Starfruit Shape Defect Estimation Based on Concave and Convex Area of a Closed Planar Curve

2012 ◽  
Author(s):  
Musa Mokji ◽  
Syed Abd. Rahman Syed Abu Bakar
Keyword(s):  
Critical Points ◽  
Shape Representation ◽  
Shape Recognition ◽  
Statistical Features ◽  
First Case ◽  
Planar Curve ◽  
Defect Estimation ◽  
Curvature Estimation ◽  
Shape Curve ◽  
Input Curve

Dalam kertas kerja ini, sebuah perwakilan bentuk berdasarkan kawasan cekung dan cembung di sepanjang keluk tertutup dipersembahkan. Teknik yang dicadangkan dalam kertas kerja ini melibatkan proses anggaran kekelukan daripada keluk masukan dan juga proses pencarian titik kritikal pada keluk masukan tersebut. Dengan mengasingkan titik kritikal tersebut kepada kategori cekung dan cembung, pengiraan kawasan cekung dan cembung dilakukan. Daripada ciri–ciri statistik ini, dua permasalahan berkaitan dengan bentuk disiasat. Di sini, teknik yang dicadangkan diuji terhadap proses penganggaran kerosakan bentuk dan pengenalan bentuk pada buah belimbing. Pada kes pertama, kerosakan bentuk belimbing diukur dengan mengira kuasa cekung di mana kuasa cekung ini adalah selanjar dengan kerosakan bentuk tersebut. Untuk kes pengenalpastian bentuk pula, tangkai belimbing adalah objek untuk dikenal pasti dan tangkai belimbing ini akan diasingkan daripada bentuk belimbing kerana ia akan menyumbang kepada kesalahan pengiraan kerosakan bentuk belimbing. Bagi kedua–dua kes, teknik yang dicadangkan diuji dengan tiga teknik penganggaran kekelukan untuk memastikan keberkesanan teknik yang dicadangkan. Kata kunci: Perwakilan bentuk, kekelukan, titik kritikal, kawasan cekung dan cembung In this paper, a shape representation based on concave and convex area along a closed curve is presented. The proposed technique involves the process of the curvature estimation from the input curve and search for its corresponding critical points. By splitting the critical points into concave and convex categories, the concave and convex area are computed. From these statistical features, two problems related to the shape (curve) are investigated. Here, the proposed technique is tested on shape defect estimation and shape recognition of starfruit. In the first case, defect is measured by computing concave energy, which is proportional to the defect. For shape recognition, starfruit’s stem is identified and removed from the starfruit’s shape, as it will contributes false computation of defect measurement. For both cases, the proposed technique is tested with three different curvature estimation techniques to validate the results. Key words: Shape representation, curvature, critical point, concave and convex area

scholarly journals Cosmological dynamics of f(R) models in dynamical system analysis

2020 ◽  
Vol 35 (22) ◽  
pp. 2050124
Author(s):  
Parth Shah ◽  
Gauranga C. Samanta
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Critical Points ◽  
System Analysis ◽  
Late Time ◽  
Field Equations ◽  
Acceleration Phase ◽  
First Case ◽  
Acceleration Of The Universe ◽  
The Universe

In this work we try to understand the late-time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe without analytically solving the field equations. We study the acceleration phase of the universe and stability properties of the critical points which could be compared with observational results. We consider an asymptotic behavior of two particular models [Formula: see text] and [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] for the study. As a first case we fix the value of [Formula: see text] and analyze for all [Formula: see text]. Later as second case, we fix the value of [Formula: see text] and calculation are done for all [Formula: see text]. At the end all the calculations for the generalized case have been shown and results have been discussed in detail.

scholarly journals PREDICTING THE PROBABILITY OF PERSISTENCE OF HIV INFECTION WITH THE STANDARD MODEL

2011 ◽  
Vol 19 (04) ◽  
pp. 747-762 ◽  
Author(s):  
HENRY C. TUCKWELL ◽  
PATRICK D. SHIPMAN
Keyword(s):  
Hiv Infection ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Equation Model ◽  
Parameter Estimates ◽  
Host Immune System ◽  
Stable Node ◽  
Asymptotically Stable ◽  
Discordant Couple ◽  
First Case

It is not well understood why the transmission of HIV may have a small probability of occurrence despite frequent high risk exposures or ongoing contact between members of a discordant couple. We explore the possible contributions made by distributions of system parameters beginning with the standard three-component differential equation model for the growth of a HIV virion population in an infected host in the absence of drug therapy. The overall dynamical behavior of the model is determined by the set of values of six parameters, some of which describe host immune system properties and others which describe virus properties. There may be one or two critical points whose natures play a key role in determining the outcome of infection and in particular whether the HIV population will persist or become extinct. There are two cases which may arise. In the first case, there is only one critical point P1at biological values and this is an asymptotically stable node. The system ends up with zero virions and so the host becomes HIV-free. In the second case, there are two critical points P1and P2at biological values. Here P1is an unstable saddle point and P2is an asymptotically stable spiral point with a non-zero virion level. In this case the HIV population persists unless parameters change. We let the parameter values take random values from distributions based on empirical data, but suitably truncated, and determine the probabilities of occurrence of the various combinations of critical points. From these simulations the probability that an HIV infection will persist, across a population, is estimated. It is found that with conservatively estimated distributions of parameters, within the framework of the standard 3-component model, the chances that a within-host HIV population will become extinct is between 0.6% and 6.9%. With less conservative parameter estimates, the probability is estimated to be as high as 24%. The many complicating factors related to the transmission and possible spontaneous elimination of the virus and the need for experimental data to clarify whether transient infections may occur are discussed. More realistic yet complicated higher dimensional models are likely to yield smaller probabilities of extinction.

scholarly journals Tracking the critical points of curves evolving under planar curvature flows

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Eszter Fehér ◽  
Gábor Domokos ◽  
Bernd Krauskopf
Keyword(s):  
Distance Function ◽  
Critical Points ◽  
Broad Class ◽  
Computational Cost ◽  
Radial Distance ◽  
Test Case ◽  
Case Examples ◽  
Planar Curve ◽  
Special Cases ◽  
Two Parameters

<p style='text-indent:20px;'>We are concerned with the evolution of planar, star-like curves and associated shapes under a broad class of curvature-driven geometric flows, which we refer to as the Andrews-Bloore flow. This family of flows has two parameters that control one constant and one curvature-dependent component for the velocity in the direction of the normal to the curve. The Andrews-Bloore flow includes as special cases the well known Eikonal, curve-shortening and affine shortening flows, and for positive parameter values its evolution shrinks the area enclosed by the curve to zero in finite time. A question of key interest has been how various shape descriptors of the evolving shape behave as this limit is approached. Star-like curves (which include convex curves) can be represented by a periodic scalar polar distance function <inline-formula><tex-math id="M1">\begin{document}$ r(\varphi) $\end{document}</tex-math></inline-formula> measured from a reference point, which may or may not be fixed. An important question is how the numbers and the trajectories of critical points of the distance function <inline-formula><tex-math id="M2">\begin{document}$ r(\varphi) $\end{document}</tex-math></inline-formula> and of the curvature <inline-formula><tex-math id="M3">\begin{document}$ \kappa(\varphi) $\end{document}</tex-math></inline-formula> (characterized by <inline-formula><tex-math id="M4">\begin{document}$ dr/d\varphi = 0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ d\kappa /d\varphi = 0 $\end{document}</tex-math></inline-formula>, respectively) evolve under the Andrews-Bloore flows for different choices of the parameters.</p><p style='text-indent:20px;'>We present a numerical method that is specifically designed to meet the challenge of computing accurate trajectories of the critical points of an evolving curve up to the vicinity of a limiting shape. Each curve is represented by a piecewise polynomial periodic radial distance function, as determined by a chosen mesh; different types of meshes and mesh adaptation can be chosen to ensure a good balance between accuracy and computational cost. As we demonstrate with test-case examples and two longer case studies, our method allows one to perform numerical investigations into subtle questions of planar curve evolution. More specifically — in the spirit of experimental mathematics — we provide illustrations of some known results, numerical evidence for two stated conjectures, as well as new insights and observations regarding the limits of shapes and their critical points.</p>

scholarly journals Active and Passive Haptic Perception of Shape: Passive Haptics Can Support Navigation

Electronics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 355 ◽  
Author(s):  
José-Luis Rodríguez ◽  
Ramiro Velázquez ◽  
Carolina Del-Valle-Soto ◽  
Sebastián Gutiérrez ◽  
Jorge Varona ◽  
...  
Keyword(s):  
Motor Activity ◽  
Haptic Perception ◽  
Shape Recognition ◽  
Haptic Interactions ◽  
Passive Haptics ◽  
First Case ◽  
Challenging Tasks ◽  
Series Of Experiments ◽  
Perceptual Characteristics ◽  
Haptic Environments

Real-time haptic interactions occur under two exploration modes: active and passive. In this paper, we present a series of experiments that evaluate the main perceptual characteristics of both exploration modes. In particular, we focus on haptic shape recognition as it represents a fundamental task in many applications using haptic environments. The results of four experiments conducted with a group of 10 voluntary subjects show that the differences in motor activity between active and passive haptics ease the perception of surfaces for the first case and the perception of pathways for the latter. In addition, the guidance nature of passive haptics makes the pathway direction easy to recognize. This work shows that this last observation could find application in more challenging tasks such as navigation in space.

AN EVALUATION OF THE NOVEL "NORMALIZED-REDUNDANCY" REPRESENTATION FOR PLANAR CURVES

1996 ◽  
Vol 10 (07) ◽  
pp. 769-789 ◽  
Author(s):  
J. FDEZ-VALDIVIA ◽  
J. A. GARCIA ◽  
M. GARCIA-SILVENTE
Keyword(s):  
Computational Complexity ◽  
Prior Knowledge ◽  
Shape Representation ◽  
Shape Recognition ◽  
General Purpose ◽  
The Novel ◽  
Time And Space ◽  
Novel Approach ◽  
Order Polynomial ◽  
Different Levels

In this paper, a novel approach for improving model-based recognition is proposed. Our approach provides a suitable shape representation by extracting only the most significant scales that best describe a planar noisy curve. The proposed representation satisfies several necessary criteria for general-purpose shape representation methods. The representation is capable of dealing with different levels of noise, it does not require user-set parameters or prior knowledge about the curve's nature, it also has a very low-order polynomial computational complexity in time and space. Hence such a shape representation is very useful for shape recognition. The method depends on the connection between the redundancy of two signals' smoothed versions and the essential structure being simultaneously isolated in both versions. Two different ways of formulating this approach are described in this paper: the global "normalized-redundancy" representation and the local "normalized-redundancy" representation. Results of applying the proposed formulation to synthetic and real 2-D shapes are presented.

scholarly journals Representation and recognition of the spatial organization of three-dimensional shapes

1978 ◽  
Vol 200 (1140) ◽  
pp. 269-294 ◽  
Keyword(s):  
Coordinate System ◽  
Spatial Organization ◽  
Shape Representation ◽  
Shape Recognition ◽  
Three Dimensional ◽  
Modular Organization ◽  
Shape Description ◽  
Shape Information ◽  
Constraint Analysis ◽  
Shape Descriptions

The human visual process can be studied by examining the computational problems associated with deriving useful information from retinal images. In this paper, we apply this approach to the problem of representing three-dimensional shapes for the purpose of recognition. 1. Three criteria, accessibility, scope and uniqueness , and stability and sensitivity , are presented for judging the usefulness of a representation for shape recognition. 2. Three aspects of a representation’s design are considered, (i) the representation’s coordinate system, (ii) its primitives, which are the primary units of shape information used in the representation, and (iii) the organization the representation imposes on the information in its descriptions. 3. In terms of these design issues and the criteria presented, a shape representation for recognition should: (i) use an object-centred coordinate system, (ii) include volumetric primitives of varied sizes, and (iii) have a modular organization. A representation based on a shape’s natural axes (for example the axes identified by a stick figure) follows directly from these choices. 4. The basic process for deriving a shape description in this representation must involve: (i) a means for identifying the natural axes of a shape in its image and (ii) a mechanism for transforming viewer-centred axis specifications to specifications in an object-centred coordinate system. 5. Shape recognition involves: (i) a collection of stored shape descriptions, and (ii) various indexes into the collection that allow a newly derived description to be associated with an appropriate stored description. The most important of these indexes allows shape recognition to proceed conservatively from the general to the specific based on the specificity of the information available from the image. 6. New constraints supplied by a conservative recognition process can be used to extract more information from the image. A relaxation process for carrying out this constraint analysis is described.

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