Differential Geometry and Its
                    Applications

Oprea, John

doi:10.1090/clrm/059

Cited by 92 publications

(82 citation statements)

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“…Years later, Lee et al proposed a model based on a parametric active contour, which also ends up enforcing a mathematical shape constraint based on the catenary curve [78]. A catenary is a perfectly flexible and inextensible string of uniform density supported by two distinct points [79; 80]; these curves have been used to model objects shaped like hanging strings, such as arches and suspension bridges [81]. The results obtained with this approach were comparable with the ones obtained by Sousa et al.…”

Section: Breast Contourmentioning

confidence: 99%

Deep Aesthetic Assessment of Breast Cancer Surgery Outcomes

2019

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Breast cancer is a highly mutable and rapidly evolving disease, with a large worldwide incidence. Even though, it is estimated that approximately 90% of the cases are treatable and curable if detected on early staging and given the best treatment. Nowadays, with the existence of breast cancer routine screening habits, better clinical treatment plans and proper management of the disease, it is possible to treat most cancers with conservative approaches, also known as breast cancer conservative treatments (BCCT). With such a treatment methodology, it is possible to focus on the aesthetic results of the surgery and the patient's Quality of Life, which may influence BCCT outcomes. In the past, this assessment would be done through subjective methods, where a panel of experts would be needed to perform the assessment; however, with the development of computer vision techniques, objective methods, such as BAT c and BCCT.core, which perform the assessment based on asymmetry measurements, have been used. On the other hand, they still require information given by the user and none of them has been considered the gold standard for this task. Recently, with the advent of deep learning techniques, algorithms capable of improving the performance of traditional methods on the detection of breast fiducial points (required for asymmetry measurements) have been proposed and showed promising results. There is still, however, a large margin for investigation on how to integrate such algorithms in a complete application, capable of performing an end-to-end classification of the BCCT outcomes. Taking this into account, this thesis shows a comparative study between deep convolutional networks for image segmentation and two different quality-driven keypoint detection architectures for the detection of the breast contour. One that uses a deep learning model that has learned to predict the quality (given by the mean squared error) of an array of keypoints, and, based on this quality, applies the backpropagation algorithm, with gradient descent, to improve them; another which uses a deep learning model which was trained with the quality as a regularization method and that used iterative refinement, in each training step, to improve the quality of the keypoints that were fed into the network. Although none of the methods surpasses the current state of the art, they present promising results for the creation of alternative methodologies to address other regression problems in which the learning of the quality metric may be easier. Following the current trend in the field of web development and with the objective of transferring BCCT.core to an online format, a prototype of a web application for the automatic keypoint detection was developed and is presented in this document. Currently, the user may upload an image, automatically detect and/or manipulate its keypoints and compute the Breast Retraction Assessment (BRA) value. This prototype is completely scalable and can be upgraded with new functionalities according to the user's needs.iii iv

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Section: Breast Contourmentioning

confidence: 99%

Deep Aesthetic Assessment of Breast Cancer Surgery Outcomes

2019

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“…Bu kısımda, vektörler ile ilgili temel kavramlar ve eğriler teorisi özet olarak verilecektir [Do Carmo 2], [Oprea,3]. Tanım 2.1.…”

Section: Temel Tanim Ve Teoremlerunclassified

Bi̇ri̇m Küre Yüzeyi̇ Üzeri̇nde Apollonian Eğri̇leri̇ - Apollonian Curves on the Surface of the Unit Sphere

Kazaz²

2014

CBU Fen Bil Dergi

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Özet: 2 Öklid düzleminde P ve Q verilen iki sabit nokta olsun. P ve Q noktalarından uzaklıkları sabit bir m : n oranında olan tüm X noktalarının geometrik yerinin bir çember olduğu iyi bilinir, burada m, n (mn ) pozitif tamsayılardır. Bu çember Apollonius'ın çemberi (veya Apollonian çemberi) olarak bilinir [Brannan-Esplen-Gray, 1]. Eğer mn  ise,     , : , 1:1 d P X d Q X  olacak şekildeki X noktalarının geometrik yeri ise [] PQ doğru parçasının orta dikme doğrusudur. Bu makalede, 2 S birim küre yüzeyi üzerinde Apollonian eğrileri tanımlanmış ve bu eğrilerin küre yüzeyi üzerinde düzlemsel eğriler (büyük çemberler) ve düzlemsel olmayan eğriler olduğu elde edilmiştir.

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“…The above exposition of Foucault's pendulum using a rectangular basis appeared in [6] and appears in more technical guise in [7].…”

Section: Acknowledgementsmentioning

confidence: 99%