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- Near_sets abstract "In mathematics, near sets are either spatially close or descriptively close. Spatially close sets have nonempty intersection. In other words, spatially close sets are not disjoint sets, since they always have at least one element in common. Descriptively close sets contain elements that have matching descriptions. Such sets can be either disjoint or non-disjoint sets. Spatially near sets are also descriptively near sets.The underlying assumption with descriptively close sets is that such sets contain elements that have location and measurable features such as colour and frequency of occurrence. The description of the element of a set is defined by a feature vector. Comparison of feature vectors provides a basis for measuring the closeness of descriptively near sets. Near set theory provides a formal basis for the observation, comparison, and classification of elements in sets based on their closeness, either spatially or descriptively. Near sets offer a framework for solving problems based on human perception that arise in areas such as image processing, computer vision as well as engineering and science problems.Near sets have a variety of applications in areas such as topology, pattern detection and classification, abstract algebra, mathematics in computer science, and solving a variety of problems based on human perception that arise in areas such as image analysis, image processing, face recognition, ethology, as well as engineering and science problems. From the beginning, descriptively near sets have proved to be useful in applications of topology, and visual pattern recognition , spanning a broad spectrum of applications that include camouflage detection, micropaleontology, handwriting forgery detection, biomedical image analysis, content-based image retrieval, population dynamics, quotient topology, textile design, visual merchandising, and topological psychology.As an illustration of the degree of descriptive nearness between two sets, consider an example of the Henry colour model for varying degrees of nearnessbetween sets of picture elements in pictures (see, e.g., §4.3). The two pairs of ovals in Fig. 1 and Fig. 2 contain coloured segments. Each segment in the figures corresponds to an equivalence class where all pixels in the class have similar descriptions, i.e., picture elements with similar colours. The ovals in Fig.1 are closer to each other descriptively than the ovals in Fig. 2.".
- Near_sets thumbnail Descriptively_Near_Sets.svg?width=300.
- Near_sets wikiPageExternalLink rtx120400536p.pdf.
- Near_sets wikiPageExternalLink 1.
- Near_sets wikiPageExternalLink index.php?option=com_content&view=article&id=51&Itemid=78.
- Near_sets wikiPageExternalLink publdoc.html?pg1=INDI&s1=334268&vfpref=html&r=12&mx-pid=3075111.
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- Near_sets wikiPageRevisionID "680626580".
- Near_sets wikiPageWikiLink Abstract_algebra.
- Near_sets wikiPageWikiLink Alternative_set_theory.
- Near_sets wikiPageWikiLink Camouflage.
- Near_sets wikiPageWikiLink Category:Abstract_algebra.
- Near_sets wikiPageWikiLink Category:Mathematical_relations.
- Near_sets wikiPageWikiLink Category:Systems_of_set_theory.
- Near_sets wikiPageWikiLink Category:Topology.
- Near_sets wikiPageWikiLink Category_(mathematics).
- Near_sets wikiPageWikiLink Category_of_topological_spaces.
- Near_sets wikiPageWikiLink Christopher_Zeeman.
- Near_sets wikiPageWikiLink Closeness_(mathematics).
- Near_sets wikiPageWikiLink Complement_(set_theory).
- Near_sets wikiPageWikiLink Computer_vision.
- Near_sets wikiPageWikiLink Content-based_image_retrieval.
- Near_sets wikiPageWikiLink Continuous_function.
- Near_sets wikiPageWikiLink Disjoint_sets.
- Near_sets wikiPageWikiLink Ethology.
- Near_sets wikiPageWikiLink Facial_recognition_system.
- Near_sets wikiPageWikiLink Feature_vector.
- Near_sets wikiPageWikiLink Felix_Hausdorff.
- Near_sets wikiPageWikiLink Frigyes_Riesz.
- Near_sets wikiPageWikiLink Henri_Poincaré.
- Near_sets wikiPageWikiLink Image_analysis.
- Near_sets wikiPageWikiLink Image_processing.
- Near_sets wikiPageWikiLink International_Congress_of_Mathematicians.
- Near_sets wikiPageWikiLink Intersection_(set_theory).
- Near_sets wikiPageWikiLink Johann_Benedict_Listing.
- Near_sets wikiPageWikiLink Kuratowski_closure_axioms.
- Near_sets wikiPageWikiLink Mathematical_structure.
- Near_sets wikiPageWikiLink Metric_space.
- Near_sets wikiPageWikiLink Micropaleontology.
- Near_sets wikiPageWikiLink Pattern_recognition.
- Near_sets wikiPageWikiLink Perception.
- Near_sets wikiPageWikiLink Pixel.
- Near_sets wikiPageWikiLink Population_dynamics.
- Near_sets wikiPageWikiLink Power_set.
- Near_sets wikiPageWikiLink Proximity_space.
- Near_sets wikiPageWikiLink Pseudometric_space.
- Near_sets wikiPageWikiLink Quotient_space_(topology).
- Near_sets wikiPageWikiLink RGB_color_model.
- Near_sets wikiPageWikiLink Rough_set.
- Near_sets wikiPageWikiLink Set_(mathematics).
- Near_sets wikiPageWikiLink Space.
- Near_sets wikiPageWikiLink Statistical_classification.
- Near_sets wikiPageWikiLink Textile_design.
- Near_sets wikiPageWikiLink Tolerance_relation.
- Near_sets wikiPageWikiLink Topological_space.
- Near_sets wikiPageWikiLink Topology.
- Near_sets wikiPageWikiLink Uniform_space.
- Near_sets wikiPageWikiLink Vadim_Arsenyevich_Efremovich.
- Near_sets wikiPageWikiLink Vadim_Arsenyevich_Yefremovich.
- Near_sets wikiPageWikiLink Vector_space.
- Near_sets wikiPageWikiLink Visual_merchandising.
- Near_sets wikiPageWikiLink File:Descriptive.svg.
- Near_sets wikiPageWikiLink File:Descriptively_Near_Sets.svg.
- Near_sets wikiPageWikiLink File:EANear_and_eAMer_Supercategories.png.
- Near_sets wikiPageWikiLink File:Frigyes_Riesz.jpeg.
- Near_sets wikiPageWikiLink File:Minimally_Descriptive_Near_Sets.svg.
- Near_sets wikiPageWikiLink File:NearImages.svg.
- Near_sets wikiPageWikiLink File:Near_gui.jpg.
- Near_sets wikiPageWikiLink File:Proximity_System.png.
- Near_sets wikiPageWikiLink File:Sample_EF-space.svg.
- Near_sets wikiPageWikiLink File:Visulization_of_nearness_measure.jpg.
- Near_sets wikiPageWikiLinkText "Near sets".
- Near_sets hasPhotoCollection Near_sets.
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- Near_sets subject Category:Abstract_algebra.
- Near_sets subject Category:Mathematical_relations.
- Near_sets subject Category:Systems_of_set_theory.
- Near_sets subject Category:Topology.
- Near_sets comment "In mathematics, near sets are either spatially close or descriptively close. Spatially close sets have nonempty intersection. In other words, spatially close sets are not disjoint sets, since they always have at least one element in common. Descriptively close sets contain elements that have matching descriptions. Such sets can be either disjoint or non-disjoint sets.".
- Near_sets label "Near sets".
- Near_sets sameAs m.064mzzz.
- Near_sets sameAs Q6984403.
- Near_sets sameAs Q6984403.
- Near_sets wasDerivedFrom Near_sets?oldid=680626580.
- Near_sets depiction Descriptively_Near_Sets.svg.
- Near_sets isPrimaryTopicOf Near_sets.