scholarly journals Theoretical foundations of hypertrace-transform: scanning techniques, mathematical apparatus and experimental verification

2018 ◽  
Vol 42 (2) ◽  
pp. 273-282 ◽  
Author(s):  
N. G. Fedotov ◽  
A. A. Syemov ◽  
A. V. Moiseev
Keyword(s):  
Mathematical Model ◽  
Image Recognition ◽  
Experimental Verification ◽  
Automatic Generation ◽  
Analytic Structure ◽  
Mathematical Tool ◽  
Mathematical Apparatus ◽  
3D Image ◽  
3D Images ◽  
Scanning Technique

We consistently describe the theoretical basis of a new geometric method of analysis and recognition of three-dimensional (3D) images. The description of a scanning technique for forming a hypertrace transform and its mathematical model are given. This method, unlike the existing ones, enables 3D images to be analyzed directly from their 3D shape, without first simplifying them or constructing plane projections. We substantiate the selection of a particular scanning tool and the need to construct a reference spherical grid to address the problem of the rotational invariance of the 3D image recognition. A mathematical apparatus of the stochastic realization of the scanning technique based on stochastic geometry and functional analysis is developed. We introduce a new mathematical tool for 3D image analysis – a hypertrex matrix that allows spatial objects of complex shape and structure to be recognized by constructing a single mathematical model of the 3D image. We describe a new type of 3D image features that have an analytic structure – hypertryplet features, whose analytical structure makes possible an automatic generation of a large number of features with predetermined properties. Results of the experimental verification are presented, demonstrating the accurate calculation of features for 3D image recognition and proving the adequacy of the developed mathematical apparatus.

Full-parallax 3D display using time-multiplexing projection technology

2020 ◽  
Vol 2020 (2) ◽  
pp. 100-1-100-6
Author(s):  
Takuya Omura ◽  
Hayato Watanabe ◽  
Naoto Okaichi ◽  
Hisayuki Sasaki ◽  
Masahiro Kawakita
Keyword(s):  
Incident Light ◽  
Polarization State ◽  
3D Image ◽  
3D Display ◽  
Time Division Multiplexing ◽  
3D Images ◽  
Polarization Gratings ◽  
Light Rays ◽  
Time Division

We enhanced the resolution characteristics of a threedimensional (3D) image using time-division multiplexing methods in a full-parallax multi-view 3D display. A time-division light-ray shifting (TDLS) method is proposed that uses two polarization gratings (PGs). As PG changes the diffraction direction of light rays according to the polarization state of the incident light, this method can shift light rays approximately 7 mm in a diagonal direction by switching the polarization state of incident light and adjusting the distance between the PGs. We verified the effect on the characteristics of 3D images based on the extent of the shift. As a result, the resolution of a 3D image with depth is improved by shifting half a pitch of a multi-view image using the TDLS method, and the resolution of the image displayed near the screen is improved by shifting half a pixel of each viewpoint image with a wobbling method. These methods can easily enhance 3D characteristics with a small number of projectors.

Investigations of properties of programs by means of the extended algorithmic logic I

1977 ◽  
Vol 1 (1) ◽  
pp. 93-119
Author(s):  
Lech Banachowski
Keyword(s):  
Mathematical Model ◽  
Mathematical Tool ◽  
Methods Of Analysis ◽  
Semantic Correctness ◽  
Algorithmic Logic ◽  
Correctness Of Programs

The present paper contains investigations concerning the semantic correctness of programs. Presented methods of analysis of programs are appropriate for every domain of computation. Algorithmic logic extended by classical quantifiers is a fundamental mathematical tool used in the paper. Interrelations between properties of programs and properties of descriptions of programs are studied (a description of a program is a mathematical model of the notion of a documentation of a program).

The Automatic Generation of a Mathematical Model for Machinery Systems

1973 ◽  
Vol 95 (2) ◽  
pp. 629-635 ◽  
Author(s):  
D. A. Smith ◽  
M. A. Chace ◽  
A. C. Rubens
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Computer Program ◽  
Mechanical System ◽  
Input Data ◽  
Automatic Generation ◽  
Electrical Networks ◽  
Lagrange’S Equation ◽  
Detailed Explanation ◽  
Independent Loops

This paper presents a detailed explanation of a technique for automatically generating a mathematical model for machinery systems. The process starts from a relatively small amount of input data and develops the information required to model a mechanical system with Lagrange’s equation. The technique uses elements of graph theory which were developed for electrical networks. The basic identifications required for mechanical systems are: paths from ground to mass centers, the independent loops of parts, if any, and paths associated with applied force effects. The techniques described in this paper have been used successfully in a generalized computer program, DAMN.

3d Confocal Microscopy and Image Analysis for Measurement of Genetic Instability

1999 ◽  
Vol 5 (S2) ◽  
pp. 1022-1023
Author(s):  
C. Ortiz de Solorzano ◽  
K. Chin ◽  
D. Knowles ◽  
A. Jones ◽  
E. Garcia ◽  
...  
Keyword(s):  
Image Analysis ◽  
Confocal Microscopy ◽  
Genetic Instability ◽  
Copy Number ◽  
3D Image ◽  
3D Images ◽  
Tissue Sections ◽  
Total Dna ◽  
Natural Tissue

Solid tumors frequently contain cells that are heterogeneous in the copy number of DNA loci. This fact implies the existence of genetic instability, which may be associated with disease aggressiveness. Accurate measurement of this phenomenon requires analysis of intact nuclei within their natural tissue context. We perform these measurements by preparing >30μm thick tissue sections, labeling them with fluorescent labels for total DNA and for specific DNA loci using fluorescence in situ hybridization (FISH) which retain the transparency of the tissue and acquiring 3D images of the tissue using confocal microscopy (figure 1). In this study, we combined automated 3D image analysis (IA) algorithms for segmenting individual nuclei based on the total DNA stain1 and for segmenting the punctuate FISH signals of DNA loci. This enables us to efficiently enumerate the copy number of specific DNA loci in individual cells and as a function of the cell's location in the tissue.

scholarly journals Mathematical model of environmental waters purification

2019 ◽  
Vol 135 ◽  
pp. 01056
Author(s):  
Yuri Skolubovich ◽  
Alexey Skolubovich ◽  
Dmitry Volkov ◽  
Tamara Krasnova ◽  
Elena Gogina
Keyword(s):  
Mathematical Model ◽  
Mathematical Analysis ◽  
Stochastic Approach ◽  
Mathematical Tool ◽  
Environmental Waters ◽  
Mass Service ◽  
Coagulation Process ◽  
Service Theory

This article describes the use of the stochastic approach, in particular, mass service theory and the development of its methods, adapted directly to the coagulation process as a mathematical tool. The coagulation process will be concerned as a) supplying water to the mixer, b) processing it with reagents (coagulants), c) settling for the mathematical analysis of water clarification effectiveness.

scholarly journals Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Mikułowski ◽  
Rafał Wiszowaty
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Experimental Verification ◽  
Load Capacity ◽  
Mechanical Energy ◽  
Specific Situation ◽  
Engineering Structures ◽  
Piston Cylinder ◽  
Proposed Model ◽  
Energy Absorbers

Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA), which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.

A Hysteresis Restoring Force Model of Disc-Shaped Metal Rubber Isolation Component

2012 ◽  
Vol 271-272 ◽  
pp. 186-189 ◽  
Author(s):  
Feng Li Cao ◽  
Hong Bai Bai ◽  
Zhong Bo He ◽  
Guo Quan Ren
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Verification ◽  
Vibration Isolation ◽  
Practical Significance ◽  
Force Model ◽  
Stiffness Coefficient ◽  
Restoring Force ◽  
Restoring Force Model ◽  
Metal Rubber

Dynamic load experiments of the disc-shaped metal rubber isolation component are performed. Through analyzing variation law of the parameters with amplitude and frequency, which are stiffness coefficient, damping coefficient and damping component factor, the hysteresis restoring force model which is able to fully reveal the dynamic characteristics of the component is established. The experimental verification results show that the theoretic calculations are consistent with the experimental data, which verifies the practicability and effectiveness of mathematical model and parameter identification. It has important practical significance for design of vibration isolation component with different requirements.

New approaches to 3D image recognition

2001 ◽  
Author(s):  
Enrique Tajahuerce ◽  
Osamu Matoba ◽  
Yann Frauel ◽  
Maria-Albertina Castro ◽  
Bahram Javidi
Keyword(s):  
Image Recognition ◽  
3D Image ◽  
New Approaches
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