Lecture

Topology: Polyhedral Products and Edge Detection

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Description

This lecture covers the concepts of topology, specifically focusing on polyhedral products and their applications. The instructor discusses the fundamental aspects of topological spaces, including the definition of connectedness and the role of pushouts in topology. The lecture also delves into edge detection in computer vision, explaining how edges serve as boundaries between regions in images. The instructor illustrates the importance of contours in recognizing objects and how they can simplify image representation. Various types of discontinuities that create edges are examined, including depth, surface normal, illumination, and reflectance discontinuities. The mathematical definition of edges is introduced, emphasizing the significance of gradients in identifying edges within images. The lecture concludes with a discussion on the challenges of detecting edges in noisy images and the importance of understanding gradients for effective edge detection.

Official source

Ontological neighbourhood

Information engineering

Artificial intelligence: Computer vision

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Cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points.

Cylinder

A cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in ball and sphere)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces.

Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids.

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In and computer vision, image segmentation is the process of partitioning a into multiple image segments, also known as image regions or image objects (sets of pixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics.

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