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## A Fully Automated Segmentation of Knee Bones and Cartilage Using Shape Context and Active Shape Models (2012)

### Citations

1796 | Shape matching and object recognition using shape contexts
- Belongie, Malik, et al.
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Citation Context ...hape is denoted by H(pi) = ∑ i C(pi, qpi(i)) (3) where the qpi(i) is the permutation of qj after applying the constraint of being one-to-one. This problem can be solved with Hungarian method in O(n3) =-=[23]-=-. A simple example of matrix form using Hungarian method is given in the following, for more details on the method and a proof of time complexity of the algorithm see [24]. 3.1 Example: Hungarian meth... |

615 |
Active shape models—Their training and application
- COOTES, TAYLOR, et al.
- 1995
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Citation Context ...learnt from the training set, we can generate new examples. This limitation is obtained from the fact that most of the data lies between three square root of variance (standard deviation of the mean) =-=[2]-=-. 4.4 Example: Statistical shape model on hand One of the popular examples of PCA in two-dimensional case is the variation of a hand. The data set which is used in this example contains 18 different h... |

583 |
Least-squares fitting of two 3-d point sets
- Arun, Huang, et al.
- 1987
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Citation Context ... Taking the singular value decomposition (SVD) of matrix N , N = UΣV T where U and V are orthogonal matrices and Σ = diag(σ1, σ2, , σd) such that σ1 ≥ σ2 ≥ · · · ≥ σd ≥ 0. From this, it can be proven =-=[32]-=- that to minimize equation 26 the rotation matrix should be defined as: R = V UT . 42 Finally the algorithm stops its iterations when the matching stays unchanged [26]. The following is a brief descri... |

357 | Statistical models of appearance for computer vision
- Cootes, Taylor
- 2004
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Citation Context ...n the object. The algorithm stops searching in one level after specific amount of iteration in that level. The number of iterations are obtained from where the algorithm converges and stops improving =-=[18]-=-. In Figures 19-21 three different resolution levels are shown. Figure 19: Normal resolution. Figure 20: 12 resolution. Figure 21: 14 resolution. 28 4.6 Active shape model The active shape model is a ... |

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Active shape model segmentation with optimal features,‖
- Ginneken, Frangi, et al.
- 2002
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Citation Context ...es above the threshold M which is usually chosen between 90%−99.5%. This means to find ∑K i=1 λi∑n i=1 λi ≥M. (12) The smallest value of K which fit to equation 12 is the desired number of components =-=[4]-=-. In this master thesis, M is 90% for Hand example and 98% for knee segmentation. 4.2 Example: PCA A simple example of PCA is the 2 dimensions random variables: Figure 12 shows the two main PCs of a p... |

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Anatomically corresponded regional analysis of cartilage in asymptomatic and osteoarthritic knees by statistical shape modelling of the bone
- Williams, Holmes, et al.
- 2010
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Citation Context ...g a surface to a binary mask 44 References 51 4 1 Introduction Osteoarthritis (OA) is one of the major diseases and causes of disability in developed countries and affects mostly the adult population =-=[1, 3]-=-. Knee bone and cartilage are the main parts of the body which are severely affected by OA. OA leads to loss of articular cartilage and pain, see Figure 1. This happens because one of the main respons... |

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Magnetic resonance imaging. http://en.wikipedia.org/wiki/Magnetic_resonance_imaging (last visited
- Wikipedia
- 2011
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Citation Context ... signal is detected and TR is the repetition time. In contrast with T1-weighted images are the T2-weighted images whose watery parts are bright and fat is dark and also they use a long TE and long TR =-=[7]-=-,[8]. The MRI scanner creates 3D objects by producing several 2D slices and adding them together. These slices are defined relative to the human body with three main directions; sagittal, coronal and ... |

2 | Delaunay triangulation, http://en.wikipedia.org/wiki/Delaunay_triangulation (last visited Dec - Wikipedia |

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Medical Image Analysis for the clinic - A Grand Challenge: Segmentation of Knee Images 2010
- Heimann, Morrison, et al.
- 2010
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Citation Context ...g a surface to a binary mask 44 References 51 4 1 Introduction Osteoarthritis (OA) is one of the major diseases and causes of disability in developed countries and affects mostly the adult population =-=[1, 3]-=-. Knee bone and cartilage are the main parts of the body which are severely affected by OA. OA leads to loss of articular cartilage and pain, see Figure 1. This happens because one of the main respons... |

1 |
Fully automatic segmentation of the knee joint using active appearance models , MICCAI grand challenge 2010
- Graham, Wolstenhholme, et al.
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Citation Context ... Score is the average of the bone and cartilage score [1]. 8 Previous work RMSD Bone AvgD Bone VOE Cart VD Cart Method 1) Fully Automatic Segmentation of the Knee Joint using Active Appearance Models =-=[12]-=- 1.35 0.81 35.45 -17.35 • Active Appearance Models • Minimum Description Length Groupwise Image Registration method • Hierarchical modeling scheme Summary Submitted as the last paper. But they didn’t ... |

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Model-based auto-segmentation of knee bones and cartilage
- Seim, Kainmueller, et al.
- 2010
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Citation Context ...t shaft in OAI model did not segment all shaft in GC. Hence they applied an additional step which used long shaft shape model. 2) Model-based Auto-Segmentation of Knee Bones and Cartilage in MRI Data =-=[13]-=- 1.39 0.93 31.6 2.5 • Statistical Shape Models • Graph based optimization • Multi object technique using generalized Hough Transform Summary Their model has a good conceptual system. They start with b... |

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Hierarchical decision framework with a priori shape models for knee joint cartilage segmentation , MICCAI grand challenge 2010
- Yin, Williams, et al.
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Citation Context ...ed this information plus cartilage thickness map to segment the cartilage. 3) Hierarchical Decision Framework with a Priori Shape Models for Knee Joint Cartilage Segmentation - MICCAI Grand Challenge =-=[14]-=- 3.67 2.13 32.35 1.85 • Optimal graph phase • Pattern recognition functionality • A detection using Haar Wavelet features and AdaBoost classifier Summary This method detects patella in the search proc... |

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Learning loca shape and Appearance for segmentation of knee cartilage
- Lee, U
- 2010
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Citation Context ...with different properties such as texture difference and thickness, identifying cross-object interacting regions. 9 4) Learning Local Shape and Appearance for Segmentation of Knee Cartilage in 3D MRI =-=[15]-=- 1.98 1.07 32.3 6.15 • Local shape and appearance • Using branch-and-mincut • Bone-cartilage interface classification using Markov random field Summary Start with bone segmentation follow by classifyi... |

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Fully automated segmentation of the knee using local deformation-model fitting , MICCAI grand challenge 2010
- Amberg, Luthi, et al.
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Citation Context ...tation using region of interest patches and probability of cartilage’s properties, shape and appearance and boundary. 5) Fully Automated Segmentation of the Knee using Local Deformation-Model Fitting =-=[16]-=- 2.66 1.56 67 -33.1 • Statistical deformation models • Localization fitting of deformation models Summary In this paper, they build the deformation model from the training image. And they use the refe... |

1 | On nonparametric Markov random field estimation for fast automatic segmentation of MRI knee data , MICCAI grand challenge 2010
- Korc, Schneider, et al.
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Citation Context ... from the training image. And they use the reference image and perform a deformation model fitting. 6) On Nonparametric Markov Random Field Estimation for Fast Automatic Segmentation of MRI Knee Data =-=[17]-=- 4.35 2.96 65.45 9.1 • Nonparametric Markov random field model • Monte Carlo simulation • Variational inference • Using atlas based prior information Summary They used the global statistical model and... |

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Chater 7: ”Model-Based Methods in Analysis of Biomedical Images
- Cootes, Taylor
- 2000
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Citation Context ...g the PCs of the landmarks of the training data. The mean shape is the initial estimate for shape parameters. Moreover, the rotation and the translation parameter initialize from the model shape [18],=-=[19]-=-. The active shape model is updated iteratively as follows: 1. Compute a suggested movement for each point by looking along normal of the surface through each landmarks to find the best match point fo... |

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Process Modeling Using the Self-Organizing Map
- Hollmn
- 1996
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Citation Context ... on the coordinate axes having the dimension K and then transform the data back by a linear combination of the basis vectors. This minimizes the error between the data and this reduced representation =-=[22]-=-. By picking the eigenvectors corresponding to the largest eigenvalues one loses as little information as possible about the whole data set. Moreover, by varying PCs and corresponding eigenvalues one ... |

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Chapter 11: Combinatorial Optimization, Algorithms and complexity
- Papadimitriou, Stieglitz
- 1982
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Citation Context ...th Hungarian method in O(n3) [23]. A simple example of matrix form using Hungarian method is given in the following, for more details on the method and a proof of time complexity of the algorithm see =-=[24]-=-. 3.1 Example: Hungarian method Consider five different jobs 1, 2, 3, 4 and 5 and five different contractors A,B,C,D and E, the cost of doing each of these jobs by each of the contractors 16 are given... |

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shape context
- Petersen
- 2008
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Citation Context ...ne and two and other way around. Next step is to find the cost matrix. After applying the Hungarian method to pair points to find the least total cost, the following pairing in Figure 11 is suggested =-=[25]-=-. Figure 11: The suggested pairing is shown with lines between the points from model to target. These lines are according to minimum cost. The iterative shape context provides consistent landmarks bet... |

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guest lecturer
- Philips
(Show Context)
Citation Context ...: minθ:X→Y,t∈Rd,R∈SO(d) ∑ x∈X ‖Rx− t− θ(x)‖2 , (25) where R is the rotation matrix, t is the translation vector and SO(d) is the set of special orthogonal matrices (rotation matrices) in d dimensions =-=[26]-=-. ICP algorithm alternate between its two steps : 1. A matching step, where a fixed given translation and rotation, the optimal matching is computed by minimizing the D, this step is the slowest part ... |

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The uncertainty in physical measurements. Chapter 11: The chi Square Test
- Fornasini
(Show Context)
Citation Context ...s’ distribution are histograms, the cost of matching two points is denoted with cost matrix, using the χ2 test statistic. The χ2 test statistic gives a comparison between expected and observed values =-=[29]-=-, K∑ k=1 (Ok − Ek)2 Ek in this case the observation is hi(k) and the expected value is hi(k)+hj(k) 2 which leads to Cij = C(pi, qj) = 1 2 K∑ k=1 (hi(k)− hj(k))2 (hi(k) + hj(k)) , (2) where hi(k) is th... |