Training Models of Shape from Sets of Examples

Cootes, Timothy F.; Taylor, Christopher J.; Cooper, D. H.; Graham, Jim

doi:10.1007/978-1-4471-3201-1_2

Cited by 215 publications

(77 citation statements)

References 4 publications

(3 reference statements)

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“…The extracted components identify important modes of joint variability in landmark locations—that is, ways in which the configuration varies as a whole. This analysis follows that suggested by Cootes et al 28. Each important mode of shape variability—that is, each principal component—can be thought of as a shape variable with a particular value corresponding to a particular shape.…”

Section: Methodsmentioning

confidence: 88%

The shape of the distal femur: a palaeopathological comparison of eburnated and non-eburnated femora

Shepstone

Rogers

Kirwan

et al. 1999

Annals of the Rheumatic Diseases

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Objectives-To determine the diVerence in shape of the distal femur, viewed axially in two dimensions, between eburnated and non-eburnated femora. Methods-A comparison of 52 noneburnated and 16 eburnated femora drawn from a large archeological skeletal population. Eburnation was taken to indicate late stage osteoarthritis. Shape variability, based on landmarks, was quantified using a principal components analysis after a Procrustes alignment. Results-A statistically significant diVerence was found between the two groups. This was with respect to the patellar groove and the shape of the medial condyle. The latter diVerence is consistent with bone remodelling as a knee stabilising mechanism. Conclusions-Anatomical shape can be quantified using an uncomplicated statistical technique. It was used to quantify the shape of the distal femur and demonstrate shape diVerences associated with osteoarthritis of the knee.

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Section: Methodsmentioning

confidence: 88%

The shape of the distal femur: a palaeopathological comparison of eburnated and non-eburnated femora

Shepstone

Rogers

Kirwan

et al. 1999

Annals of the Rheumatic Diseases

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“…Computationally, this was achieved using 100 equally spaced points for each function (interpolated using cubic splines), as outlined by Ramsay and Silverman 16. Each principal component can be considered as a “mode” of shape variation 17. A subset of the first principal components was used for further analysis.…”

Section: Methodsmentioning

confidence: 99%

Shape of the intercondylar notch of the human femur: a comparison of osteoarthritic and non-osteoarthritic bones from a skeletal sample

Shepstone¹,

Rogers²,

Kirwan³

et al. 2001

Annals of the Rheumatic Diseases

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Objectives-To compare objectively the shape of the intercondylar notch in human osteoarthritic and non-osteoarthritic femora. Methods-A sample of 96 human femora from a large skeletal population were selected for study. These femora included subjects with evidence of late stage osteoarthritis (that is, with eburnation present) and subjects with no such evidence. The distal end of the femur, viewed axially, was recorded with a video camera, and digitised computer images were produced. The outline of the intercondylar notch was extracted and represented mathematically as two functions. A functional principal components analysis was used to identify important modes of shape variation. These variations in shape were compared between eburnated and noneburnated femora. Results-A statistically significant diVerence in the shape of the intercondylar notch was found between the two groups. The diVerence related mostly to the shape of the edge of the medial condyle: in the non-osteoarthritic group this tended to exhibit a concavity; in the osteoarthritic group it tended to be straight. Conclusions-This observed diVerence may be a predisposing factor to the development of osteoarthritis. The morphology of the intercondylar notch is related to the functioning of and possible damage to the cruciate ligaments, and damage to the cruciate ligaments is a known risk factor for osteoarthritis. Alternatively, this difference may be due to bony remodelling secondary to the onset of osteoarthritis, perhaps in response to altered biomechanics. (Ann Rheum Dis 2001;60:968-973) Osteoarthritis (OA) of the knee is a common, painful, and debilitating condition. It aVects up to 30% of Western populations over the age of 65, 1 presenting a large burden for healthcare services.

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“…A boundary PDM is a tuple of boundary points on an object, with points corresponding across the training cases. Frequently, studies using PDMs capture shape variations through the statistical method of Principal Component Analysis ( PCA ) (Cootes et al, 1992, 1995), and classification is done using Linear Discriminant Analysis ( LDA ) or the Support Vector Machine ( SVM ) (Davies et al, 2003). …”

Section: Introductionmentioning

confidence: 99%

Non-Euclidean classification of medically imaged objects via s-reps

Hong

Vicory

Schulz

et al. 2016

Medical Image Analysis

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Classifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging. We propose a novel classification scheme that uses a skeletal representation to provide rich non-Euclidean geometric object properties. Our statistical method combines distance weighted discrimination (DWD) with a carefully chosen Euclideanization which takes full advantage of the geometry of the manifold on which these non-Euclidean geometric object properties (GOPs) live. Our method is evaluated via the task of classifying 3D hippocampi between schizophrenics and healthy controls. We address three central questions. 1) Does adding shape features increase discriminative power over the more standard classification based only on global volume? 2) If so, does our skeletal representation provide greater discriminative power than a conventional boundary point distribution model (PDM)? 3) Especially, is Euclideanization of non-Euclidean shape properties important in achieving high discriminative power? Measuring the capability of a method in terms of area under the receiver operator characteristic (ROC) curve, we show that our proposed method achieves strongly better classification than both the classification method based on global volume alone and the s-rep-based classification method without proper Euclideanization of non-Euclidean GOPs. We show classification using Euclideanized s-reps is also superior to classification using PDMs, whether the PDMs are first Euclideanized or not. We also show improved performance with Euclideanized boundary PDMs over non-linear boundary PDMs. This demonstrates the benefit that proper Euclideanization of non-Euclidean GOPs brings not only to s-rep-based classification but also to PDM-based classification.

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Training Models of Shape from Sets of Examples

Cited by 215 publications

References 4 publications

The shape of the distal femur: a palaeopathological comparison of eburnated and non-eburnated femora

The shape of the distal femur: a palaeopathological comparison of eburnated and non-eburnated femora

Shape of the intercondylar notch of the human femur: a comparison of osteoarthritic and non-osteoarthritic bones from a skeletal sample

Non-Euclidean classification of medically imaged objects via s-reps

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