Lightweight Spatial Geometric Models Assisting Shape Description and Retrieval

2021 ◽  
pp. 209-230
Author(s):  
S. Priyanka ◽  
M. S. Sudhakar
Keyword(s):  
Shape Description ◽  
Geometric Models

scholarly journals Geometric Models for Seed Shape Description and Quantification in the Cactaceae

Plants ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 2546
Author(s):  
José Javier Martín-Gómez ◽  
Diego Gutiérrez del Pozo ◽  
Ángel Tocino ◽  
Emilio Cervantes
Keyword(s):  
Seed Coat ◽  
Shape Description ◽  
Seed Shape ◽  
Geometric Models ◽  
The Third ◽  
Inner Surface ◽  
New Models ◽  
Peripheral Type ◽  
Analysis Of Variation ◽  
Shape Quantification

Seed shape in species of the Cactaceae is described by comparison with geometric models. Three new groups of models are presented, two for symmetric seeds, and a third group for asymmetric seeds. The first two groups correspond, respectively, to superellipses and the combined equations of two semi-ellipses. The third group contains models derived from the representation of polar equations of Archimedean spirals that define the shape of asymmetric seeds in genera of different subfamilies. Some of the new models are geometric curves, while others are composed with a part resulting from the average silhouettes of seeds. The application of models to seed shape quantification permits the analysis of variation in seed populations, as well as the comparison of shape between species. The embryos of the Cactaceae are of the peripheral type, strongly curved and in contact with the inner surface of the seed coat. A relationship is found between seed elongation and the models, in which the genera with elongated seeds are represented by models with longer trajectories of the spiral. The analysis of seed shape opens new opportunities for taxonomy and allows quantification of seed shape in species of the Cactaceae.

scholarly journals New Techniques for Seed Shape Description in Silene Species

Taxonomy ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 1-19
Author(s):  
Ana Juan ◽  
José Javier Martín-Gómez ◽  
José Luis Rodríguez-Lorenzo ◽  
Bohuslav Janoušek ◽  
Emilio Cervantes
Keyword(s):  
Dorsal View ◽  
Morphological Diversity ◽  
Seed Morphology ◽  
Shape Description ◽  
Seed Shape ◽  
Species Classification ◽  
New Techniques ◽  
Geometric Models ◽  
Mathematical Equations ◽  
Silene Species

Seed shape in Silene species is often described by means of adjectives such as reniform, globose, and orbicular, but the application of seed shape for species classification requires quantification. A method for the description and quantification of seed shape consists in the comparison with geometric models. Geometric models based on mathematical equations were applied to characterize the general morphology of the seeds in 21 species of Silene. In addition to the previously described four models (M1 is the cardioid, and M2 to M4 are figures derived from it), we present four new geometric models (model 5–8). Models 5 and 6 are open cardioids that resemble M3, quite different from the flat models, M2 and M4. Models 7 and 8 were applied to those species not covered by models 2 to 6. Morphological measures were obtained to describe and characterize the dorsal view of the seeds. The analyses done on dorsal views revealed a notable morphological diversity and four groups were identified. A correlation was found between roundness of dorsal view and the geometric models based on lateral views, such that some of the groups defined by seed roundness are also characterized by the similarity to particular models. The usefulness of new morphological tools of seed morphology to taxonomy is discussed.

Mathematical morphology for shape description

2002 ◽  
Vol 12 (1) ◽  
pp. 87-116 ◽  
Author(s):  
M. Schmitt
Keyword(s):  
Mathematical Morphology ◽  
Shape Description

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

2019 ◽  
pp. 40-47
Author(s):  
E. A. Mironchik
Keyword(s):  
Geometric Model ◽  
Main Idea ◽  
Formal Logic ◽  
High Complexity ◽  
Geometric Models ◽  
Complexity Problem ◽  
Logical Expression ◽  
State Examination

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

Volumetric Representation and Manipulation of Geometric Models

2001 ◽  
Author(s):  
Greg Turk ◽  
F. S. Nooruddin ◽  
James F. O'Brien ◽  
Gary Yngve
Keyword(s):  
Geometric Models ◽  
Volumetric Representation

Anyon Networks from Geometric Models of Matter

2021 ◽  
Author(s):  
Michael Atiyah ◽  
Matilde Marcolli
Keyword(s):  
Normal Bundle ◽  
Present Form ◽  
Joint Work ◽  
Geometric Models ◽  
Tensor Networks

Abstract This paper, completed in its present form by the second author after the first author passed away in 2019, describes an intended continuation of the previous joint work on anyons in geometric models of matter. This part outlines a construction of anyon tensor networks based on four-dimensional orbifold geometries and braid representations associated with surface-braids defined by multisections of the orbifold normal bundle of the surface of orbifold points.

Geometric models for measuring sediment wedge volume in retention check dams

2016 ◽  
Vol 30 (1-2) ◽  
pp. 119-127 ◽  
Author(s):  
Iván Ramos-Diez ◽  
Joaquín Navarro-Hevia ◽  
Roberto San Martín Fernández ◽  
Virginia Díaz-Gutiérrez ◽  
Jorge Mongil-Manso
Keyword(s):  
Geometric Models ◽  
Check Dams ◽  
Wedge Volume
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