Digital and Discrete Geometry

Chen, Li M.

doi:10.1007/978-3-319-12099-7

Cited by 28 publications

(36 citation statements)

References 11 publications

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“…It is a very complex field of computer science and mathematics, and the keywords provided in Table 1 are a very restricted core of topics of relevance for automated image analysis. 7,11 The availability of image analysis software products is steadily increasing. Each vendor of slide scanners or microscopic systems is currently offering its own system with a wide variety of features and components of automated image analysis with varying capabilities.…”

Section: Automated Vmmentioning

confidence: 99%

The Pathologist 2.0: An Update on Digital Pathology in Veterinary Medicine

2017

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Using light microscopy to describe the microarchitecture of normal and diseased tissues has changed very little since the middle of the 19th century. While the premise of histologic analysis remains intact, our relationship with the microscope is changing dramatically. Digital pathology offers new forms of visualization, and delivery of images is facilitated in unprecedented ways. This new technology can untether us entirely from our light microscopes, with many pathologists already performing their jobs using virtual microscopy. Several veterinary colleges have integrated virtual microscopy in their curriculum, and some diagnostic histopathology labs are switching to virtual microscopy as their main tool for the assessment of histologic specimens. Considering recent technical advancements of slide scanner and viewing software, digital pathology should now be considered a serious alternative to traditional light microscopy. This review therefore intends to give an overview of the current digital pathology technologies and their potential in all fields of veterinary pathology (ie, research, diagnostic service, and education). A future integration of digital pathology in the veterinary pathologist's workflow seems to be inevitable, and therefore it is proposed that trainees should be taught in digital pathology to keep up with the unavoidable digitization of the profession.

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Section: Automated Vmmentioning

confidence: 99%

The Pathologist 2.0: An Update on Digital Pathology in Veterinary Medicine

2017

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“…This effectively removes all singular values close to either one or zero. As a result, the linear system P Ay = P b (13) has numerical rank χ( mach , N R ), and a solution y can be obtained in O(N R log 2 (N R )) operations, e. g. through randomized algorithms [22].…”

Section: An Approximation Algorithm By Projection Onto the Plunge Regionmentioning

confidence: 99%

“…[13, Theorem 5.4] The boundary δS of a regular 2-dimensional manifold S is itself regular, and the union of closed regular curves.…”

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confidence: 99%

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Function Approximation on Arbitrary Domains Using Fourier Extension Frames

Matthysen¹,

Huybrechs²

2018

SIAM J. Numer. Anal.

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Fourier extension is an approximation scheme in which a function on an arbitary bounded domain is approximated using a classical Fourier series on a bounding box. On the smaller domain the Fourier series exhibits redundancy, and it has the mathematical structure of a frame rather than a basis. It is not trivial to construct approximations in this frame using function evaluations in points that belong to the domain only, but one way to do so is through a discrete least squares approximation. The corresponding system is extremely ill-conditioned, due to the redundancy in the frame, yet its solution via a regularized SVD is known to be accurate to very high (and nearly spectral) precision. Still, this computation requires O(N 3 ) operations. In this paper we describe an algorithm to compute such Fourier extension frame approximations in only O(N 2 log 2 N ) operations for general 2D domains. The cost improves to O(N log 2 N ) operations for simpler tensor-product domains. The algorithm exploits a phenomenon called the plunge region in the analysis of time-frequency localization operators, which manifests itself here as a sudden drop in the singular values of the least squares matrix. It is known that the size of the plunge region scales like O(log N ) in one dimensional problems. In this paper we show that for most 2D domains in the fully discrete case the plunge region scales like O(N log N ), proving a discrete equivalent of a result that was conjectured by Widom for a related continuous problem. The complexity estimate depends on the Minkowski or box-counting dimension of the domain boundary, and as such it is larger than O(N log N ) for domains with fractal shape.

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“…Another disadvantage is that the method is not mathematically proven in terms of preserving the mathematical properties including topological properties of the original object [73]. A variety of algorithms built on the original marching cubes method have been designed, and a quite comprehensive survey about those techniques is introduced in [74].…”

Section: Surface Reconstructionmentioning

confidence: 99%

Customized 3D Clothes Modeling for Virtual Try-on System based on Multiple Kinects

Huang

Lee

2016

Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications

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Most existing 3D virtual try-on systems put clothes designed in one environment on a human captured in another environment, which cause the mismatching color and brightness problem. And also typical 3D clothes modeling starts with manually designed 2D patterns, deforms them to fit on a human, and applies stitching to sew those patterns together. Such work usually relies on labor work.In this thesis, we describe an approach to reconstruct clothes and human that both are from the same space. With multiple Kinects, it models the 3D clothes directly out of a dressed mannequin without the need of the predefined 2D clothes patterns, and fits them to a human user. Our approach has several advantages: (i) a simple hardware setting consisted of multiple Kinects to capture a human model; (ii) 3D clothes modeling directly out of captured human figure. To the best of our knowledge, our work is the first one which separates clothes out of captured human figure; (iii) resizing of clothes adapting to any sized human user; (iv) a novel idea of virtual try-on where clothes and human are captured in the same location.iii

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Digital and Discrete Geometry

Cited by 28 publications

References 11 publications

The Pathologist 2.0: An Update on Digital Pathology in Veterinary Medicine

The Pathologist 2.0: An Update on Digital Pathology in Veterinary Medicine

Function Approximation on Arbitrary Domains Using Fourier Extension Frames

Customized 3D Clothes Modeling for Virtual Try-on System based on Multiple Kinects

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