jmri.22643.

12.

Mahapatra

, Cardiac image segmentation from cine cardiac MRI using graph cuts and shape priors, J Digit Imaging 26(4) (2013), 721–730. doi:10.1007/s10278-012-9548-5.

13.

Boykov

Y.Y.

and Jolly

M.P.

, Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images, in: IEEE International Conference on Computer Vision, Vancouver, Canada, 2001 07–14 July.

14.

Lempitsky

Kohli

Rother

and Sharp

, Image segmentation with a bounding box prior, in: IEEE International Conference on Computer Vision, Kyoto, Japan, 2009 29 September–2 October.

15.

Vezhnevets

and Konouchine

, GrowCut – interactive multi-label N-D image segmentation by cellular automata, in: Proceedings of Graphicon, Novosibirsk Akademgorodok, Russia, 2005 20–24 June.

16.

Kapur

Beardsley

Gibson

Grimson

and Wells

, Model-based segmentation of clinical knee MRI, in: International Conference on Medical Image Computing and Computer-Assisted Intervention, MA, USA, 1998 11–13 October.

17.

Mortensen

Morse

Barrett

and Udupa

, Adaptive boundary detection using ‘live-wire’ two-dimensional dynamic programming, in: Proceedings of Computers in Cardiology, Durham, NC, 1992 11–14 October.

18.

Barrett

W.A.

and Mortensen

E.N.

, Interactive live-wire boundary extraction, Med Image Anal 1(4) (1997), 331–341. doi:10.1016/S1361-8415(97)85005-0.

19.

Falcao

A.X.

Udupa

J.K.

and Miyazawa

F.K.

, An ultra-fast user-steered image segmentation paradigm: Live wire on the fly, IEEE Trans Med Imaging 19(1) (2000), 55–62. doi:10.1109/42.832960.

20.

Sinop

A.K.

and Grady

, A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm, in: IEEE 11th International Conference on Computer Vision, Rio de Janeiro, Brazil, 2007 14–21 October.

21.

Couprie

Grady

Najman

and Talbot

, Power watershed: A unifying graph-based optimization framework, IEEE Transactions on Pattern Analysis and Machine Intelligence 33(7) (2011), 1384–1399. doi:10.1109/TPAMI.2010.200.

22.

Davies

E.R.

, Machine Vision: Theory, Algorithms, Practicalities, 4th edn, Morgan Kaufmann Publishers Inc., 2012, 912 p.

23.

Grady

, Random walks for image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence 28(11) (2006), 1768–1783. doi:10.1109/TPAMI.2006.233.

24.

Eckstein

Hudelmaier

Wirth

Kiefer

Jackson

et al., Double echo steady state magnetic resonance imaging of knee articular cartilage at 3 tesla: A pilot study for the osteoarthritis initiative, Ann Rheum Dis 65(4) (2006), 433–441. doi:10.1136/ard.2005.039370.

25.

Peterfy

C.G.

Schneider

and Nevitt

, The osteoarthritis initiative: Report on the design rationale for the magnetic resonance imaging protocol for the knee, Osteoarthritis Cartilage 16(12) (2008), 1433–1441. doi:10.1016/j.joca.2008.06.016.

26.

Yang

and Huang

S.C.

, Method for evaluation of different MRI segmentation approaches, in: IEEE Conference on Nuclear Science Symposium, Toronto, Canada, 1998 08–14 November.

27.

Shen

Firpi

H.A.

Saykin

A.J.

and West

J.D.

, Parametric surface modeling and registration for comparison of manual and automated segmentation of the hippocampus, Hippocampus 19(6) (2009), 588–595. doi:10.1002/hipo.20613.

28.

Cicuttini

Hankin

Jones

and Wluka

, Comparison of conventional standing knee radiographs and magnetic resonance imaging in assessing progression of tibiofemoral joint osteoarthritis, Osteoarthritis Cartilage 13(8) (2005), 722–727. doi:10.1016/j.joca.2005.04.009.

29.

Entis

J.J.

Doerga

Barrett

L.F.

and Dickerson

B.C.

, A reliable protocol for the manual segmentation of the human amygdala and its subregions using ultra-high resolution MRI, NeuroImage 60(2) (2012), 1226–1235. doi:10.1016/j.neuroimage.2011.12.073.

30.

Hong-Seng

Tian-Swee

Liang-Xuan

Weng-Kit

Sayuti

K.A.

Karim

A.H.A.

et al., Interactive knee cartilage extraction using efficient segmentation software: Data from the osteoarthritis initiative, Bio-Med Mater Eng 24(6) (2014), 3145–3157.

31.

Gan

H.S.

Tan

T.S.

Sayuti

K.A.

Karim

A.H.A.

and Kadir

M.R.A.

, Multilabel graph based approach for knee cartilage segmentation: Data from the osteoarthritis initiative, in: Biomedical Engineering and Sciences (IECBES), 2014 IEEE Conference on, 2014 8–10 Dec.

32.

Shim

Chang

Tao

Wang

J.-H.

Kwoh

C.K.

and Bae

K.T.

, Knee cartilage: Efficient and reproducible segmentation on high-spatial-resolution MR images with the semiautomated graph-cut algorithm method, Radiology 251(2) (2009), 548–556. doi:10.1148/radiol.2512081332.

33.

Bae

K.T.

Shim

Tao

Chang

Wang

J.H.

Boudreau

et al., Intra- and inter-observer reproducibility of volume measurement of knee cartilage segmented from the OAI MR image set using a novel semi-automated segmentation method, Osteoarthritis Cartilage 17(12) (2009), 1589–1597. doi:10.1016/j.joca.2009.06.003.

34.

Hong-Seng

Tan Tian

Karim

A.H.A.

Sayuti

K.A.

Kadir

M.R.A.

Weng-Kit

et al., Medical image visual appearance improvement using bihistogram Bezier curve contrast enhancement: Data from the osteoarthritis initiative, The World Scientific Journal 2014 (2014), 1–13.

Investigation of random walks knee cartilage segmentation model using inter-observer reproducibility: Data from the osteoarthritis initiative

Abstract

Background:

Objectives:

Methods:

Results:

Conclusion:

Keywords

1. Introduction

2. Materials and methods

2.1. Image dataset

2.2. Overview of segmentation procedures

2.4.2. Graph structure of random walks

2.4.3. Discrete Dirichlet problem

2.6. Statistical analysis

3.1. Segmentation reproducibility

Table 1 Reproducibility results generated by whole cartilage KL Observer 1 Observer 2 Dice Sens Spec Dice Sens Spec 0 0.83 0.82 0.996 0.82 0.86 0.995 (0.028) (0.040) (0.0012) (0.026) (0.032) (0.0099) 1–4 0.80 0.84 0.994 0.83 0.86 0.994 (0.069) (0.033) (0.0021) (0.029) (0.027) (0.0011)

4. Conclusions

Footnotes

Acknowledgements

Conflict of interest

References

Table 1
Reproducibility results generated by whole cartilage

KL Observer 1 Observer 2

Dice Sens Spec Dice Sens Spec

0 0.83 0.82 0.996 0.82 0.86 0.995

(0.028) (0.040) (0.0012) (0.026) (0.032) (0.0099)

1–4 0.80 0.84 0.994 0.83 0.86 0.994

(0.069) (0.033) (0.0021) (0.029) (0.027) (0.0011)